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Product of distances of n-gon inscribed in unit circle

Product of distances of n-gon inscribed in unit circle
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2015-08-04 13:45
CirclePolygonGeometric Construction
This example demonstrates the calculation of the product of distances from one vertex to all other vertices of a regular n-gon inscribed in a unit circle. Key mathematical concepts include distance formulas in geometry, trigonometric properties of regular polygons, and coordinate representation on the unit circle. Construction involves GeoGebra commands such as Circle, Point, Sequence, and Product to create the figure and compute the product. Suitable for high school students or college students in geometry and trigonometry studies, useful for math competitions or classroom demonstrations.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → C
  3. Segment(A, C) → a
  4. Sequence(Rotate[C, ((i * 2) * π / n), A], i, 0, n) → list1
  5. Sequence(Segment[Element[list1, i], Element[list1, i + 1]], i, 1, n) → list2
  6. Sequence(Segment[C, Element[list1, i + 1]], i, 1, n - 1) → BlueSegments
  7. Product(BlueSegments) → ProductOfBlueSegments
  8. LaTeX(BlueSegments, true, true) → text1
  9. Point(c) → D
  10. Segment(A, D) → d
  11. Text(Sequence[(Element[BlueSegments, i] * x), i, 1, n - 1]) → text2
  12. LaTeX(ProductOfBlueSegments, true, true) → text3
  13. Sequence(Segment[C, Element[list1, i + 1]], i, 1, b) → list3
  14. Product(list3) → ProductOfFirstBBlueSegments

AI Drawing Prompt Reference

Draw a regular n-gon inscribed in a unit circle and plot the distances from one vertex to all other vertices, then calculate the product of these distances. Use blue lines to represent the distances and label the product and the formulas for each distance next to the diagram.
The prompt above was compiled from the original drawing commands and is for reference only.