IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
Proving Pythagoras Like Einstein? There are many ways to prove Pythagoras' theorem - Einstein reputedly used the sketch above to prove this using similar triangles. To keep in the spirit of discovery I also just took this diagram as a starting point and tried to prove this myself, (though Einstein's version turns out to be... Continue Reading →
A geometric proof for the Arithmetic and Geometric Mean There is more than one way to define the mean of a number. The arithmetic mean is the mean we learn at secondary school - for 2 numbers a and b it is: (a + b) /2. The geometric mean on the other hand is defined... Continue Reading →
Non Euclidean Geometry - An Introduction It wouldn't be an exaggeration to describe the development of non-Euclidean geometry in the 19th Century as one of the most profound mathematical achievements of the last 2000 years. Ever since Euclid (c. 330-275BC) included in his geometrical proofs an assumption (postulate) about parallel lines, mathematicians had been trying... Continue Reading →
http://www.youtube.com/watch?v=w-I6XTVZXww Unbelievable: 1+2+3+4.... = -1/12 ? The above video by the excellent team at Numberphile has caused a bit of an internet stir - by providing a proof that 1+2+3+4+5+... = -1/12 It's well worth watching as an example of what proof means - if something is proved which we "know" is wrong, then should... Continue Reading →
Fermat's Theorem on the sum of two squares Not as famous as Fermat's Last Theorem (which baffled mathematicians for centuries), Fermat's Theorem on the sum of two squares is another of the French mathematician's theorems. Fermat asserted that all odd prime numbers p of the form 4n + 1 can be expressed as: where x... Continue Reading →
Divisibility tests allow us to calculate whether a number can be divided by another number. For example, can 354 be divided by 3? Can 247,742 be divided by 11? So what are the rules behind divisibility tests, and more interestingly, how can we prove them? Divisibility rule for 3 The most well known divisibility rule... Continue Reading →
https://www.youtube.com/watch?v=t8XMeocLflc This classic clip "proves" how 25/5 = 14, and does it three different ways. Maths is a powerful method for providing proof - but we need to be careful that each step is based on correct assumptions. One of the most well known fake proofs is as follows: let a = b Then a2... Continue Reading →