'The Man Who Loved Only numbers'

by Paul Hoffman]]>

AND SO DO I

Eeek!

]]>Here's something weird that I found out whilst doing some coursework: if one of the sides is one unit less than the hypotenuse, the other side has a length equal to the square root of the other two sides' sum.

e.g. 3²+4²=5² --> 3²=4+5

hi

do u like reading my fav boo is harry potter

]]>The difference between 3² and 4² is the X's below:

OOOX

OOOX

OOOX

XXXX

So, how many X's do we need to add to grow the square from 3x3 to 4x4? Answer: 3+3+1

Likewise, to go from a 4x4 to 5x5 needs:

OOOOX

OOOOX

OOOOX

OOOOX

XXXXX

How many X's? 4+4+1

Hehe

]]>A Pythagorean triple is a set of three whole numbers , such that one number squared added to another number squared equals the third number squared. Euclid could prove that there are an infinite number of such Pythagorean triples.

Euclid's proof begins with the observation that the difference between successive square numbers is always an odd number.

4 - 1 = 3, 9 - 4 = 5, 16 - 9 = 7, 25 - 16 = 9, 36 - 25 = 11, 49 - 36 = 13 etc.

For a Right-Angled Triangle, if you take the length of the longest side (the hypotenuse) and square it (multiply it by itself) then that will be the same value as adding up the squares of the other two sides:

|\

A | \ C

| \

|___\

B

A²+B²=C²

Try it with any size triangle, so long as there is a right angle in it!

]]>5² = 12+13 YES! ... how interesting. I wonder why.

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