Generator of Pythagorean Triples

set of triples

1

This is a Pythagorean triple: {3,4,5}

It is easy to check that:

2

3

+

2

4

=

2

5

This is the perimeter of the triangle: 12

This is the area of the triangle: 6

This is another Pythagorean triple:{4,3,5}

It is easy to check that:

2

4

+

2

3

=

2

5

This is the perimeter of the triangle: 12

This is the area of the triangle: 6

This is another Pythagorean triple: = {12,5,13}

It is easy to check that:

2

12

+

2

5

=

2

13

This is the perimeter of the triangle: 30

This is the area of the triangle: 30

This is another Pythagorean triple: {48,55,73}

It is easy to check that:

2

48

+

2

55

=

2

73

This is the perimeter of the triangle: 176

This is the area of the triangle: 1320

This is another Pythagorean triple = {60,91,109}

It is easy to check that:

2

60

+

2

91

=

2

109

This is the perimeter of the triangle: 260

This is the area of the triangle: 2730

A Pythagorean triple

{a,b,c}

consists of three positive integers

a

,

b

,

c

, that satisfy

2

a

+

2

b

=

2

c

.

This Demonstration can generate 5000 Pythagorean triples. It calculates five triples at a time, together with the perimeter and area of the corresponding Pythagorean triangle with sides

a

and

b

and hypotenuse

c

.