Title  maths videos & proofs Length: 25, Words: 4 

Description  high quality mathematics videos and proofs for students
Length: 55, Words: 8 
Keywords  pusty 
Robots  
Charset  UTF8 
Og Meta  Title  exist 
Og Meta  Description  exist 
Og Meta  Site name  exist 
Words/Characters  4391 

Text/HTML  16.77 % 
Headings  H1 25
H2 1 H3 1 H4 0 H5 0 H6 0 
H1  maths videos & proofs


H2  high quality mathematics videos and proofs for students 
H3  other posts 
H4  
H5  
H6 
strong  sin(ab)=sin(a)cos(b)cos(a)sin(b) proof


b  
i  
em  sin(ab)=sin(a)cos(b)cos(a)sin(b) proof important facts about the diagram property 1: property 2: property 3: also note: proving that sin(ab)=sin(a)cos(b)cos(a)sin(b) need a better explanation? watch this video… related videos: https://www.youtube.com/watch?v=4k6xr8hjktw https://www.youtube.com/watch?v=n6h6ct00 https://www.youtube.com/watch?v=gdogt6ncd60 the trigonometric identity playlist related posts: *what are the weird properties of c^2..? it turns out that a1=a2 and a3=a4. a2 + a4 = c^2. related: related: video adding up all the even numbers from 0 to 2: adding up all the even numbers from 0 to 4: adding up all the even numbers from 0 to 6: adding up all the even numbers from 0 to 8: what we’ve discovered: alternative method: counting all the odd numbers from 0 to 1: counting all the odd numbers from 0 to 3: counting all the odd numbers from 0 to 5: counting all the odd numbers from 0 to 7: counting all the odd numbers from 0 to 9: the formula which can be used to add up all the odd numbers from 0 to n, whereby n is an odd number: alternative method: in a cafeteria, all students shook hands with one another. there were 66 handshakes in total. how many students were in the cafeteria? experiments + mini questions will a pattern emerge?? 1. firstly, let’s think about how many handshakes there’d be with only one student in this cafeteria. 2. secondly, how many handshakes would there be if there are 2 students in this cafeteria? 3. thirdly, how many handshakes would there be if there are 3 students in the cafeteria? 4. fourthly, how many handshakes would there be if there are 4 students in this cafeteria? 5. fifthly, how many handshakes would there be if there are 5 students in this cafeteria? can we solve the main problem with a formula? what pattern will define the formula? with this information, we can conclude that: [ s x (s1) ] / 2 = h 12 students in the cafeteria like probabilities? why not check out the “hannah sweets” problem? related: taylor series taylor series maclaurin series related: 
Bolds  strong 49 b 0 i 0 em 49 

twitter:title  pusty 

twitter:description  pusty 
google+ itemprop=name  pusty 
Pliki zewnętrzne  39 
Pliki CSS  10 
Pliki javascript  29 
Linki  302 

Linki wewnętrzne  3 
Linki zewnętrzne  299 
Linki bez atrybutu Title  258 
Linki z atrybutem NOFOLLOW  0 
search  #searchcontainer 

skip to content  #content 
ok  # 
maths videos & proofs  http://mathsvideos.net/ 

algebra  http://mathsvideos.net/algebra/ 
trigonometry  http://mathsvideos.net/trigonometry/ 
calculus  http://mathsvideos.net/calculus/ 
vectors  http://mathsvideos.net/vectors/ 
video playlists  http://mathsvideos.net/videoplaylists/ 
navigation (page by page)  http://mathsvideos.net/navigationpagebypage/ 
all posts (archives)  http://mathsvideos.net/allpostsarchives/ 
xml sitemap  http://mathsvideos.net/sitemap.xml 
  http://mathsvideos.net/2016/10/09/derivetheformulatofindareasunderneathcurves/ 
areas  http://mathsvideos.net/category/areas2/ 
calculus  http://mathsvideos.net/category/calculus/ 
integration  http://mathsvideos.net/category/integration2/ 
visualising mathematics  http://mathsvideos.net/category/visualisingmathematics/ 
derive the formula to find areas underneath curves  http://mathsvideos.net/2016/10/09/derivetheformulatofindareasunderneathcurves/ 
  http://mathsvideos.net/2015/06/23/cosinerulemasterypdfdownload/ 
algebra  http://mathsvideos.net/category/algebra/ 
cosine rule  http://mathsvideos.net/category/cosinerule/ 
proofs  http://mathsvideos.net/category/proofs/ 
cosine rule mastery – pdf download  http://mathsvideos.net/2015/06/23/cosinerulemasterypdfdownload/ 
  http://mathsvideos.net/2014/05/16/simplebutelegantwaytoprovethatsinabsinacosbcosasinbedexcelproofsimplified/ 
algebra  http://mathsvideos.net/category/algebra/ 
angles  http://mathsvideos.net/category/angles/ 
soh cah toa  http://mathsvideos.net/category/sohcahtoa/ 
trigonometry  http://mathsvideos.net/category/trigonometry/ 
simple but elegant way to prove that sin(a+b)=sinacosb+cosasinb (edexcel proof simplified)  http://mathsvideos.net/2014/05/16/simplebutelegantwaytoprovethatsinabsinacosbcosasinbedexcelproofsimplified/ 
  http://mathsvideos.net/2014/05/16/howtocomeupwithpythagorasequation/ 
algebra  http://mathsvideos.net/category/algebra/ 
areas  http://mathsvideos.net/category/areas2/ 
lengths  http://mathsvideos.net/category/lengths/ 
trigonometry  http://mathsvideos.net/category/trigonometry/ 
how to come up with pythagoras’ equation  http://mathsvideos.net/2014/05/16/howtocomeupwithpythagorasequation/ 
  http://mathsvideos.net/2014/05/16/trapeziumruleformuladerivation/ 
algebra  http://mathsvideos.net/category/algebra/ 
areas  http://mathsvideos.net/category/areas2/ 
calculus  http://mathsvideos.net/category/calculus/ 
trapezium rule formula – derivation  http://mathsvideos.net/2014/05/16/trapeziumruleformuladerivation/ 
  http://mathsvideos.net/2014/05/10/areasoftrianglesthesinrule/ 
algebra  http://mathsvideos.net/category/algebra/ 
sine rule  http://mathsvideos.net/category/sinerule/ 
trigonometry  http://mathsvideos.net/category/trigonometry/ 
areas of triangles & the sine rule  http://mathsvideos.net/2014/05/10/areasoftrianglesthesinrule/ 
algebra  http://mathsvideos.net/category/algebra/ 
angles  http://mathsvideos.net/category/angles/ 
lengths  http://mathsvideos.net/category/lengths/ 
pythagoras  http://mathsvideos.net/category/pythagoras/ 
soh cah toa  http://mathsvideos.net/category/sohcahtoa/ 
trigonometry  http://mathsvideos.net/category/trigonometry/ 
how to prove that sin(ab)=sin(a)cos(b)cos(a)sin(b) geometrically  http://mathsvideos.net/2016/09/29/howtoprovethatsinabsinacosbcosasinbgeometrically/ 
http://mathsvideos.net/2016/09/29/howtoprovethatsinabsinacosbcosasinbgeometrically/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
leave a comment  http://mathsvideos.net/2016/09/29/howtoprovethatsinabsinacosbcosasinbgeometrically/#respond 
  http://mathsvideos.net/wpcontent/uploads/2016/09/sinabproof.png 
https://www.youtube.com/watch?v=4k6xr8hjktw  https://www.youtube.com/watch?v=4k6xr8hjktw 
https://www.youtube.com/watch?v=n6h6ct00  https://www.youtube.com/watch?v=n6h6ct00 
https://www.youtube.com/watch?v=gdogt6ncd60  https://www.youtube.com/watch?v=gdogt6ncd60 
the trigonometric identity playlist  https://www.youtube.com/playlist?list=plfm03zqesz2mvj_4r9szifmtl0re19lhk 
simple but elegant way to prove that sin(a+b)=sinacosb+cosasinb (edexcel proof simplified)  http://mathsvideos.net/2014/05/16/simplebutelegantwaytoprovethatsinabsinacosbcosasinbedexcelproofsimplified/ 
algebra  http://mathsvideos.net/tag/algebra2/ 
angles  http://mathsvideos.net/tag/angles2/ 
soh cah toa  http://mathsvideos.net/tag/sohcahtoa/ 
trigonometry  http://mathsvideos.net/tag/trigonometry2/ 
pythagoras  http://mathsvideos.net/category/pythagoras/ 
properties of c squared, pythagorean theorem  http://mathsvideos.net/2016/09/27/propertiesofcsquaredpythagoreantheorem/ 
http://mathsvideos.net/2016/09/27/propertiesofcsquaredpythagoreantheorem/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
pythagoras’ theorem  http://mathsvideos.net/2016/09/27/2waystoderivepythagorasequationfromscratch/ 
2 ways to derive pythagoras’ equation from scratch  http://mathsvideos.net/2016/09/27/2waystoderivepythagorasequationfromscratch/ 
proofs  http://mathsvideos.net/tag/proofs/ 
pythagoras' theorem  http://mathsvideos.net/tag/pythagorastheorem/ 
algebra  http://mathsvideos.net/category/algebra/ 
proofs  http://mathsvideos.net/category/proofs/ 
pythagoras  http://mathsvideos.net/category/pythagoras/ 
trigonometry  http://mathsvideos.net/category/trigonometry/ 
2 ways to derive pythagoras’ equation from scratch  http://mathsvideos.net/2016/09/27/2waystoderivepythagorasequationfromscratch/ 
http://mathsvideos.net/2016/09/27/2waystoderivepythagorasequationfromscratch/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
leave a comment  http://mathsvideos.net/2016/09/27/2waystoderivepythagorasequationfromscratch/#respond 
how to come up with pythagoras’s equation  http://mathsvideos.net/2014/05/16/howtocomeupwithpythagorassequation/ 
adjacent  http://mathsvideos.net/tag/adjacent/ 
hypotenuse  http://mathsvideos.net/tag/hypotenuse/ 
opposite  http://mathsvideos.net/tag/opposite/ 
proofs  http://mathsvideos.net/tag/proofs/ 
pythagoras  http://mathsvideos.net/tag/pythagoras/ 
pythagoras' equation  http://mathsvideos.net/tag/pythagorasequation/ 
pythagoras' theorem  http://mathsvideos.net/tag/pythagorastheorem/ 
trigonometry  http://mathsvideos.net/tag/trigonometry2/ 
adding  http://mathsvideos.net/category/adding/ 
even numbers  http://mathsvideos.net/category/evennumbers/ 
how to add up all the even numbers from 0 onwards quickly  http://mathsvideos.net/2016/09/16/howtoaddupalltheevennumbersfrom0onwardsquickly/ 
http://mathsvideos.net/2016/09/16/howtoaddupalltheevennumbersfrom0onwardsquickly/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
leave a comment  http://mathsvideos.net/2016/09/16/howtoaddupalltheevennumbersfrom0onwardsquickly/#respond 
adding  http://mathsvideos.net/tag/adding/ 
even numbers  http://mathsvideos.net/tag/evennumbers/ 
summing up  http://mathsvideos.net/tag/summingup/ 
adding  http://mathsvideos.net/category/adding/ 
