Mathematical Proof and Paradox [IB Maths Resources]

I always loved doing tricks like these on my friends!

IB Maths Resources from British International School Phuket

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 = ab
a2 – b2 = ab – b2
(a-b)(a+b) = b(a-b)
a+b = b (divide by a-b )
b+b = b (as a = b)
2b = b
2 = 1

Can you spot the step that causes the proof to be incorrect?

Another well known maths problem that appears to prove the impossible is the following:


This was created by magician Paul Curry – and is called Curry’s Paradox.  You can work out the areas of all the 4 different coloured shapes on both triangles, and yet by simply rearranging…

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