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Pegasus Geometric Model Demonstration

Pegasus Geometric Model Demonstration
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2020-01-27 22:19
CirclePolygonSolid GeometryTransformationGeometric Construction
This example demonstrates the comprehensive construction and property展示 of geometric figures including polygons, circles, and transformations; Core math concepts involve centroids, circumcircles, incircles, geometric transformations (rotation), volume calculations, and symmetry; Construction highlights use of GeoGebra commands/objects like Circle, Point, Line, Intersect, Segment, Rotate, Angle, Polygon, Octahedron; Suitable for high school students and math enthusiasts for learning geometric constructions, transformations, and spatial reasoning.

GeoGebra Commands & Parameters

  1. Circle(A, a_2) → c
  2. Point(c) → B
  3. Line(A, B) → f_1
  4. Intersect(c, f_1, 2) → C
  5. Segment(B, C) → g
  6. Rotate(B, 90°, A) → B'
  7. Angle(B, A, B') → α
  8. Line(B', A) → h
  9. Intersect(c, h, 2) → D
  10. Segment(B', D) → i
  11. Point(Circle[A, d]) → E
  12. Segment(A, E) → j
  13. Segment(D, E) → k
  14. Segment(B, E) → l
  15. Segment(B', E) → m
  16. Segment(C, E) → n
  17. Polygon(C, E, 3) → poly1, f, p, q, F
  18. Polygon(D, E, 3) → poly2, r, s_1, t, G
  19. Polygon(E, B, 3) → poly3, b, e, g_1, H
  20. Polygon(E, B', 3) → poly4, h_1, i_1, j_1, I
  21. Octahedron(poly1, true) → s, J, faceJKL, edgeCL, edgeFL, edgeCJ, edgeJL, edgeEJ, edgeEK, edgeJK, edgeFK, edgeKL, K, L, faceCFL, faceCJL, faceCEJ, faceEJK, faceEFK, faceFKL
  22. Octahedron(poly2, true) → u, M, faceMNO, edgeDO, edgeGO, edgeDM, edgeMO, edgeEM, edgeEN, edgeMN, edgeGN, edgeNO, N, O, faceDGO, faceDMO, faceDEM, faceEMN, faceEGN, faceGNO
  23. Octahedron(poly3, true) → v, P, facePQR, edgeER, edgeHR, edgeEP, edgePR, edgeBP, edgeBQ, edgePQ, edgeHQ, edgeQR, Q, R, faceEHR, faceEPR, faceBEP, faceBPQ, faceBHQ, faceHQR
  24. Octahedron(poly4, true) → a, S, faceSTU, edgeEU, edgeIU, edgeES, edgeSU, edgeB'S, edgeB'T, edgeST, edgeIT, edgeTU, T, U, faceEIU, faceESU, faceB'ES, faceB'ST, faceB'IT, faceITU