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Value of π

Value of π
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2013-04-24 21:45
CircleTrigonometryGeometric Construction
In collections Trig
This example demonstrates the value of π. By constructing a circle and calculating the ratio of its circumference to its diameter, the definition of π is intuitively shown. Commands used include Circle, Intersect, and Rotate. Suitable for middle school and above students to learn about the properties of circles and the concept of π.

GeoGebra Commands & Parameters

  1. Circle(O, 3) → c
  2. OrthogonalLine(O, a) → b
  3. Intersect(c, b, 2) → A
  4. Rotate(b, (-((360 * ° / n))), O) → b'
  5. Intersect(c, b', 2) → B
  6. Polygon(B, A, n) → poly1, b_1, D, E, F, G, H, d, e, f, g, k, q, r, C
  7. Segment(A, O) → l
  8. Segment(O, B) → m
  9. OrthogonalLine(O, b_1) → p
  10. Intersect(p, b_1) → AB
  11. Angle(A, AB, O) → α
  12. Segment(O, AB) → j
  13. Angle(AB, O, A) → β
  14. Angle(B, O, AB) → γ
  15. Segment(A, AB) → h
  16. Segment(AB, B) → i

AI Drawing Prompt Reference

Draw a circle with radius 3, then draw a perpendicular line that intersects the circle at point A. Rotate this line around the center to find point B. Use A and B as two vertices to construct an n-sided polygon. Draw line segments OA and OB, then draw a perpendicular line to AB and find its intersection with AB. Measure the angles AOB, ABO, and BAO, and finally draw line segments OA, OB, and AB.
The prompt above was compiled from the original drawing commands and is for reference only.