Friday, 20 March 2015

We'll give you any number with just four squares

Pierre Fermat, who lived in Toulouse, wrote in 1638 that any number can be made by any one of these ways:

1. Add three triangle numbers.

These are the triangle numbers:
2. Add four square numbers.
These are the square numbers
49   36   25   16   9   4   1   0
3. Add five pentagonal numbers.
 These are the pentagonal numbers:
 4. Add six hexagonal numbers.
These are the hexagonal numbers:

We had a go at the easiest one: making lots of numbers with four square numbers. We all picked a number, and then thought hard about which combination of squares would make it (Zero is a square number too.)


  1. In my house I have done three samples:
    - 51= 49+1+1+0
    - 73=36+36+1+0
    - 96=64+16+16+0
    I had lots of fun

  2. Well done Cristina! That's three we hadn't done! I thought we'd maybe do some more of these this week as a class too!