3477 Words14 Pages

Investigating Pythagoras
Introduction
============
[IMAGE]For this piece of work I am investigating Pythagoras.
Pythagoras was a Greek mathematician. Pythagoras lived on the island
of Samos and was born around 569BC. He did not write anything but he
is regarded as one of the world's most important characters in maths.
His most famous theorem is named after him and is called the
Pythagoras Theorem. It is basically aÂ²+bÂ²=cÂ². This is what the
coursework is based on.
I am going to look at the patterns, which surround this theorem and
look at the different sequences that can be formed.
The coursework
The numbers 3, 4 and 5 satisfy the condition 3Â²+4Â²=5Â² because
3Â²=3x3=9
4Â²=4x4=16
5Â²=5x5=25
And so
3Â²+4Â²=9+16=25=5Â²
I will now check that the following sets of numbers also satisfy the
similar condition of (smallest number) Â²+(middle number) Â²=(largest
number) Â²
a) 5, 12, 13
5Â²=5x5=25
12Â²=12x12=144
25+144=169
âˆš169 = 13
This satisfies the condition as
5Â²+12Â²=25+144=169=13Â²
b) 7, 24, 25
7Â²=7x7=49
24Â²=24x24=576
49+576=625
âˆš625=25
This satisfies the condition as
7Â²+24Â²=49+576=625=25Â²
The numbers 3,4 and 5 can be the lengths - in appropriate units - of
the side of a right-angled triangle.
[IMAGE]
5
3
[IMAGE]
The perimeter and area of this triangle are:
Perimeter = 3+4+5=12 units
Area = Â½x3x4=6 units Â²
[IMAGE]
The numbers 5,12,13 can also be the lengths - in appropriate units -
of a right-angled triangle.
[IMAGE]
Perimeter = 5+12+13=30
Area=Â½x5x12=30
[IMAGE] This is also true for the numbers 7,24,25
[IMAGE]
Perimeter = 7+24+25=56
Area=Â½x7x24=84
I have put these results into a table to see if I can work out any
patterns.
Length of shortest side
Length of middle side
Length of longest side
Perimeter

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