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Interior Angles in a Regular Polygon

Interior Angles in a Regular Polygon
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2016-02-12 11:53
PolygonAngleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the relationships between the interior angles formed by the diagonals of a regular polygon. It involves core math concepts like polygons, angles, trigonometry, and geometric constructions. The construction uses commands such as Sequence for vertices, Polygon for the shape, Angle for measurement, and Slider for interactive exploration, making it suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Sequence((cos(((k * 2) * π / n)), sin(((k * 2) * π / n))), k, 1, n) → list1
  2. Polygon(list1) → poly1
  3. Sequence(Segment[P, Element[list1, i]], i, 1, n) → list2
  4. Angle(Element[list1, i], P, Element[list1, i + 1]) → β
  5. Polygon(P, Element[list1, 1], Element[list1, 2]) → poly3, j, p, l
  6. Polygon(P, Element[list1, i], Element[list1, i + 1]) → poly2, a, p_1, b
  7. Angle(Element[list1, 1], P, Element[list1, 2]) → δ
  8. Sequence(Angle[Element[list1, k], P, Element[list1, k + 1]], k, 1, i) → list4