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Pythagorean Theorem Demonstration 63 cm

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0.2mm layer, 2 walls, 15% infill
0.2mm layer, 2 walls, 15% infill
Designer
35 min
1 plate

0.2mm layer, 2 walls, 15% infill, dimensions 12,5 cm
0.2mm layer, 2 walls, 15% infill, dimensions 12,5 cm
Designer
1.6 h
2 plates

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PYTHAGOREAN THEOREM DEMONSTRATION

 

The Pythagorean theorem is a theorem of Euclidean geometry that establishes a fundamental relationship between the sides of a right-angled triangle.

This is the most elegant demonstration I have ever seen, the square built on the hypotenuse divided in such a way as to form the two triangles of the legs, leaving the empty space of the right-angled triangle.

By printing the pieces twice, they can then be arranged in the configuration that we all know.

 

Applications of the Theorem
The Pythagorean theorem has a wide range of applications in various fields of mathematics, geometry and physics. For example, it is used to calculate distances between points in space. In trigonometry, it underlies the definitions of the sine, cosine and tangent functions.

 

Statement
In every right-angled triangle the area of the square constructed on the hypotenuse is equal to the sum of the areas of the squares constructed on the legs.

 

Given a right-angled triangle with sides A, B and C, and indicating with C its hypotenuse and with A and B its legs, the theorem is expressed by the equation:

 

   A² + B² = C²

 

The origin of the Pythagorean theorem
Legend has it that Pythagoras formulated his theorem while waiting for an audience with the tyrant Polycrates in the palace of Samos, observing the square tiles on the floor of the waiting room. A tile was broken diagonally, forming two isosceles triangles. Pythagoras imagined building a square on the diagonal of the half-tile and noticed that its surface area was perfectly equal to the sum of the areas of the squares built on the other two sides of the right-angled triangle. This also demonstrates that great insights often derive from small facts that are in plain sight. A broken tile or an apple falling from a tree.

 

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