odd numbers  http://mathsvideos.net/category/oddnumbers/ 
summations  http://mathsvideos.net/category/summations/ 
how to add up odd numbers from 0 upwards  http://mathsvideos.net/2016/09/16/howtoaddupoddnumbersfrom0upwards/ 
http://mathsvideos.net/2016/09/16/howtoaddupoddnumbersfrom0upwards/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
leave a comment  http://mathsvideos.net/2016/09/16/howtoaddupoddnumbersfrom0upwards/#respond 
adding  http://mathsvideos.net/tag/adding/ 
counting  http://mathsvideos.net/tag/counting/ 
odd numbers  http://mathsvideos.net/tag/oddnumbers/ 
carl friedrich gauss  http://mathsvideos.net/category/carlfriedrichgauss/ 
combinations  http://mathsvideos.net/category/combinations/ 
summations  http://mathsvideos.net/category/summations/ 
solving the student handshake problem  http://mathsvideos.net/2016/09/13/solvingthestudenthandshakeproblem/ 
http://mathsvideos.net/2016/09/13/solvingthestudenthandshakeproblem/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
leave a comment  http://mathsvideos.net/2016/09/13/solvingthestudenthandshakeproblem/#respond 
carl friedrich gauss  https://en.wikipedia.org/wiki/carl_friedrich_gauss 
completing the square  http://mathsvideos.net/completingthesquare/ 
complete the square  http://mathsvideos.net/completingthesquare/ 
carl friedrich gauss  http://mathsvideos.net/tag/carlfriedrichgauss/ 
combinations  http://mathsvideos.net/tag/combinations/ 
completing the square  http://mathsvideos.net/tag/completingthesquare/ 
handshake problem  http://mathsvideos.net/tag/handshakeproblem/ 
quadratic equation  http://mathsvideos.net/tag/quadraticequation/ 
summations  http://mathsvideos.net/tag/summations/ 
summing up  http://mathsvideos.net/tag/summingup/ 
sine rule  http://mathsvideos.net/category/sinerule/ 
the quickest sine rule proof  http://mathsvideos.net/2016/09/06/thequickestsineruleproof/ 
http://mathsvideos.net/2016/09/06/thequickestsineruleproof/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
algebra  http://mathsvideos.net/tag/algebra2/ 
proofs  http://mathsvideos.net/tag/proofs/ 
sine rule  http://mathsvideos.net/tag/sinerule/ 
chance  http://mathsvideos.net/category/chance/ 
probabilities  http://mathsvideos.net/category/probabilities/ 
rolling 3 dice… what is most likely to happen?  http://mathsvideos.net/2016/09/05/rolling3dicewhatismostlikelytohappen/ 
http://mathsvideos.net/2016/09/05/rolling3dicewhatismostlikelytohappen/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
what kind of sums you should expect to get when you roll 3 dice  http://www.1010011010.xyz/rolling_3_dice.html 
https://plus.google.com/b/100450538547176385655/communities/106007058741903558109  https://plus.google.com/b/100450538547176385655/communities/106007058741903558109 
hannah sweets maths problem – edexcel (june 2015)  http://mathsvideos.net/2016/03/08/hannahsweetsmathsproblemedexceljune2015/ 
chance  http://mathsvideos.net/tag/chance/ 
css  http://mathsvideos.net/tag/css/ 
html  http://mathsvideos.net/tag/html/ 
mysql  http://mathsvideos.net/tag/mysql/ 
php  http://mathsvideos.net/tag/php/ 
probabilities  http://mathsvideos.net/tag/probabilities/ 
rolling 3 dice  http://mathsvideos.net/tag/rolling3dice/ 
euler's identity  http://mathsvideos.net/category/eulersidentity/ 
maclaurin series  http://mathsvideos.net/category/maclaurinseries/ 
how to derive euler’s identity using the maclaurin series  http://mathsvideos.net/2016/08/11/howtoderiveeulersidentityusingthemaclaurinseries/ 
http://mathsvideos.net/2016/08/11/howtoderiveeulersidentityusingthemaclaurinseries/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
leave a comment  http://mathsvideos.net/2016/08/11/howtoderiveeulersidentityusingthemaclaurinseries/#respond 
maclaurin series  http://mathsvideos.net/2016/08/10/derivingthetaylorseriesfromscratch/ 
here  http://mathsvideos.net/wpcontent/uploads/2016/08/maclaurinexpansion.png 
this page  http://mathsvideos.net/taylorseriesexpansionsusefultables/ 
deriving the taylor series from scratch  http://mathsvideos.net/2016/08/10/derivingthetaylorseriesfromscratch/ 
cosx  http://mathsvideos.net/tag/cosx/ 
euler's identity  http://mathsvideos.net/tag/eulersidentity/ 
imaginary number  http://mathsvideos.net/tag/imaginarynumber/ 
maclaurin series  http://mathsvideos.net/tag/maclaurinseries/ 
sinx  http://mathsvideos.net/tag/sinx/ 
maclaurin series  http://mathsvideos.net/category/maclaurinseries/ 
taylor series  http://mathsvideos.net/category/taylorseries/ 
deriving the taylor series from scratch  http://mathsvideos.net/2016/08/10/derivingthetaylorseriesfromscratch/ 
http://mathsvideos.net/2016/08/10/derivingthetaylorseriesfromscratch/  
tiago hands  http://mathsvideos.net/author/thiagomaths/ 
leave a comment  http://mathsvideos.net/2016/08/10/derivingthetaylorseriesfromscratch/#respond 
  http://mathsvideos.net/wpcontent/uploads/2016/08/taylorseries11.png 
here  http://mathsvideos.net/wpcontent/uploads/2016/08/taylorseries11.png 
taylor series  https://en.wikipedia.org/wiki/taylor_series 
maclaurin series  http://mathworld.wolfram.com/maclaurinseries.html 
how to derive euler’s identity using the maclaurin series  http://mathsvideos.net/2016/08/11/howtoderiveeulersidentityusingthemaclaurinseries/ 
differentiation  http://mathsvideos.net/tag/differentiation/ 
functions  http://mathsvideos.net/tag/functions2/ 
maclaurin series  http://mathsvideos.net/tag/maclaurinseries/ 
taylor series  http://mathsvideos.net/tag/taylorseries/ 
2  http://mathsvideos.net/page/2/ 
11  http://mathsvideos.net/page/11/ 
next →  http://mathsvideos.net/page/2/ 
feedburner  https://feedburner.google.com 
derive the formula to find areas underneath curves views 155  http://mathsvideos.net/2016/10/09/derivetheformulatofindareasunderneathcurves/ 
how to prove that sin(ab)=sin(a)cos(b)cos(a)sin(b) geometrically views 207  http://mathsvideos.net/2016/09/29/howtoprovethatsinabsinacosbcosasinbgeometrically/ 
properties of c squared, pythagorean theorem views 94  http://mathsvideos.net/2016/09/27/propertiesofcsquaredpythagoreantheorem/ 
2 ways to derive pythagoras’ equation from scratch views 94  http://mathsvideos.net/2016/09/27/2waystoderivepythagorasequationfromscratch/ 
how to add up all the even numbers from 0 onwards quickly views 92  http://mathsvideos.net/2016/09/16/howtoaddupalltheevennumbersfrom0onwardsquickly/ 
how to add up odd numbers from 0 upwards views 82  http://mathsvideos.net/2016/09/16/howtoaddupoddnumbersfrom0upwards/ 
solving the student handshake problem views 83  http://mathsvideos.net/2016/09/13/solvingthestudenthandshakeproblem/ 
the quickest sine rule proof views 87  http://mathsvideos.net/2016/09/06/thequickestsineruleproof/ 
october 2016  http://mathsvideos.net/2016/10/ 
september 2016  http://mathsvideos.net/2016/09/ 
august 2016  http://mathsvideos.net/2016/08/ 
march 2016  http://mathsvideos.net/2016/03/ 
february 2016  http://mathsvideos.net/2016/02/ 
december 2015  http://mathsvideos.net/2015/12/ 
november 2015  http://mathsvideos.net/2015/11/ 
september 2015  http://mathsvideos.net/2015/09/ 
august 2015  http://mathsvideos.net/2015/08/ 
july 2015  http://mathsvideos.net/2015/07/ 
june 2015  http://mathsvideos.net/2015/06/ 
may 2015  http://mathsvideos.net/2015/05/ 
march 2015  http://mathsvideos.net/2015/03/ 
february 2015  http://mathsvideos.net/2015/02/ 
january 2015  http://mathsvideos.net/2015/01/ 
december 2014  http://mathsvideos.net/2014/12/ 
july 2014  http://mathsvideos.net/2014/07/ 
june 2014  http://mathsvideos.net/2014/06/ 
may 2014  http://mathsvideos.net/2014/05/ 
home  http://www.mathsvideos.net 
about us  http://mathsvideos.net/aboutus/ 
philosophy  http://mathsvideos.net/philosophy/ 
donate to the project  http://mathsvideos.net/donatetotheproject/ 
mathematics: invented or discovered?  http://mathsvideos.net/2014/05/20/wasmathematicsinventedordiscovered/ 
basic information about numbers  http://mathsvideos.net/basicinformationaboutnumbers/ 
symbols & notations  http://mathsvideos.net/symbolsnotations/ 
basic logic tables  http://mathsvideos.net/2015/02/25/basicmathematicallogic2/ 
mathematical logic (1)  http://mathsvideos.net/2015/02/19/moremathematicallogic/ 
times tables  http://mathsvideos.net/timestables/ 
powers  http://mathsvideos.net/powers/ 
powers of ten  http://mathsvideos.net/powersoften/ 
derive the value of surds  http://mathsvideos.net/2015/11/02/theirrationalnumbervalueindex/ 
useful algebraic formulas  http://mathsvideos.net/usefulalgebraicformulas/ 
percentage / decimal / fraction table  http://mathsvideos.net/percentagefractiontable/ 
inverse shortcuts  http://mathsvideos.net/inverseshortcuts/ 
trigonometry rules  http://mathsvideos.net/trigonometry/trigonometryrules/ 
deriving trigonometric identities without the use of unit circles  http://mathsvideos.net/derivingtrigonometricidentitieswithouttheuseofunitcircles/ 
trigonometric identity proofs  http://mathsvideos.net/trigonometricidentityproofs/ 
graph transformation tricks  http://mathsvideos.net/2014/05/23/ordinarygraphtransformations/ 
modulus formulas  http://mathsvideos.net/modulusformulas/ 
log formulas  http://mathsvideos.net/logformulas/ 
differentiation formulas  http://mathsvideos.net/differentiationformulas/ 
integration formulas  http://mathsvideos.net/integrationformulas/ 
algebra  http://mathsvideos.net/algebra/ 
completing the square  http://mathsvideos.net/completingthesquare/ 
trigonometry  http://mathsvideos.net/trigonometry/ 
calculus  http://mathsvideos.net/calculus/ 
vectors  http://mathsvideos.net/vectors/ 
volume of cones formula  http://volumeofconesformula.blogspot.co.uk/ 
maclaurin series derivatives – useful tables  http://mathsvideos.net/taylorseriesexpansionsusefultables/ 
useful tables (taylor & maclaurin series)  http://mathsvideos.net/usefultablestaylormaclaurinseries/ 
