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Cutting in Equal Parts

Cutting in Equal Parts
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2017-07-22 15:05
CircleFunctionTransformationGeometric ConstructionSlider Animation
In collections Fractions الكسور
This example demonstrates the process of dividing a circle or shape into equal parts. It involves core math concepts like equal division, geometric transformations, ratios, and function graphing. Construction highlights include using GeoGebra commands such as Point, Circle, Rotate, CircleSector, and Translate. Suitable for high school mathematics teaching on plane geometry division, transformations, and function applications.

GeoGebra Commands & Parameters

  1. Point(yAxis) → O
  2. Circle(O, 3) → c
  3. Point(c) → A
  4. Rotate(A, 90°, O) → A'
  5. Rotate(A', 90°, O) → A''
  6. Rotate(A'', 90°, O) → A'''
  7. CircleSector(O, A, A') → s1
  8. CircleSector(O, A', A'') → s2
  9. CircleSector(O, A'', A''') → s3
  10. CircleSector(O, A''', A) → s4
  11. Translate(Rotate[s2, (((-a) * 45))°, O], Vector[(a * Vector[A, (-5, -8)])]) → s2'
  12. Translate(Rotate[s3, (((-a) * 135))°, O], Vector[(a * Vector[A, (0, -8)])]) → s3'
  13. Translate(Rotate[s4, ((a * 135))°, O], Vector[(a * Vector[A, (5, -8)])]) → s4'
  14. Translate(Rotate[s1, ((a * 45))°, O], Vector[(a * Vector[A, (10, -8)])]) → s1'

AI Drawing Prompt Reference

Draw a circle centered at the origin with a radius of 3, then select four points A, A', A'', and A''' on the circle and rotate each 90 degrees around the origin to get A', A'', and A'''. Draw four sectors with 90-degree angles. Finally, rotate the second sector -45 degrees, the third sector -135 degrees, the fourth sector 135 degrees, and the first sector 45 degrees, then translate them to specific positions.
The prompt above was compiled from the original drawing commands and is for reference only.