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Chocolate Bar Paradox

Chocolate Bar Paradox
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2019-09-29 05:01
Calculus
This example demonstrates the chocolate bar paradox, illustrating the concept of area preservation through geometric transformations. It involves core math concepts like area, rectangle, translation, angles, calculus, and similar triangles. The construction uses GeoGebra commands such as Polygon with objects like D, C, B, A, poly2, a, b, c, d, etc. Suitable for high school and above to explore geometric transformations and calculus applications.

GeoGebra Commands & Parameters

  1. Polygon(A, A + (4, 0), A + (4, 3), A + (0, 2)) → poly2, a, b, c, d
  2. Polygon(B, B + (0, 3), B + (-3, 3), B - (3, 0.75)) → poly3, e, f, g, h
  3. Polygon(D, D + (1, 0), D + (1, 1), D + (0, 1)) → poly5, m, n, p, q
  4. Polygon(C, C - (1, 0), C - (1, 3), C - (0, 2.75)) → poly4, i, j, k, l

AI Drawing Prompt Reference

Draw a rectangle and a similar but differently sized triangle, demonstrating geometric transformations that preserve area through translation and rotation, including multiple small rectangles and triangles to illustrate the concept of similar triangles and area calculation in calculus.
The prompt above was compiled from the original drawing commands and is for reference only.