mean deviation vs standard deviation  http://mathsvideos.net/meandeviationstandarddeviation/ 
free resources / downloads  http://mathsvideos.net/freeresourcesdownloads/ 
mathematical art & design  http://mathsvideos.net/mathematicalartdesign/ 
video playlists  http://mathsvideos.net/videoplaylists/ 
all posts (archives)  http://mathsvideos.net/allpostsarchives/ 
navigation (page by page)  http://mathsvideos.net/navigationpagebypage/ 
rss feed  http://feeds.feedburner.com/maths_videos 
xml sitemap  http://mathsvideos.net/sitemap.xml 
contact us  http://mathsvideos.net/contactus/ 
trig table (1)  http://mathsvideos.net/trigtable1/ 
trig table (2)  http://mathsvideos.net/trigtable2/ 
adding  http://mathsvideos.net/tag/adding/ 
algebra  http://mathsvideos.net/tag/algebra2/ 
angles  http://mathsvideos.net/tag/angles2/ 
areas  http://mathsvideos.net/tag/areas/ 
calculus  http://mathsvideos.net/tag/calculus2/ 
circles  http://mathsvideos.net/tag/circles/ 
completing the square  http://mathsvideos.net/tag/completingthesquare/ 
cones  http://mathsvideos.net/tag/cones/ 
continued fractions  http://mathsvideos.net/tag/continuedfractions/ 
curves  http://mathsvideos.net/tag/curves/ 
differentiation  http://mathsvideos.net/tag/differentiation/ 
even numbers  http://mathsvideos.net/tag/evennumbers/ 
formulas  http://mathsvideos.net/tag/formulas/ 
fractions  http://mathsvideos.net/tag/fractions/ 
functions  http://mathsvideos.net/tag/functions2/ 
golden ratio  http://mathsvideos.net/tag/goldenratio/ 
implicit differentiation  http://mathsvideos.net/tag/implicitdifferentiation/ 
indices  http://mathsvideos.net/tag/indices/ 
integration  http://mathsvideos.net/tag/integration/ 
irrational numbers  http://mathsvideos.net/tag/irrationalnumbers/ 
logarithms  http://mathsvideos.net/tag/logarithms2/ 
logic  http://mathsvideos.net/tag/logic/ 
maclaurin series  http://mathsvideos.net/tag/maclaurinseries/ 
mathematical programming  http://mathsvideos.net/tag/mathematicalprogramming/ 
multiplication  http://mathsvideos.net/tag/multiplication2/ 
odd numbers  http://mathsvideos.net/tag/oddnumbers/ 
pi  http://mathsvideos.net/tag/pi/ 
probabilities  http://mathsvideos.net/tag/probabilities/ 
proofs  http://mathsvideos.net/tag/proofs/ 
pythagoras  http://mathsvideos.net/tag/pythagoras/ 
pythagoras' theorem  http://mathsvideos.net/tag/pythagorastheorem/ 
quadratic formula  http://mathsvideos.net/tag/quadraticformula/ 
roots  http://mathsvideos.net/tag/roots2/ 
sine  http://mathsvideos.net/tag/sine/ 
sine rule  http://mathsvideos.net/tag/sinerule/ 
soh cah toa  http://mathsvideos.net/tag/sohcahtoa/ 
statistics  http://mathsvideos.net/tag/statistics/ 
summing up  http://mathsvideos.net/tag/summingup/ 
surds  http://mathsvideos.net/tag/surds2/ 
trigonometric identities  http://mathsvideos.net/tag/trigonometricidentities/ 
trigonometry  http://mathsvideos.net/tag/trigonometry2/ 
vectors  http://mathsvideos.net/tag/vectors/ 
videos  http://mathsvideos.net/tag/videos/ 
volumes  http://mathsvideos.net/tag/volumes/ 
privacy & cookies policy  http://mathsvideos.net/privacycookiespolicy/ 
learn more about cookies (information commisioner’s office)  https://ico.org.uk/forthepublic/online/cookies/ 
terms of use  http://mathsvideos.net/termsofuse/ 
disclaimer  http://mathsvideos.net/disclaimer/ 
proudly powered by wordpress  https://wordpress.org/ 
read more  http://mathsvideos.net/privacycookiespolicy/ 
Zdjęcia  120 

Zdjęcia bez atrybutu ALT  2 
Zdjęcia bez atrybutu TITLE  33 
http://mathsvideos.net/wpcontent/uploads/2016/10/areas_underneath_curves_thumbnail672x372.jpg
http://mathsvideos.net/wpcontent/uploads/2015/06/cosine_rule_thumb672x372.jpg
http://mathsvideos.net/wpcontent/uploads/2014/05/saplusbthumb672x372.jpg
http://mathsvideos.net/wpcontent/uploads/2014/05/20161004_225151672x372.jpg
http://mathsvideos.net/wpcontent/uploads/2014/05/trapeziumrulethumb672x372.jpg
http://mathsvideos.net/wpcontent/uploads/2014/05/areas_triangles_thumbnail672x372.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/sinabproof.png
http://mathsvideos.net/wpcontent/uploads/2016/09/pythagoras_2.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/pythagoras.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_11.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_21.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_31.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_41.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/image_2.png
http://mathsvideos.net/wpcontent/uploads/2016/09/part_1.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_2.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_3.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_4.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/part_5.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/image_1.png
http://mathsvideos.net/wpcontent/uploads/2016/09/sum_diagram_handshakes_problem255x300.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/tiago_hands_quote_11024x768.jpg
http://mathsvideos.net/wpcontent/uploads/2016/09/rolling_3_dice300x225.jpg
http://mathsvideos.net/wpcontent/uploads/2016/08/maclaurinseries1.png
http://mathsvideos.net/wpcontent/uploads/2016/08/maclaurinexpansion.png
http://mathsvideos.net/wpcontent/uploads/2016/08/values.png
http://mathsvideos.net/wpcontent/uploads/2016/08/e^xformula.png
http://mathsvideos.net/wpcontent/uploads/2016/08/e^ixexpanded.png
http://mathsvideos.net/wpcontent/uploads/2016/08/cosxsinx.png
http://mathsvideos.net/wpcontent/uploads/2016/08/20160810_1641231024x699.jpg
http://mathsvideos.net/wpcontent/uploads/2016/08/taylorseries11.png
http://mathsvideos.net/wpcontent/uploads/2016/08/taylorseries.png
http://mathsvideos.net/wpcontent/uploads/2016/08/maclaurinseries.png
http://mathsvideos.net/wpcontent/uploads/2016/10/areas_underneath_curves_thumbnail672x372.jpg
http://mathsvideos.net/wpcontent/uploads/2014/05/saplusbthumb672x372.jpg
maths videos & proofs search primary menu skip to content algebra trigonometry calculus vectors video playlists navigation (page by page) all posts (archives) xml sitemap search for: areas, calculus, integration, visualising mathematics derive the formula to find areas underneath curves algebra, cosine rule, proofs cosine rule mastery – pdf download algebra, angles, soh cah toa, trigonometry simple but elegant way to prove that sin(a+b)=sinacosb+cosasinb (edexcel proof simplified) algebra, areas, lengths, trigonometry how to come up with pythagoras’ equation algebra, areas, calculus trapezium rule formula – derivation algebra, sine rule, trigonometry areas of triangles & the sine rule algebra, angles, lengths, pythagoras, soh cah toa, trigonometry how to prove that sin(ab)=sin(a)cos(b)cos(a)sin(b) geometrically stickyseptember 29, 2016 tiago hands leave a comment in this post i’ll be demonstrating how one can prove that sin(ab)=sin(a)cos(b)cos(a)sin(b) geometrically… first of all, let me show you this diagram… sin(ab)=sin(a)cos(b)cos(a)sin(b) proof *if you click on the diagram, you will be able to see its full size version. important facts about the diagram now, to begin with, i will have to write about some of the properties related to the diagram… property 1: angle b + (a – b) = b + a – b = a therefore, angle por = a. property 2: angle ops = 90 degrees property 3: length os = 1 also note: all angles within a triangle on a flat plane should add up to 180 degrees. if you understand this rule, you will be able to discover why the angles shown on the diagram are correct. angles which are 90 degrees are shown on the diagram too. proving that sin(ab)=sin(a)cos(b)cos(a)sin(b) since i’ve noted down some of the important properties related to the diagram, i can now focus on demonstrating why the formula above is true. i will demonstrate why the formula above is true using mathematics and the soh cah toa rule… but it turns out that… because: now, what is pr and what is pq? and finally, to sum it all up: need a better explanation? watch this video… related videos: https://www.youtube.com/watch?v=4k6xr8hjktw [sin(a+b)=sin(a)cos(b)+cos(a)sin(b) proof – geometrical] https://www.youtube.com/watch?v=n6h6ct00 [cos(a+b)=cos(a)cos(b)sin(a)sin(b) proof – geometrical] https://www.youtube.com/watch?v=gdogt6ncd60 [cos(ab)=cos(a)cos(b)+sin(a)sin(b) proof – geometrical] the trigonometric identity playlist related posts: simple but elegant way to prove that sin(a+b)=sinacosb+cosasinb (edexcel proof simplified) algebraanglessoh cah toatrigonometry pythagoras properties of c squared, pythagorean theorem september 27, 2016 tiago hands in this post, i’ll be writing about some peculiar properties of c squared in pythagoras’ theorem. look at this diagram very carefully… *what are the weird properties of c^2..? it turns out that a1=a2 and a3=a4. a2 + a4 = c^2. it turns out out that area a1 is equal to area a2, and that area a3 is equal to area a4: a1 = a2 a3 = a4 this can be proven because: now, due to the above: but… b^2 is actually the area a1 and cx is the area a2, which means that a1=a2. now, if b^2=cx, this means that: however, a^2 is equal to the area a3, and c(cx) is equal to the area a4 – which means that a3=a4. hence, we’ve proven that: a1=a2 a3=a4 related: 2 ways to derive pythagoras’ equation from scratch proofspythagoras' theorem algebra, proofs, pythagoras, trigonometry 2 ways to derive pythagoras’ equation from scratch september 27, 2016 tiago hands leave a comment the other day i discovered one more way to derive pythagoras’ equation from scratch, completely by accident. i was deriving pythagoras’ equation using the usual method, whilst navigating a diagram similar to the one below, but without (ba) measurements… *note (regarding diagram above): x+y = 90 degrees the usual method goes like this… the area