Pythagorean Theorem Coursework

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Jaymin Patel 10Q                                                               Page  of

        

        

Pythagoras’ theorem states that a²+b²=c²                

As you can see, a is the longest side, b is the middle side and c is the longest side (hypotenuse). The point of this coursework is to find b when a is an odd number and all of the sides are positive integers. Then after that I will go looking when a is a positive number.

The numbers 3, 4 and 5 work in Pythagoras’ theorem,

3²+4²=5²

because        3²=3×3=9

                4²=4×4=16

                5²=5×5=25

and so                3²+4²=9+16=25=5²

The numbers 5, 12 and 13 also work,

5²+12²=13²

because        5²=5×5=25

                12²=12×12=144

                13²=13×13=169

and so                5²+12²=25+144=169=13²

The numbers 7, 24 and 25 also work,

                7²+24²=25²

because        7²=7×7=49

                24²=24×24=576

                25²=25×25=625

and so                7²+24²=49+576=625=25²

3, 4 and 5

Perimeter= 3+4+5=12

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Area= ½ ×3×4=6

5, 12 and 13

Perimeter= 5+12+13=30

Area= ½ ×5×12=30

7, 24 and 25

Perimeter= 7+24+25=56

Area= ½ ×7×24=84

From the first three terms I have realised that: -

  • a increases by 2 each time

  • a is equal to the formula ×2+1 from n

  • b is always even

  • c is always odd

  • c is always +1 of b

  • b=(a×n) + n

I have also added 2 more terms using what I think are my formulae.

Here are my formulas. They are formulas on how ...

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