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History
The Pythagorean theorem is named after Pythagoras - a Greek mathematician. The
theorem states that:
| In any right triangle, the area of the
square whose side is the hypotenuse is equal to the sum of areas of the
squares whose sides are the two legs. |
It is still unknown who found this theorem for the first time.
Some people think it was discovered several times independently by various
scientists. Whatever the truth is, the Pythagorean theorem may have more known
proofs than any other theorem. Currently they are several hundreds proofs.
Education
This Elica application implements an interactive visual proof of the theorem.
The proof is presented in 7 slides. Students can go the the next or the
previous slide at any time. To view the proof with various initial
configurations the first slide provides a way for the student to drag a
parametrization point . The proof displayed in the other slides is
automatically synchronized. The parametrization is available in all slides. The
proof can be traversed in reversed order - starting from the last slide and
going towards the first one.
The game is distributed with its Elica Logo source. It can be
used to demostrate how to create composite dynamic objects, how to react to to
mouse, how to arrange objects in 3D space and then to fly through the scene.
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Understand one of the many proofs of
the Pythagorean theorem. Visit slides from the first to the last.
Try the validity of the proof when
you change the initial right-triangle.
Change the triangle at any stage of
the proof and inspect how this affects the geometrical construction.
Traverse the proof in reversed order
- form the last to the first slide. Try to figure out whether the reversed
proof is a proof too.
Learn how to build interactive
geomet-rical models to visualize famous theorems and how to fly through these
models.
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