of the largest square is: it is also: which means that: now, when i added the lengths (ba) to my diagram, which are included in the diagram above, i discovered a new way to derive pythagoras’ equation… i did this by focusing on the area c^2. it turns out that: and since: i was able to say that: obviously, i was quite pleased. have you discovered other ways in which to derive pythagoras’ equation?? related: video on how to come up with pythagoras’s equation… how to come up with pythagoras’s equation adjacenthypotenuseoppositeproofspythagoraspythagoras' equationpythagoras' theoremtrigonometry adding, even numbers how to add up all the even numbers from 0 onwards quickly september 16, 2016 tiago hands leave a comment in this post, i’ll be demonstrating how you can add up all the even numbers from 0 onwards. adding up all the even numbers from 0 to 2: in this diagram, we are going to say that n=2. the height of the rectangle is (n+2) and its length is n/2. this means that the area shaded in red, which is in fact equal to all the even numbers from 0 to 2 added up, is: adding up all the even numbers from 0 to 4: in this diagram, we are going to say that n=4. the height of the rectangle is (n+2) and its length is n/2. this means that the area shaded in red, which is in fact equal to all the even numbers from 0 to 4 added up, is: adding up all the even numbers from 0 to 6: in this diagram, we are going to say that n=6. the height of the rectangle is (n+2) and its length is n/2. this means that the area shaded in red, which is in fact equal to all the even numbers from 0 to 6 added up, is: adding up all the even numbers from 0 to 8: in this diagram, we are going to say that n=8. the height of the rectangle is (n+2) and its length is n/2. this means that the area shaded in red, which is in fact equal to all the even numbers from 0 to 8 added up, is: what we’ve discovered: we’ve discovered that a simple formula can be used to add up all the even numbers from 0 to “n”, whereby “n” is an even number. this formula is: alternative method: there is also an alternative formula you can use to add up even numbers, from 0 onwards. that is: addingeven numberssumming up adding, odd numbers, summations how to add up odd numbers from 0 upwards september 16, 2016 tiago hands leave a comment in this post, i’ll be demonstrating how to add up all the odd numbers from 0 to any specific odd number. to create a robust demonstration, i’ll be taking the footsteps below: i’ll first be showing you how to add up all the odd numbers from 0 to 1, using a diagram and formula. i’ll then be showing you how to add up all the odd numbers from 0 to 3, using a diagram and formula. i’ll also be showing you how to add up all the odd numbers from 0 to 5, using a diagram and also the same formula which was used to count up all the odd numbers from 0 to 1 and 0 to 3. and finally, i’ll be using similar diagrams and formulas used to count odd numbers from 0 to 1, 0 to 3 and 0 to 5 to count odd numbers from 0 to 7 and 0 to 9. what you will find, after i complete the tasks above – is that a pattern emerges. you will notice that the formula i use to count odd numbers from 0 to n (n which is an odd number) is very robust and will allow you to count all the odd numbers from 0 to n very easily. counting all the odd numbers from 0 to 1: if you count all the odd numbers from 0 to 1, what you will get is obviously 1. furthermore, what you will also get as a formula (if n=1, h=height and l=length) is: *if you plug the value 1 into n, you will get 1. 1 is the value of all the odd numbers added up from 0 to 1. counting all the odd numbers from 0 to 3: if you count all the odd numbers from 0 to 3, what you will get is 4. furthermore, what you will also get as a formula (if n=3, h=height and l=length) is: *if you plug the value 3 into n, you will get 4. 4 is the value of all the odd numbers added up from 0 to 3. counting all the odd numbers from 0 to 5: if you count all the odd numbers from 0 to 5, what you will get is 9. furthermore, what you will also get as a formula (if n=5, h=height and l=length) is: *if you plug the value 5 into n, you will get 9. 9 is the value of all the odd numbers added up from 0 to 5. counting all the odd numbers from 0 to 7: if you count all the odd numbers from 0 to 7, what you will get is 16. furthermore, what you will also get as a formula (if n=7, h=height and l=length) is: *if you plug the value 7 into n, you will get 16. 16 is the value of all the odd numbers added up from 0 to 7. counting all the odd numbers from 0 to 9: if you count all the odd numbers from 0 to 9, what you will get is 25. furthermore, what you will also get as a formula (if n=9, h=height and l=length) is: *if you plug the value 9 into n, you will get 25. 25 is the value of all the odd numbers added up from 0 to 9. the formula which can be used to add up all the odd numbers from 0 to n, whereby n is an odd number: if you look at each and every diagram and formula above, what you will notice is that the formula will allow you to add up all the odd numbers from 0 to n, whereby n is an odd number. the diagrams above have demonstrated why this formula is robust and completely logical. if you need to add up all the odd numbers from 0 to n (n is an odd number), the formula above is one you can trust. alternative method: using the table below, we can come up with an alternative method of calculating every odd number from 0 to n (n is an odd number): n: sum total total (exponential form) 1 1 1 1^2 3 1+3 4 2^2 5 1+3+5 9 3^2 7 1+3+5+7 16 4^2 9 1+3+5+7+9 25 5^2 it turns out that: *note that 2x+1 can be used to denote an odd number. addingcountingodd numbers carl friedrich gauss, combinations, summations solving the student handshake problem september 13, 2016 tiago hands leave a comment the other day, a question came up on a site called brainly.com. it went like this… in a cafeteria, all students shook hands with one another. there were 66 handshakes in total. how many students were in the cafeteria? as this question is quite interesting, i’m going to explain how you can answer it, and in the process – i’ll also be revealing its answer. now, to answer such a question we first have to perform a few experiments and ask ourselves mini questions. the data from these experiments and mini questions will have to be recorded, so that we can spot potential patterns which may ultimately help us create a formula to solve the main problem. experiments + mini questions will a pattern emerge?? 1. firstly, let’s think about how many handshakes there’d be with only one student in this cafeteria. well, we can say 0. why would someone shake their own hand? 2. secondly, how many handshakes would there be if there are 2 students in this cafeteria? well, the answer to this question is 1. these two students would be able to shake hands with one another. 3. thirdly, how many handshakes would there be if there are 3 students in the cafeteria? haha, now things get a little more complicated… to answer this mini question, let’s attach the variables a, b and c to these students {a, b, c}. it turns out that: a can shake hands with b (a,b). a can shake hands with c (a,c). b can shake hands with c (b, c). *possible combinations: (a, b), (a, c) and (b, c). so the answer to this mini question has to be 3. 4. fourthly, how many handshakes would there be if there are 4 students in this cafeteria? to answer this question we can use the same strategy we used to answer the third question. let’s attach the variables a, b, c and d to these students {a, b, c, d}. it turns out that: a can shake hands with b (a,b). a can shake hands with c (a, c). a can shake hands with d. (a, d). b can shake hands with c (b, c). b can shake hands with d (b, d). c can shake hands with d (c,d). * possible combinations: (a, b), (a, c), (a, d), (b, c), (b, d) and (c, d). so, the answer to this mini question would have to be 6. 5. fifthly, how many handshakes would there be if there are 5 students in this cafeteria? using the same strategy we used to answer mini questions 3 and 4 – we will answer this question too. let’s attach the variables a, b, c, d and e to these students {a, b, c, d, e}. it turns out that: a can shake hands with b (a, b). a can shake hands with c (a, c). a can shake hands with d (a, d). a can shake hands with e (a, e). b can shake hands with c (b, c). b can shake hands with d (b, d). b can shake hands with e (b, e). c can shake hands with d (c, d). c can shake hands with e (c, e). d can shake hands with e (d, e). so, the answer to this mini question would have to be 10. possible combinations: (a,b), (a, c), (a, d), (a, e), (b, c), (b, d), (b, e), (c, d), (c, e) and (d, e). can we solve the main problem with a formula? what pattern will define the formula? alright… now that we’ve performed a few experiments and have answered a few mini questions – let’s see if we can spot a pattern in our data. if we can spot a pattern in our data, we may be able to solve the problem relating to 66 handshakes. we need to find a pattern so that we don’t have to answer the main question using brute force and hundreds, if not, thousands of calculations. remember, solving mathematical problems is all about spotting patterns. to spot patterns, the best tool we can use is a table. let’s create a table which contains the information we’ve just produced, related to the mini questions… student(s) handshakes pattern (related to handshakes) 1 0 0 2 1 1 3 3 1+2 4 6 1+2+3 5 10 1+2+3+4 ok… let’s look at this table carefully. it turns out that a pattern has emerged… as a pattern, we get tidy little sums. the kind of sums that carl friedrich gauss was able to add up, thanks to diagrams such as the one below… diagram explanation: to add up the sum 1+2+3+4, you simply have to multiply 5 (which is the variable ‘s’ in this case) by (51) which is 4, then divide their product ( 5 x (51) ) by 2. (5×4)/2 = 10 = 1+2+3+4. notice that: when there was one student in the cafeteria, there were 0 handshakes. (0) is 1 less than the number 1. when there were two students in the cafeteria, there was 1 handshake. (1) is 1 less than 2. when there were 3 students in the cafeteria, there were 3 handshakes. 