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GeoGebra Geometric Construction: Intersection of Polygons and Circles

GeoGebra Geometric Construction: Intersection of Polygons and Circles
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2023-03-14 04:24
CirclePolygonGeometric Construction
In collections geometriadinamica.es
This example demonstrates geometric construction in GeoGebra, showing the intersection of polygons and circles. Key mathematical concepts include geometric construction, properties of circles, and vertex positioning of polygons. Construction involves using commands like Segment, Point, OrthogonalLine, Circle, Intersect, and objects such as Q2, Q1, p1, P1. Suitable for middle or high school mathematics education to understand geometric relationships and construction techniques.

GeoGebra Commands & Parameters

  1. Segment(Q1, Q2) → p1
  2. Point(p1) → P1
  3. Segment(P1, Q2) → p3
  4. Point(p3) → P2
  5. Segment(Q5, Q6) → p5
  6. Point(p5) → P5
  7. OrthogonalLine(C, xAxis) → zz2
  8. Circle(C, 0.62) → zz0
  9. Intersect(zz0, zz2, 1) → ZZ4
  10. Intersect(zz0, zz2, 2) → ZZ3
  11. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  12. Point(zElipse2) → Z
  13. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  14. Angle(ZZ8, C, Z) → zAngInc
  15. OrthogonalLine(C, yAxis) → zz1
  16. Intersect(zz0, zz1, 2) → ZZ2
  17. Intersect(zz0, zz1, 1) → ZZ1
  18. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  19. Point(zElipse1) → XY
  20. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  21. Angle(ZZ6, C, XY) → zAngRot
  22. Segment(Q3, Q4) → p2
  23. Point(p2) → P3
  24. Segment(P3, Q4) → p4
  25. Point(p4) → P4
  26. Segment(ZZ5, ZZ6) → zz4
  27. Segment(ZZ7, ZZ8) → zz3
  28. Intersect(zElipse2, zElipse1, 1) → zPunto1
  29. Intersect(zElipse2, zElipse1, 4) → zPunto2
  30. Segment(zPunto1, zPunto2) → zSeg2
  31. CurveCartesian((r / 2 * ((((a + (b * sin((((c * u) * 2) * 3.14159)))) * cos(α)) * sin(zAngRot)) + (((a + (b * sin((((c * u) * 2) * 3.14159)))) * sin(α)) * cos(zAngRot)))), (r / 2 * (((((-(a + (b * sin((((c * u) * 2) * 3.14159))))) * cos(α)) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (b * sin((((c * u) * 2) * 3.14159)))) * sin(α)) * sin(zAngRot)) * sin(zAngInc)) + (u * cos(zAngInc)))) - 6, u, u1, u2) → curva2
  32. Sequence(CurveCartesian[(r / 2 * ((((a + (b * sin((((c * u) * 2) * 3.14159)))) * cos(v)) * sin(zAngRot)) + (((a + (b * sin((((c * u) * 2) * 3.14159)))) * sin(v)) * cos(zAngRot)))), (r / 2 * (((((-(a + (b * sin((((c * u) * 2) * 3.14159))))) * cos(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (b * sin((((c * u) * 2) * 3.14159)))) * sin(v)) * sin(zAngRot)) * sin(zAngInc)) + (u * cos(zAngInc)))) - 6, v, v1, v2], u, u1, u2, paso) → list2
  33. CurveCartesian((r / 2 * ((((a + (b * sin((((c * β) * 2) * 3.14159)))) * cos(v)) * sin(zAngRot)) + (((a + (b * sin((((c * β) * 2) * 3.14159)))) * sin(v)) * cos(zAngRot)))), (r / 2 * (((((-(a + (b * sin((((c * β) * 2) * 3.14159))))) * cos(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (b * sin((((c * β) * 2) * 3.14159)))) * sin(v)) * sin(zAngRot)) * sin(zAngInc)) + (β * cos(zAngInc)))) - 6, v, v1, v2) → a1
  34. CurveCartesian((r / 2 * ((((a + (b * sin((((c * 4.5) * 2) * 3.14159)))) * cos(v)) * sin(zAngRot)) + (((a + (b * sin((((c * 4.5) * 2) * 3.14159)))) * sin(v)) * cos(zAngRot)))), (r / 2 * (((((-(a + (b * sin((((c * 4.5) * 2) * 3.14159))))) * cos(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (b * sin((((c * 4.5) * 2) * 3.14159)))) * sin(v)) * sin(zAngRot)) * sin(zAngInc)) + (4.5 * cos(zAngInc)))) - 6, v, v1, v2) → curva1
  35. Sequence(CurveCartesian[(r / 2 * ((((a + (b * sin((((c * u) * 2) * 3.14159)))) * cos(v)) * sin(zAngRot)) + (((a + (b * sin((((c * u) * 2) * 3.14159)))) * sin(v)) * cos(zAngRot)))), (r / 2 * (((((-(a + (b * sin((((c * u) * 2) * 3.14159))))) * cos(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (b * sin((((c * u) * 2) * 3.14159)))) * sin(v)) * sin(zAngRot)) * sin(zAngInc)) + (u * cos(zAngInc)))) - 6, u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a geometric construction showing the intersection of polygons and circles, highlighting polygon vertex positioning and circle properties. Start by drawing a line segment and creating points on it to form a polygon. Then, draw a circle centered at a point and find its intersections with perpendicular lines to the coordinate axes. Use these intersection points to draw two ellipses, and find their intersections with the lines. Finally, connect points on the ellipses and draw a curve connecting these points to create a complex geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.