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

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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