3 =1+(2). 2 is 1 less than 3. when there were 4 students in the cafeteria, there were 6 handshakes. 6=1+2+(3). 3 is 1 less than 4. when there were 5 students in the cafeteria, there were 10 handshakes. 10=1+2+3+(4). 4 is 1 less than 5. also notice that: *to understand the pattern below and how it was intuitively discovered, see the diagram which helped carl friedrich gauss neatly add up sums such as 1+2+3+4. [ 1 x (11) ] / 2 = 0 which is the same as : [ 1 x 0 ] / 2 = 0 [ 2 x (21) ] / 2 = 1 which is the same as : [ 2 x 1 ] / 2 = 1 [ 3 x (31) ] / 2 = 3 which is the same as : [ 3 x 2 ] / 2 = 3 [ 4 x (41) ] / 2 = 6 which is the same as : [ 4 x 3 ] / 2 = 6 [ 5 x (51) ] / 2 = 10 which is the same as : [ 5 x 4 ] / 2 = 10 with this information, we can conclude that: s = number of students h = handshakes [ s x (s1) ] / 2 = h and this is the formula we can use to solve all student handshake problems such as the one mentioned at the top of this post. if we plug the value 66 into this formula, we will discover how many students there were in the cafeteria whereby 66 handshakes took place. at the beginning of this post, i said that i would reveal the answer to the main question. to reveal it though, i will have to solve a quadratic equation by completing the square. i will also have to turn the variable ‘h’ into 66. let’s do this… we now know that there were 12 students in the cafeteria. obviously, this problem could have been solved when we knew that s x (s1) = 132, because 12 x 11 = 132. however, if you get a larger problem, you will need to produce a quadratic formula and complete the square to get an answer. i hope that this post has shed light on how to solve handshake / people problems. if you have any questions or feedback, please leave a comment below. 🙂 carl friedrich gausscombinationscompleting the squarehandshake problemquadratic equationsummationssumming up sine rule the quickest sine rule proof september 6, 2016 tiago hands in this post i’ll be demonstrating how to prove that the sine rule is true in the quickest manner possible. first of all, let’s begin with writing down the 3 formulas which can be used to find the area of a triangle: now, let’s make the first two formulas above equivalent to one another… alright, now watch what happens when we multiply both sides of the equation by a handy expression… if we do this, what we’re going to be left with is… so far so good! let’s now make these two area formulas equivalent to one another… and now, let’s multiply both sides of the equation we’ve just created by a handy expression… if we do this, what we’re going to be left with is… and it turns out, because: we can say that: i’ve made a video related to this sine rule proof. you can watch it below if you wish. hope you enjoyed reading this post! 🙂 algebraproofssine rule chance, probabilities rolling 3 dice… what is most likely to happen? september 5, 2016 tiago hands understanding probabilities / chance can sometimes be difficult. this is why i’ve written (in detail) an article about what kind of sums you should expect to get when you roll 3 dice and why you should expect to get them. this article reveals some of the mechanics behind our probabilistic theories and should help maths students gain a deeper understanding of the nature of randomness and chance. recently, i’ve been doing a bit of coding in html, css, php and mysql. i’ll be looking to improve mathsvideos.net and also provide students with more mathematics resources. i’m also providing businesses with automation solutions in order to fund my maths project. thanks for stopping by!! tiago. 🙂 for more mathematics proofs, visit https://plus.google.com/b/100450538547176385655/communities/106007058741903558109. like probabilities? why not check out the “hannah sweets” problem? hannah sweets maths problem – edexcel (june 2015) chancecsshtmlmysqlphpprobabilitiesrolling 3 dice euler's identity, maclaurin series how to derive euler’s identity using the maclaurin series august 11, 2016 tiago hands leave a comment in this post i’ll be showing you how to derive euler’s identity using the maclaurin series. it turns out that the maclaurin series looks like this: and expanded, it looks like this: [*a larger version of this image can be found here.] now, since we want to derive euler’s identity, we first have to find out what the formula for e^x looks like. in order to get this formula we must use the table below: derivatives of e^x when x=0 ok. so we’ve got a useful table just above. let’s write out the function of e^x in its maclaurin series form: now, let’s replace with the values from the table. if we do this, the formula for e^x will become: alright, so far, so good. we are certainly on the right track. our next goal will be to discover what e^(i*x) is. this is because to produce euler’s identity, we need to come up with: to come up with the formula above, we will need the table below, because our latest e^(x) formula will have to be transformed. x will be turned into i*x. imaginary numbers exponentiated as we’ve got the table above, we can figure out what the formula e^(i*x) would look like: since: [*to find out why it’s the case, visit this page.] this means that: and finally, when x=π: this is because: you have produced euler’s identity from almost absolute scratch. give yourself a pat on the back! 🙂 related: deriving the taylor series from scratch cosxeuler's identityimaginary numbermaclaurin seriessinx maclaurin series, taylor series deriving the taylor series from scratch august 10, 2016 tiago hands leave a comment [please note: in order to derive the taylor series, you will need to understand how to differentiate. if you know how to differentiate, finding the taylor series won’t be much of a problem. you also need to know that 0!=1, 1!=1, 2!=2, 3!=6, x^0=1, x^1=x.] in this post i will be demonstrating how one can produce the taylor series from absolute scratch. first of all, let’s look at the diagram above. now, let’s suppose that the equation of the function above is: ok, so we have the equation for the function, however, it isn’t complete. c_0, c_1, c_2, c_3 etc are hidden constants. this means that our second task will be to discover these constants. we need to discover these constants to find the complete equation of the function so that we can arrive at the taylor series. fortunately, this task won’t be too difficult. let me show you how c_0, c_1, c_2, c_3 etc can be found fairly easily… when x=0: now: when x=0: also: when x=0: and, finally: when x=0: alright, so now that we have discovered the hidden constants c_0, c_1, c_2 and c_3, our third task is to write down the complete equation of the function f(x+a). thanks to the information we have above, the fact that x^0=1 and x^1=x, plus our ability to spot patterns, we will be able to do this quite quickly… [*image can be seen here if it appears to be too small on this page.] and it turns out that the equation we have just above is the taylor series function. it can be simplified to look like this… what is also interesting is that if we transform a=0, we get the maclaurin series function which can be used to discover formulas for things such as e^x. if you have any questions regarding this post, please leave your comments below. once again, thanks for stopping by! 🙂 related: how to derive euler’s identity using the maclaurin series differentiationfunctionsmaclaurin seriestaylor series posts navigation 1 2 … 11 next → rss feed receive our latest posts. just enter your email address in the box below and hit the subscribe button. you shall receive a confirmation email to complete your subscription.delivered by feedburner subscribe to our youtube channel receive notifications about our latest videos as soon as they become available. we've produced some of the best gcse and a level mathematics proofs on the web. other posts derive the formula to find areas underneath curves views 155 how to prove that sin(ab)=sin(a)cos(b)cos(a)sin(b) geometrically views 207 properties of c squared, pythagorean theorem views 94 2 ways to derive pythagoras’ equation from scratch views 94 how to add up all the even numbers from 0 onwards quickly views 92 how to add up odd numbers from 0 upwards views 82 solving the student handshake problem views 83 the quickest sine rule proof views 87 archives october 2016 (1) september 2016 (8) august 2016 (3) march 2016 (1) february 2016 (2) december 2015 (1) november 2015 (1) september 2015 (2) august 2015 (4) july 2015 (1) june 2015 (2) may 2015 (1) march 2015 (7) february 2015 (7) january 2015 (8) december 2014 (29) july 2014 (12) june 2014 (4) may 2014 (15) high quality mathematics videos and proofs for students home about us philosophy donate to the project mathematics: invented or discovered? basic information about numbers symbols & notations basic logic tables mathematical logic (1) times tables powers powers of ten derive the value of surds useful algebraic formulas percentage / decimal / fraction table inverse shortcuts trigonometry rules deriving trigonometric identities without the use of unit circles trigonometric identity proofs graph transformation tricks modulus formulas log formulas differentiation formulas integration formulas algebra completing the square trigonometry calculus vectors volume of cones formula maclaurin series derivatives – useful tables useful