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)
M 4 Triangles M 6 All previous and: Geometry in the plane, Pythagorean theorem M 7 All previous and: Quadrilateral properties Geometry All previous Right Triangles, Pythagorean theorem, Trigonometry Algebra Exponents Algebra II General Trigonometry
For more information about Pythagorean Theorem: Alexander Bogomolny: Cut the knot: #112 proofs of the Pythagorean Theorem: http://www.cut-the-knot.org/pythagoras/
1.1.5 Code 9 - minor improvement in contextual menu