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Ryan Morgan Conjecture

Ryan Morgan Conjecture
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2022-05-02 00:06
TrianglePolygonGeometric Construction
This example explores a geometrical conjecture discovered by a 15-year-old boy. It involves triangles, ratios, reflections, and polygons. Key GeoGebra commands used include Polygon, Sequence, and Intersect. Suitable for middle school and above students to learn geometric construction and explore mathematical conjectures.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Sequence(Segment[A, B + (k / n * (C - B))], k, 1, n - 1) → l1, {3.4293249166765465, 3.1885633480941236}
  3. Sequence(Segment[B, C + (k / n * (A - C))], k, 1, n - 1) → l2, {4.505821602878253, 4.253816162193139}
  4. Sequence(Segment[C, A + (k / n * (B - A))], k, 1, n - 1) → l3, {3.7210299000219274, 4.200818140721563}
  5. Intersect(l1(n1), l2(n2)) → D
  6. Intersect(l2(n1), l3(n2)) → E
  7. Intersect(l1(n1), l3(n2)) → F
  8. Intersect(l2(n1), l1(n2)) → G
  9. Intersect(l2(n2), l3(n1)) → H
  10. Intersect(l1(n2), l3(n1)) → I
  11. Polygon(G, I, H, D, F, E) → poly1, g, i, h, d, f, e

AI Drawing Prompt Reference

Draw a triangle and construct three line segments on each side, extending from the vertices to the division points on the opposite sides. Find all intersections of these segments and connect them to form a hexagon. The final image should include a triangle with a hexagon inscribed within it, illustrating a geometric construction relationship.
The prompt above was compiled from the original drawing commands and is for reference only.