tables (taylor & maclaurin series) mean deviation vs standard deviation free resources / downloads mathematical art & design video playlists all posts (archives) navigation (page by page) rss feed xml sitemap contact us trigonometric tablestrig table (1) trig table (2) tag cloudadding algebra angles areas calculus circles completing the square cones continued fractions curves differentiation even numbers formulas fractions functions golden ratio implicit differentiation indices integration irrational numbers logarithms logic maclaurin series mathematical programming multiplication odd numbers pi probabilities proofs pythagoras pythagoras' theorem quadratic formula roots sine sine rule soh cah toa statistics summing up surds trigonometric identities trigonometry vectors videos volumes categoriescategories select category adding addition algebra angles areas binomial expansions brainly calculus carl friedrich gauss cartesian coordinates chance coordinate geometry combinations continued fractions cosine rule decimals differentiation dimensions division ellipses ellipsoids equation editors euler’s identity even numbers exponentials fractions functions google apps graphs hypersurfaces implicit differentiation integration irrational numbers isometric projection lengths logarithms logic maclaurin series magnitudes mathematics proofs multidimensional multiplication natural law news odd numbers parameters percentages pinterest probabilities proofs pythagoras python roots sine rule singularities soh cah toa statistics summations surds sympy taylor series trigonometry tutorials universe vectors videos visualising mathematics legalprivacy & cookies policy learn more about cookies (information commisioner’s office) terms of use disclaimer proudly powered by wordpress we use cookies so that visitors can have a pleasant experience on our website. if you continue to use this site, we will assume that you are satisfied with our privacy and cookies policy.okread more
One word  Two words phrases  Three words phrases 
the  6.22% (283) and  2.75% (125) you  1.61% (73) for  1.56% (71) this  1.54% (70) number  1.45% (66) that  1.34% (61) all  1.3% (59) numbers  1.19% (54) from  1.17% (53) hands  1.14% (52) can  1.14% (52) are  1.12% (51) formula  1.03% (47) how  0.97% (44) shake  0.92% (42) will  0.92% (42) with  0.9% (41) odd  0.9% (41) add  0.88% (40) out  0.75% (34) use  0.68% (31) …  0.68% (31) let  0.66% (30) able  0.66% (30) diagram  0.57% (26) student  0.57% (26) what  0.57% (26) which  0.55% (25) there  0.53% (24) area  0.53% (24) series  0.53% (24) have  0.51% (23) get  0.51% (23) now  0.48% (22) proof  0.48% (22) our  0.46% (21) one  0.46% (21) pythagoras  0.46% (21) equation  0.46% (21) question  0.46% (21) handshake  0.46% (21) students  0.44% (20) trig  0.42% (19) (a,  0.4% (18) not  0.4% (18) even  0.4% (18) post  0.4% (18) angle  0.4% (18) also  0.4% (18) table  0.37% (17) above  0.37% (17) rule  0.37% (17) let’s  0.35% (16) count  0.35% (16) answer  0.35% (16) pat  0.33% (15) when  0.33% (15) sum  0.33% (15) is:  0.33% (15) handshakes  0.33% (15) 2016  0.33% (15) sine  0.33% (15) were  0.31% (14) turn  0.31% (14) maclaurin  0.31% (14) length  0.31% (14) that:  0.31% (14) cafeteria  0.31% (14) problem  0.31% (14) derive  0.31% (14) pattern  0.31% (14) algebra  0.31% (14) –  0.31% (14) discover  0.31% (14) proofs  0.29% (13) value  0.29% (13) i’ll  0.29% (13) using  0.29% (13) video  0.26% (12) trigonometry  0.26% (12) turns  0.26% (12) (b,  0.26% (12) more  0.24% (11) related  0.24% (11) below  0.24% (11) mean  0.24% (11) tiago  0.24% (11) 2015  0.24% (11) pythagoras’  0.24% (11) taylor  0.24% (11) identity  0.24% (11) formulas  0.24% (11) now,  0.24% (11) function  0.22% (10) adding  0.22% (10) mini  0.22% (10) added  0.22% (10) look  0.22% (10) any  0.22% (10) september  0.22% (10) would  0.22% (10) about  0.22% (10) means  0.22% (10) height  0.2% (9) need  0.2% (9) a  0.2% (9) used  0.2% (9) prove  0.2% (9) angles  0.2% (9) leave  0.2% (9) like  0.2% (9) find  0.2% (9) (1)  0.2% (9) square  0.2% (9) comment  0.2% (9) than  0.2% (9) why  0.2% (9) mathematics  0.2% (9) equal  0.18% (8) scratch  0.18% (8) same  0.18% (8) come  0.18% (8) first  0.18% (8) these  0.18% (8) questions  0.18% (8) other  0.18% (8) complete  0.18% (8) show  0.18% (8) views  0.18% (8) we’ve  0.18% (8) areas  0.18% (8) 1+2  0.18% (8) into  0.18% (8) was  0.18% (8) discovered  0.18% (8) log  0.18% (8) ratio  0.18% (8) some  0.18% (8) way  0.18% (8) own  0.18% (8) euler’s  0.15% (7) say  0.15% (7) going  0.15% (7) red,  0.15% (7) many  0.15% (7) its  0.15% (7) videos  0.15% (7) d).  0.15% (7) algebra,  0.15% (7) c).  0.15% (7) solve  0.15% (7) because  0.15% (7) diagram,  0.15% (7) counting  0.13% (6) plug  0.13% (6) site  0.13% (6) 1+2+3  0.13% (6) cafeteria,  0.13% (6) less  0.13% (6) combinations  0.13% (6) calculus  0.13% (6) differentiation  0.13% (6) posts  0.13% (6) too  0.13% (6) soh  0.13% (6) cah  0.13% (6) but  0.13% (6) demonstrating  0.13% (6) probabilities  0.13% (6) *if  0.13% (6) produce  0.13% (6) properties  0.13% (6) is…  0.13% (6) fact  0.13% (6) spot  0.13% (6) theorem  0.13% (6) watch  0.13% (6) toa  0.13% (6) (c,  0.13% (6) right  0.11% (5) up,  0.11% (5) such  0.11% (5) ask  0.11% (5) fraction  0.11% (5) ten  0.11% (5) tables  0.11% (5) logic  0.11% (5) (2)  0.11% (5) variable  0.11% (5) gauss  0.11% (5) x=0  0.11% (5) e^x  0.11% (5) chance  0.11% (5) handshakes.  0.11% (5) furthermore,  0.11% (5) (if  0.11% (5) friedrich  0.11% (5) cafeteria?  0.11% (5) h=height and  0.11% (5) information  0.11% (5) 🙂  0.11% (5) l=length)  0.11% (5) carl  0.11% (5) just  0.11% (5) e).  0.11% (5) maths  0.11% (5) understand  0.11% (5) very  0.11% (5) post,  0.11% (5) trigonometric  0.11% (5) above,  0.11% (5) sin(ab)=sin(a)cos(b)cos(a)sin(b)  0.11% (5) down  0.11% (5) method  0.11% (5) shaded  0.09% (4) d),  0.09% (4) 1+2+3+4  0.09% (4) since  0.09% (4) mathematical  0.09% (4) i’ve  0.09% (4) possible  0.09% (4) c),  0.09% (4) should  0.09% (4) because:  0.09% (4) two  0.09% (4) main  0.09% (4) may  0.09% (4) patterns  0.09% (4) experiments  0.09% (4) related:  0.09% (4) sums  0.09% (4) degrees  0.09% (4) thanks  0.09% (4) x=0:  0.09% (4) cookies  0.09% (4) pythagoras'  0.09% (4) vectors  0.09% (4) fractions  0.09% (4) art  0.09% (4) integration  0.09% (4) 2014  0.09% (4) youtube  0.09% (4) feed  0.09% (4) your  0.09% (4) constants  0.09% (4) deriving  0.09% (4) task  0.09% (4) useful  0.09% (4) august  0.09% (4) dice  0.09% (4) see  0.09% (4) n/2.  0.09% (4) completing  0.09% (4) quadratic  0.09% (4) reveal  0.09% (4) which  0.09% (4) ways  0.09% (4) please  0.09% (4) onwards  0.09% (4) number.  0.09% (4) 1+3  0.09% (4) create  0.09% (4) summations  0.09% (4) this…  0.09% (4) showing  0.09% (4) alternative  0.09% (4) lengths  0.09% (4) notice  0.09% (4) whereby  0.09% (4) rectangle  0.09% (4) (n+2)  0.09% (4) robust  0.07% (3) order  0.07% (3) geometrically  0.07% (3) all,  0.07% (3) edexcel  0.07% (3) this,  0.07% (3) alright,  0.07% (3) identity,  0.07% (3) quickest  0.07% (3) solving  0.07% (3) full  0.07% (3) know  0.07% (3) begin  0.07% (3) write  0.07% (3) diagrams  0.07% (3) property  0.07% (3) por  0.07% (3) quite  0.07% (3) (51)  0.07% (3) triangle  0.07% (3) multiply  0.07% (3) number)  0.07% (3) problems  0.07% (3) top  0.07% (3) visit  0.07% (3) looks  0.07% (3) curves  0.07% (3) continue  0.07% (3) summing  0.07% (3) functions  0.07% (3) tag  0.07% (3) navigation  0.07% (3) surds  0.07% (3) areas,  0.07% (3) project  0.07% (3) june  0.07% (3) (4)  0.07% (3) archives  0.07% (3) receive  0.07% (3) simple  0.07% (3) rss  0.07% (3) cosine  0.07% (3) transform  0.07% (3) simplified  0.07% (3) c_2  0.07% (3) quickly  0.07% (3) rule,  0.07% (3) c_3  0.07% (3) c_1,  0.07% (3) c_0,  0.07% (3) produced  0.07% (3) latest  0.07% (3) new  0.07% (3) roll  0.07% (3) obviously  0.07% (3) squared  0.07% (3) true  0.07% (3) however,  0.07% (3) third  0.07% (3) c^2.  0.07% (3) has  0.07% (3) b),  0.07% (3) data  0.07% (3) a1=a2  0.07% (3) combinations:  0.07% (3) finally,  0.07% (3) 1+3+5  0.07% (3) few  0.07% (3) geometrical]  0.07% (3) attach  0.07% (3) {a,  0.07% (3) total  0.07% (3) variables  0.07% (3) a3=a4  0.07% (3) below,  0.07% (3) b).  0.07% (3) help  0.07% (3) playlist  0.07% (3) x^0=1  0.04% (2) (3)  0.04% (2) every  0.04% (2) c_2,  0.04% (2) problem.  0.04% (2) pythagorean  0.04% (2) (8)  0.04% (2) underneath  0.04% (2) march  0.04% (2) february  0.04% (2) etc  0.04% (2) december  0.04% (2) visualising  0.04% (2) perform  0.04% (2) won’t  0.04% (2) become  0.04% (2) subscribe  0.04% (2) hidden  0.04% (2) onwards.  0.04% (2) plus  0.04% (2) email  0.04% (2) a3=a4.  0.04% (2) 16,  0.04% (2) constants.  0.04% (2) second  0.04% (2) upwards  0.04% (2) by!  0.04% (2) numbers,  0.04% (2) 27,  0.04% (2) writing  0.04% (2) interesting  0.04% (2) without  0.04% (2) regarding  0.04% (2) a2,  0.04% (2) july  0.04% (2) multiplication  0.04% (2) resources  0.04% (2) playlists  0.04% (2) continued  0.04% (2) “n”  0.04% (2) 1+3+5+7  0.04% (2) implicit  0.04% (2) irrational  0.04% (2) logarithms  0.04% (2) similar  0.04% (2) b^2  0.04% (2) roots  0.04% (2) statistics  0.04% (2) proofs,  0.04% (2) brainly  0.04% (2) search  0.04% (2) google  0.04% (2) day  0.04% (2) policy  0.04% (2) completely  0.04% (2) deviation  0.04% (2) cones  0.04% (2) (7)  0.04% (2) i’m  0.04% (2) method:  0.04% (2) answer.  0.04% (2) basic  0.04% (2) download  0.04% (2) sitemap  0.04% (2) times  0.04% (2) powers  0.04% (2) xml  0.04% (2) percentage  0.04% (2) volume  0.04% (2) decimal  0.04% (2) (archives)  0.04% (2) identities  0.04% (2) unit  0.04% (2) circles  0.04% (2) graph  0.04% (2) page)  0.04% (2) (page  0.04% (2) proven  0.04% (2) series,  0.04% (2) imaginary  0.04% (2) angles,  0.04% (2) formula.  