MathPlotAI Logo MathPlotAI

Regular Polygons (with Limits)

Regular Polygons (with Limits)
Loading the math board and drawing, please wait…
2019-04-15 07:34
CirclePolygonLimit
This example demonstrates the construction of regular polygons and their relationship with circles. Key concepts include regular polygons, limits, and pi. Using GeoGebra commands like Sequence, Element, and Circle, the example dynamically shows the side lengths, angles, and radii of regular polygons. Suitable for high school math education, helping students understand the geometric relationship between regular polygons and circles.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[A + (r, 0), ((k * 2) * π / n), A], k, 0, n) → pointList1
  2. Sequence(Segment[Element[pointList1, k], Element[pointList1, k + 1]], k, 1, n) → segList
  3. Sequence(Midpoint[Element[segList, k]], k, 1, n) → midPtList
  4. Sequence(Segment[A, Element[midPtList, k]], k, 1, n) → apothemList
  5. Element(apothemList, 1) → radius_2
  6. Circle(A, radius_2) → circle_2
  7. Circumference(circle_2) → circum_2
  8. Segment(A, A + (r, 0)) → radius_1
  9. Sequence(Rotate[radius_1, (360° * k / n), A], k, 1, n) → radiiList
  10. Circle(A, r) → circle_1
  11. Sequence(Sector[circle_1, Element[pointList1, k], Element[pointList1, k + 1]], k, 1, n) → sectorList
  12. Sequence(((Element[segList, k] * Element[apothemList, k])) / 2, k, 1, n) → apothArea
  13. Sequence(Element[sectorList, k] - Element[apothArea, k], k, 1, n) → segmentArea
  14. Sum(segmentArea, n) → valueSegAreaTotal
  15. Sum(apothArea, n) → areaPolygon
  16. Sequence(Arc[circle_1, Element[pointList1, k], Element[pointList1, k + 1]], k, 1, n) → arclist
  17. Area(circle_1) → areaCircle_1
  18. Circumference(circle_1) → circum_1
  19. If(n < 13, Element[polyList, n - 2], n + Element[polyList, 11]) → showPolyName
  20. Textfield(n) → inputBox1
  21. Area(circle_2) → areaCircle_2
  22. TableText({{"Regular " + showPolyName, TableText[{{"No.Sides", n}, {"Area", areaPolygon}, {"Perimeter", perimeterPoly}}, "c|111_"]}}, "vc_|11") → polyText
  23. TableText({{"Circle_1 A circumscribed", TableText[{{"Radius", r}, {"Area", areaCircle_1}, {"Circumference", circum_1}}, "c|111_"]}}, "vc_|11") → circle_1Text
  24. TableText({{"Shaded Space", TableText[{{"Area", valueSegAreaTotal}, {"% of Circle", (ratioCircleSegment2Circle * 100) + "\%"}}, "c|11_"]}}, "vc_|11|") → shadeText
  25. TableText({{"White Space", TableText[{{"Area", areaPolygon}, {"% of Circle", (100 * ratioPolyArea2Circle_1) + "\%"}}, "c|11_"]}}, "vc_|11|") → whiteText
  26. TableText({{"Circle_2 A circumscribed", TableText[{{"Radius", radius_2}, {"Area", areaCircle_2}, {"Circumference", circum_2}}, "c|111_"]}}, "vc_|11") → circle_2Text
  27. First(radiiList) → radius_f
  28. First(apothemList) → apothem_f
  29. TableText({{"Central Triangle A", TableText[{{"Chord", Element[segList, 1]}, {"Apothem", Element[apothemList, 1]}, {"Area", Element[apothArea, 1]}}, "c|111_"]}}, "vc_|11") → trianText

AI Drawing Prompt Reference

Draw a regular polygon with the number of sides specified in the input box, along with its circumscribed and inscribed circles. Show the side length, angles, and radius of the regular polygon, and their relationships with the circumscribed and inscribed circles. Calculate and display the area, perimeter, and the areas and circumferences of the circumscribed and inscribed circles.
The prompt above was compiled from the original drawing commands and is for reference only.