Touch Pythagoras

Açıklaması Touch Pythagoras

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
More about this: Pythagorean triples: http://en.wikipedia.org/wiki/Pythagorean_triples
Touch Math Apps:
http://www.nummolt.com
MathTools classification: http://mathforum.org/mathtools/tool/206418/
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/