0.04% (2) pythagoras’s  0.04% (2) adding,  0.04% (2) then  0.04% (2) been  0.04% (2) important  0.04% (2) larger  0.04% (2) (ba)  0.04% (2) hope  0.04% (2) below.  0.04% (2) (s1)  0.04% (2) make  0.04% (2) equivalent  0.04% (2) another…  0.04% (2) both  0.04% (2) sides  0.04% (2) handy  0.04% (2) expression…  0.04% (2) (a,b).  0.04% (2) we’re  0.04% (2) strategy  0.04% (2) question.  0.04% (2) diagram…  0.04% (2) (d,  0.04% (2) e),  0.04% (2) patterns,  0.04% (2) best  0.04% (2) table.  0.04% (2) equation…  0.04% (2) too.  0.04% (2) shown  0.04% (2) allow  0.04% (2) kind  0.04% (2) *to  0.04% (2) focus  0.04% (2) since:  0.04% (2) obviously,  0.04% (2) so,  0.04% (2) demonstrate  0.04% (2) 1+2+3+4.  0.04% (2) note:  0.04% (2) also:  0.04% (2) *note  0.04% (2) left  0.04% (2) far  0.04% (2) scratch.  0.04% (2) their  0.04% (2) this:  0.04% (2) version  0.04% (2) image  0.04% (2) found  0.04% (2) sin(a+b)=sinacosb+cosasinb  0.04% (2) derivatives  0.04% (2) elegant  0.04% (2) got  0.04% (2) above.  0.04% (2) series.  0.04% (2) toa,  0.04% (2) next  0.04% (2) e^(i*x)  0.04% (2) squared,  0.04% (2) formula?  0.04% (2) well,  0.04% (2) page.]  0.04% (2) cafeteria.  0.04% (2) absolute  0.04% (2) 25.  0.04% (2) 16.  0.04% (2) rolling  0.04% (2) php  0.04% (2) most  0.04% (2) understanding  0.04% (2) difficult.  0.04% (2) (in  0.04% (2) article  0.04% (2) expect  0.04% (2) usual  0.04% (2) below:  0.04% (2) gain  0.04% (2) little  0.04% (2) (edexcel  0.04% (2) stopping  0.04% (2) pythagoras,  0.04% (2) hannah  0.04% (2) sweets  0.04% (2) things  0.04% (2) euler's  0.04% (2) another.  0.04% (2) lengths,  0.04% (2) simplified)  0.04% (2) privacy  0.04% (2)  from 0  0.95% (43) all the  0.79% (36) numbers from  0.79% (36) odd numbers  0.73% (33) the odd  0.53% (24) you will  0.48% (22) hands with  0.46% (21) if you  0.44% (20) shake hands  0.44% (20) how to  0.44% (20) can shake  0.42% (19) add up  0.4% (18) even numbers  0.37% (17) at the  0.37% (17) in this  0.35% (16) up all  0.35% (16) to add  0.33% (15) of the  0.33% (15) is the  0.31% (14) maclaurin series  0.31% (14) the formula  0.31% (14) in the  0.29% (13) the value  0.29% (13) sine rule  0.29% (13) to the  0.29% (13) what you  0.26% (12) it turns  0.26% (12) this post  0.26% (12) we can  0.26% (12) which is  0.26% (12) the even  0.26% (12) turns out  0.26% (12) that the  0.24% (11) to derive  0.24% (11) will a  0.24% (11) out that  0.24% (11) there were  0.24% (11) have to  0.24% (11) the area  0.24% (11) will get  0.22% (10) the diagram  0.22% (10) means that  0.22% (10) tiago hands  0.22% (10) can be  0.22% (10) taylor series  0.22% (10) 2016 tiago  0.22% (10) used to  0.2% (9) the cafeteria  0.2% (9) i’ll be  0.2% (9) students in  0.2% (9) added up  0.2% (9) a formula  0.18% (8) equal to  0.18% (8) pythagoras’ equation  0.18% (8) will be  0.18% (8) the same  0.18% (8) a comment  0.18% (8) of all  0.18% (8) leave a  0.18% (8) a pattern  0.15% (7) euler’s identity  0.15% (7) on the  0.15% (7) this means  0.15% (7) to find  0.15% (7) hands leave  0.15% (7) that s  0.15% (7) able to  0.15% (7) the taylor  0.15% (7) how many  0.15% (7) going to  0.15% (7) need to  0.15% (7) from scratch  0.13% (6) using the  0.13% (6) an odd  0.13% (6) derive pythagoras’  0.13% (6) come up  0.13% (6) say that  0.13% (6) that: a  0.13% (6) and it  0.13% (6) soh cah  0.13% (6) count all  0.13% (6) to this  0.13% (6) plug the  0.13% (6) *if you  0.13% (6) with d  0.13% (6) up with  0.13% (6) prove that  0.13% (6) value of  0.13% (6) cah toa  0.13% (6) mini questions  0.13% (6) with c  0.13% (6) will also  0.13% (6) this diagram  0.13% (6) to answer  0.13% (6) be used  0.11% (5) many handshakes  0.11% (5) we will  0.11% (5) out that:  0.11% (5) answer to  0.11% (5) 1 less  0.11% (5) you can  0.11% (5) we are  0.11% (5) get is  0.11% (5) up from  0.11% (5) into n,  0.11% (5) numbers added  0.11% (5) you plug  0.11% (5) counting all  0.11% (5) you count  0.11% (5) that we  0.11% (5) to count  0.11% (5) get as  0.11% (5) h=height and l=length)  0.11% (5) n, you  0.11% (5) the cafeteria,  0.11% (5) furthermore, what  0.11% (5) also get  0.11% (5) formula (if  0.11% (5) friedrich gauss  0.11% (5) l=length) is:  0.11% (5) when there  0.11% (5) this post,  0.11% (5) is: *if  0.11% (5) have a  0.11% (5) the maclaurin  0.11% (5) cafeteria, there  0.11% (5) to solve  0.11% (5) demonstrating how  0.11% (5) the table  0.11% (5) to say  0.11% (5) the function  0.11% (5) i will  0.11% (5) to prove  0.11% (5) the equation  0.11% (5) be demonstrating  0.11% (5) related to  0.11% (5) less than  0.11% (5) be able  0.11% (5) to discover  0.11% (5) carl friedrich  0.11% (5) above is  0.11% (5) you how  0.11% (5) same as  0.11% (5) to get  0.09% (4) derive euler’s  0.09% (4) some of  0.09% (4) formula above  0.09% (4) rectangle is  0.09% (4) out the  0.09% (4) what is  0.09% (4) be showing  0.09% (4) look at  0.09% (4) now that  0.09% (4) comment in  0.09% (4) (b, c).  0.09% (4) this mini  0.09% (4) 2015 (1)  0.09% (4) derive the  0.09% (4) handshake problem  0.09% (4) if there  0.09% (4) there be  0.09% (4) handshakes would  0.09% (4) when x=0:  0.09% (4) would there  0.09% (4) that sin(ab)=sin(a)cos(b)cos(a)sin(b)  0.09% (4) so that  0.09% (4) there are  0.09% (4) can use  0.09% (4) this question  0.09% (4) we have  0.09% (4) to come  0.09% (4) this formula  0.09% (4) with e  0.09% (4) this is  0.09% (4) properties of  0.09% (4) the height  0.09% (4) are going  0.09% (4) how you  0.09% (4) fact equal  0.09% (4) red, which  0.09% (4) shaded in  0.09% (4) is equal  0.09% (4) length is  0.09% (4) and its  0.09% (4) is (n+2)  0.09% (4) the rectangle  0.09% (4) height of  0.09% (4) this diagram,  0.09% (4) up, is:  0.09% (4) is: adding  0.09% (4) added up,  0.09% (4) in fact  0.09% (4) adding up  0.09% (4) in red,  0.09% (4) area shaded  0.09% (4) diagram, we  0.09% (4) is n/2.  0.09% (4) its length  0.09% (4) (n+2) and  0.09% (4) to all  0.09% (4) n/2. this  0.09% (4) completing the  0.09% (4) use to  0.09% (4) the main  0.09% (4) diagram and  0.09% (4) post, i  0.09% (4) such as  0.09% (4) showing you  0.09% (4) will have  0.09% (4) now, let’s  0.09% (4) of this  0.07% (3) is also  0.07% (3) identity using  0.07% (3) b), (a,  0.07% (3) post i’ll  0.07% (3) sin(ab)=sin(a)cos(b)cos(a)sin(b) geometrically  0.07% (3) in order  0.07% (3) at this  0.07% (3) combinations: (a,  0.07% (3) {a, b,  0.07% (3) 3 dice  0.07% (3) find a  0.07% (3) pythagoras' theorem  0.07% (3) summing up  0.07% (3) do this,  0.07% (3) mathematics proofs  0.07% (3) 6, 2016  0.07% (3) out what  0.07% (3) the quickest  0.07% (3) equation of  0.07% (3) experiments and  0.07% (3) we need  0.07% (3) with a  0.07% (3) possible combinations:  0.07% (3) useful table  0.07% (3) series from  0.07% (3) students {a,  0.07% (3) to these  0.07% (3) you have  0.07% (3) with b  0.07% (3) the variables  0.07% (3) will need  0.07% (3) let’s attach  0.07% (3) c_0, c_1,  0.07% (3) our latest  0.07% (3) answer this  0.07% (3) can spot  0.07% (3) this cafeteria?  0.07% (3) these students  0.07% (3) which can  0.07% (3) 2 ways  0.07% (3) why the  0.07% (3) student handshake  0.07% (3) 90 degrees  0.07% (3) alternative method  0.07% (3) the one  0.07% (3) all, let  0.07% (3) first of  0.07% (3) which means  0.07% (3) cosine rule  0.07% (3) formula i  0.07% (3) is that  0.07% (3) count odd  0.07% (3) and finally,  0.07% (3) using a  0.07% (3) odd number.  0.07% (3) means that:  0.07% (3) formula to  0.07% (3) create a  0.07% (3) post, i’ll  0.07% (3) attach the  0.07% (3) 66 handshakes  0.07% (3) – geometrical]  0.07% (3) variables a,  0.07% (3) proof –  0.07% (3) solve the  0.07% (3) deriving the  0.04% (2) what the  0.04% (2) more mathematics  0.04% (2) about some  0.04% (2) this page.]  0.04% (2) 🙂 related:  0.04% (2) to understand  0.04% (2) cah toa,  0.04% (2) the sine  0.04% (2) expect to  0.04% (2) how one  0.04% (2) algebra, areas,  0.04% (2) you should  0.04% (2) absolute scratch.  0.04% (2) trigonometry how  0.04% (2) (edexcel proof  0.04% (2) one can  0.04% (2) image can  0.04% (2) for stopping  0.04% (2) 27, 2016  0.04% (2) the diagram,  0.04% (2) identity, we  0.04% (2) first have  0.04% (2) like this:  0.04% (2) which are  0.04% (2) because: now,  0.04% (2) for e^x  0.04% (2) squared, pythagorean  0.04% (2) elegant way  0.04% (2) with the  0.04% (2) use the  0.04% (2) now, to  0.04% (2) me show  0.04% (2) from the  0.04% (2) formula for  0.04% (2) is because  0.04% (2) euler’s identity,  0.04% (2) hannah sweets  0.04% (2) be found  0.04% (2) that sin(a+b)=sinacosb+cosasinb  0.04% (2) toa, trigonometry  0.04% (2) c_1, c_2,  0.04% (2) logic maclaurin  0.04% (2) 2015 (2)  0.04% (2) june 2015  0.04% (2) 2015 (7)  0.04% (2) useful tables  0.04% (2) posts (archives)  0.04% (2) xml sitemap  0.04% (2) trig table  0.04% (2) angles areas  0.04% (2) continued fractions  0.04% (2) integration irrational  0.04% (2) proofs pythagoras  0.04% (2) 2016 (1)  0.04% (2) all posts  0.04% (2) quadratic formula  0.04% (2) roots sine  0.04% (2) toa statistics  0.04% (2) by page)  0.04% (2) vectors videos  0.04% (2) algebra angles  0.04% (2) irrational numbers  0.04% (2) navigation (page  0.04% (2) probabilities proofs  0.04% (2) cookies policy  0.04% (2) visualising mathematics  0.04% (2) (1) september  0.04% (2) c_3 etc  0.04% (2) spot patterns,  0.04% (2) discover these  0.04% (2) complete equation  0.04% (2) simple but  0.04% (2) be too  0.04% (2) rolling 3  0.04% (2) c_2, c_3  0.04% (2) algebra, angles,  0.04% (2) alright, so  0.04% (2) hidden constants  0.04% (2) the complete  0.04% (2) information we  0.04% (2) just above  0.04% (2) the student  0.04% (2) look like  0.04% (2) get the  0.04% (2) thanks for  0.04% (2) stopping by!  0.04% (2) underneath curves  0.04% (2) rss feed  0.04% (2) below and  0.04% (2) find areas  0.04% (2) c squared,  0.04% (2) pythagorean theorem  0.04% (2) views 94  0.04% (2) that area  0.04% (2) we’re going  0.04% (2) area a2,  0.04% (2) pattern in  0.04% (2) table below,  0.04% (2) (a, d).  