Touch Pythagoras

The Pythagorean Theorem interactive including 6 proofs. Visual and algebra.

The Pythagorean Theorem Interactive: a^2 + b^2 = c^2

App :

change the lengths of the legs (dragging).

change the length of the hypotenuse with two fingers.

zoom (pinch zoom) and rotate the figure (dragging).

There are 6 ways to view the Pythagorean theorem.

- Unit surfaces.

- Two equivalent square containing the same surface.

- The square for each leg in the square of the hypotenuse (Euclid)

- Pingi - Dudeney proof.

- Da Vinci.

- Bhaskara reasoning.

Change the precision of the lengths. (In the contextual menu)

This application is also a small laboratory to investigate about the Pythagorean Theorem:

For example, you can experiment easily, looking for the exact solutions of the Pythagorean Theorem:

3² + 4² = 5² is not the only exact solution:

Below 21, there are 3 primitive triples:

3² + 4² = 5²

5² + 12² = 13²

6² + 8² = 10² (Not a true primitive result: Multiple of 3,4,5)

8² + 15² = 17²

9² + 12² = 15² (Not a true primitive result: Multiple of 3,4,5)

12² + 16² = 20² (Not a true primitive result: Multiple of 3,4,5)

Likewise it is also possible to find the solutions below 31 (11 solutions in all: but only 5 primitives)

Or solutions below 101 (52 solutions in all: but only 16 primitives)

More primitive pythagorean triples:

9² + 40² = 41²

11² + 60² = 61²

12² + 35² = 37²

13² + 84² = 85²

15² + 112² = 113²

16² + 63² = 65²

17² + 144² = 145²

19² + 180² = 181²

20² + 21² = 29²

20² + 99² = 101²

24² + 143² = 145²

28² + 45² = 53²

33² + 56² = 65²

36² + 77² = 85²

39² + 80² = 89²

44² + 117² = 125²

48² + 55² = 73²

51² + 140² = 149²

52² + 165² = 173²

57² + 176² = 185²

60² + 91² = 109²

65² + 72² = 97²

85² + 132² = 157²

88² + 105² = 137²

95² + 168² = 193²

104² + 153² = 185²

119² + 120² = 169²

133² + 156² = 205²

140² + 171² = 221²

Touch Pythagoras is a part of the collection Touch Math Apps