0.04% (2) whereby n  0.04% (2) (b, d).  0.04% (2) (d, e).  0.04% (2) you to  0.04% (2) main problem  0.04% (2) will allow  0.04% (2) n, whereby  0.04% (2) spot a  0.04% (2) allow you  0.04% (2) solving the  0.04% (2) in our  0.04% (2) will notice  0.04% (2) to spot  0.04% (2) a table  0.04% (2) the information  0.04% (2) we’ve just  0.04% (2) let’s look  0.04% (2) also be  0.04% (2) of sums  0.04% (2) formula. i’ll  0.04% (2) (a, c).  0.04% (2) we used  0.04% (2) notice that:  0.04% (2) we first  0.04% (2) b (a,b).  0.04% (2) the cafeteria?  0.04% (2) these two  0.04% (2) video playlists  0.04% (2) one student  0.04% (2) so the  0.04% (2) questions will  0.04% (2) 4 students  0.04% (2) few experiments  0.04% (2) question we  0.04% (2) is quite  0.04% (2) same strategy  0.04% (2) strategy we  0.04% (2) answer the  0.04% (2) a question  0.04% (2) comment the  0.04% (2) (a,b). a  0.04% (2) c), (a,  0.04% (2) d), (b,  0.04% (2) c), (b,  0.04% (2) (c, d).  0.04% (2) so, the  0.04% (2) question would  0.04% (2) x (51)  0.04% (2) student in  0.04% (2) can say  0.04% (2) one another…  0.04% (2) any questions  0.04% (2) please leave  0.04% (2) september 27,  0.04% (2) area a4  0.04% (2) all, let’s  0.04% (2) begin with  0.04% (2) find the  0.04% (2) area a1  0.04% (2) make the  0.04% (2) equivalent to  0.04% (2) both sides  0.04% (2) complete the  0.04% (2) a handy  0.04% (2) expression… if  0.04% (2) this, what  0.04% (2) left with  0.04% (2) handy expression…  0.04% (2) to area  0.04% (2) what we’re  0.04% (2) be left  0.04% (2) with is…  0.04% (2) area a3  0.04% (2) the other  0.04% (2) to produce  0.04% (2) 16, 2016  0.04% (2) and this  0.04% (2) 0 handshakes.  0.04% (2) alternative method:  0.04% (2) there was  0.04% (2) were 3  0.04% (2) 6 handshakes.  0.04% (2) 0 onwards.  0.04% (2) 5 students  0.04% (2) september 16,  0.04% (2) and how  0.04% (2) onwards quickly  0.04% (2) formula we  0.04% (2) x (s1)  0.04% (2) pythagoras’s equation  0.04% (2) all student  0.04% (2) with pythagoras’s  0.04% (2) were in  0.04% (2) was able  0.04% (2) that: and  0.04% (2) c^2. it  0.04% (2) a quadratic  0.04% (2) equation by  0.04% (2) area of  0.04% (2) usual method  0.04% (2) calculus vectors  0.04% (2)  from 0 to  0.81% (37) numbers from 0  0.79% (36) odd numbers from  0.53% (24) the odd numbers  0.53% (24) all the odd  0.53% (24) shake hands with  0.44% (20) can shake hands  0.42% (19) up all the  0.35% (16) to add up  0.33% (15) all the even  0.26% (12) what you will  0.26% (12) even numbers from  0.26% (12) the even numbers  0.26% (12) it turns out  0.26% (12) add up all  0.24% (11) 2016 tiago hands  0.22% (10) you will get  0.22% (10) a can shake  0.2% (9) how to add  0.18% (8) leave a comment  0.18% (8) in this post  0.15% (7) tiago hands leave  0.15% (7) the taylor series  0.15% (7) hands leave a  0.15% (7) students in the  0.13% (6) which is the  0.13% (6) to derive pythagoras’  0.13% (6) hands with c  0.13% (6) count all the  0.13% (6) hands with d  0.13% (6) come up with  0.13% (6) derive pythagoras’ equation  0.13% (6) plug the value  0.13% (6) b can shake  0.13% (6) the value of  0.13% (6) the same as  0.11% (5) added up from  0.11% (5) you will also  0.11% (5) value of all  0.11% (5) into n, you  0.11% (5) *if you plug  0.11% (5) h=height and l=length) is:  0.11% (5) is the same  0.11% (5) same as :  0.11% (5) carl friedrich gauss  0.11% (5) is 1 less  0.11% (5) the cafeteria, there  0.11% (5) counting all the  0.11% (5) a formula (if  0.11% (5) if you count  0.11% (5) is the value  0.11% (5) the answer to  0.11% (5) how many handshakes  0.11% (5) the maclaurin series  0.11% (5) will get is  0.11% (5) you count all  0.11% (5) up from 0  0.11% (5) odd numbers added  0.11% (5) of all the  0.11% (5) n, you will  0.11% (5) 1 less than  0.11% (5) you plug the  0.11% (5) l=length) is: *if  0.11% (5) as a formula  0.11% (5) can be used  0.11% (5) furthermore, what you  0.11% (5) numbers added up  0.11% (5) is: *if you  0.11% (5) turns out that:  0.11% (5) also get as  0.11% (5) will also get  0.11% (5) in the cafeteria,  0.11% (5) be used to  0.11% (5) to say that  0.11% (5) be demonstrating how  0.11% (5) be able to  0.11% (5) to prove that  0.11% (5) which is the  0.09% (4) cafeteria, there were  0.09% (4) equation from scratch  0.09% (4) hands with e  0.09% (4) derive euler’s identity  0.09% (4) properties of c  0.09% (4) a comment in  0.09% (4) have to be  0.09% (4) will have to  0.09% (4) would there be  0.09% (4) if there are  0.09% (4) pythagoras’ equation from  0.09% (4) some of the  0.09% (4) answer to this  0.09% (4) many handshakes would  0.09% (4) there be if  0.09% (4) to come up  0.09% (4) out that: a  0.09% (4) you how to  0.09% (4) in this diagram,  0.09% (4) be showing you  0.09% (4) we are going  0.09% (4) of the rectangle  0.09% (4) fact equal to  0.09% (4) which is in  0.09% (4) comment in this  0.09% (4) n/2. this means  0.09% (4) is (n+2) and  0.09% (4) when there were  0.09% (4) that the area  0.09% (4) its length is  0.09% (4) showing you how  0.09% (4) shaded in red,  0.09% (4) this post i’ll  0.07% (3) ways to derive  0.07% (3) post i’ll be  0.07% (3) a diagram and  0.07% (3) 6, 2016 tiago  0.07% (3) up, is: adding  0.07% (3) student handshake problem  0.07% (3) let’s attach the  0.07% (3) variables a, b  0.07% (3) these students {a,  0.07% (3) post, i’ll be  0.07% (3) hands with b  0.07% (3) c (b, c).  0.07% (3) first of all,  0.07% (3) will be able  0.07% (3) with c (b,  0.07% (3) students in this  0.07% (3) using a diagram  0.07% (3) how to derive  0.07% (3) c can shake  0.07% (3) which can be  0.07% (3) how to prove  0.07% (3) that sin(ab)=sin(a)cos(b)cos(a)sin(b) geometrically  0.07% (3) we can spot  0.07% (3) of c squared  0.07% (3) this post, i’ll  0.07% (3) an odd number)  0.07% (3) using the maclaurin  0.07% (3) of the function  0.07% (3) prove that sin(ab)=sin(a)cos(b)cos(a)sin(b)  0.07% (3) to these students  0.07% (3) taylor series from  0.07% (3) so that we  0.07% (3) b). a can  0.07% (3) with b (a,  0.07% (3) the variables a,  0.07% (3) proof – geometrical]  0.07% (3) formula above is  0.07% (3) related to the  0.07% (3) euler’s identity using  0.07% (3) 2 ways to  0.07% (3) logic maclaurin series  0.04% (2) (page by page)  0.04% (2) equivalent to one  0.04% (2) will need to  0.04% (2) algebra angles areas  0.04% (2) to find the  0.04% (2) have any questions  0.04% (2) can use to  0.04% (2) hands in this  0.04% (2) the quickest sine  0.04% (2) probabilities proofs pythagoras  0.04% (2) do this, what  0.04% (2) both sides of  0.04% (2) now that we  0.04% (2) out what the  0.04% (2) to find areas  0.04% (2) derive the formula  0.04% (2) out that the  0.04% (2) and it turns  0.04% (2) complete equation of  0.04% (2) c_0, c_1, c_2,  0.04% (2) what the formula  0.04% (2) the complete equation  0.04% (2) to discover these  0.04% (2) c_1, c_2, c_3  0.04% (2) of all, let’s  0.04% (2) demonstrating how one  0.04% (2) you will need  0.04% (2) x will be  0.04% (2) to find out  0.04% (2) a handy expression…  0.04% (2) of the equation  0.04% (2) this, what we’re  0.04% (2) going to be  0.04% (2) left with is…  0.04% (2) quickest sine rule  0.04% (2) to one another…  0.04% (2) multiply both sides  0.04% (2) by a handy  0.04% (2) can be found  0.04% (2) expression… if we  0.04% (2) we’re going to  0.04% (2) be left with  0.04% (2) kind of sums  0.04% (2) you should expect  0.04% (2) thanks for stopping  0.04% (2) the formula to  0.04% (2) we can say  0.04% (2) 5 x (51)  0.04% (2) 16, 2016 tiago  0.04% (2) the usual method  0.04% (2) the area of  0.04% (2) on how to  0.04% (2) with pythagoras’s equation  0.04% (2) 0 onwards quickly  0.04% (2) september 16, 2016  0.04% (2) demonstrating how to  0.04% (2) 27, 2016 tiago  0.04% (2) and formula. i’ll  0.04% (2) used to count  0.04% (2) used to add  0.04% (2) whereby n is  0.04% (2) you will notice  0.04% (2) an odd number.  0.04% (2) comment the other  0.04% (2) to the area  0.04% (2) the student handshake  0.04% (2) = 90 degrees  0.04% (2) but elegant way  0.04% (2) sin(a+b)=sinacosb+cosasinb (edexcel proof  0.04% (2) cah toa, trigonometry  0.04% (2) let me show  0.04% (2) i will have  0.04% (2) properties related to  0.04% (2) simple but elegant  0.04% (2) equal to the  0.04% (2) way to prove  0.04% (2) that sin(a+b)=sinacosb+cosasinb (edexcel  0.04% (2) squared, pythagorean theorem  0.04% (2) september 27, 2016  0.04% (2) tiago hands in  0.04% (2) look at this  0.04% (2) this means that:  0.04% (2) this formula is  0.04% (2) this question is  0.04% (2) as the one  0.04% (2) answer this question  0.04% (2) c), (a, d),  0.04% (2) (b, c), (b,  0.04% (2) mini question would  0.04% (2) 5 students in  0.04% (2) the same strategy  0.04% (2) we used to  0.04% (2) c (a, c).  0.04% (2) (a, c). a  0.04% (2) d (c, d).  0.04% (2) a pattern in  0.04% (2) to solve the  0.04% (2) the main question  0.04% (2) let’s look at  0.04% (2) that a pattern  0.04% (2) was able to  0.04% (2) d). b can  0.04% (2) with b (a,b).  0.04% (2) how you can  0.04% (2) find areas underneath  0.04% (2) we first have  0.04% (2) few experiments and  0.04% (2) that we can  0.04% (2) solve the main  0.04% (2) mini questions will  0.04% (2) one student in  0.04% (2) 2 students in  0.04% (2) {a, b, c,  0.04% (2) hands with one  0.04% (2) 3 students in  0.04% (2) (a,b). a can  0.04% (2) (a, b), (a,  0.04% (2) same strategy we  0.04% (2) used to answer  0.04% (2) variables a, b,  0.04% (2) cah toa statistics  0.04% (2) 