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Beta Tauri Geometry Example

Beta Tauri Geometry Example
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2020-01-16 23:19
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction and properties of polygons, octahedra, centroids, midpoints, circles, points, lines, intersections, and line segments. Core mathematical concepts include geometric construction, symmetry, trigonometry, and volume calculation. Key GeoGebra commands used are Polygon, Octahedron, Centroid, Midpoint, Circle, Point, Line, Intersect, and Segment. Suitable for high school and above, for teaching and exploring geometric transformations, solid geometry, and analytical geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f_2, g, h, C
  2. Octahedron(poly1, true) → a, D, faceDEF, edgeAF, edgeCF, edgeAD, edgeDF, edgeBD, edgeBE, edgeDE, edgeCE, edgeEF, E, F, faceACF, faceADF, faceABD, faceBDE, faceBCE, faceCEF
  3. Polygon(E, D, B) → t1, b, e, d
  4. Polygon(E, B, C) → t2, c, e_1, b_1
  5. Centroid(t1) → G
  6. Centroid(t2) → H
  7. Midpoint(C, E) → I
  8. Midpoint(E, B) → J
  9. Midpoint(C, B) → K
  10. Circle(I, J, K) → k
  11. Midpoint(E, D) → L
  12. Midpoint(B, D) → M
  13. Circle(L, M, J) → p
  14. Point(k) → N
  15. Line(N, H) → i
  16. Intersect(i, k, 1) → O
  17. Segment(N, O) → j
  18. Point(p) → P
  19. Line(P, G) → l
  20. Intersect(l, p, 1) → Q
  21. Segment(P, Q) → m
  22. Segment(O, Q) → n
  23. Segment(O, P) → q
  24. Segment(O, G) → r
  25. Segment(N, Q) → s
  26. Segment(N, P) → t
  27. Segment(N, G) → f

AI Drawing Prompt Reference

Start with an equilateral triangle as a base, then construct a regular octahedron on it, whose six vertices form a symmetric 3D structure. Select three vertices to form two triangular faces, and find the centroid of each triangle. Take midpoints of three edges of the octahedron and draw a circle through them; then take midpoints of two other edges and one previous midpoint to draw another circle. Pick a point on each circle, connect it to the corresponding centroid, and find the intersection with the circle. Finally, connect these intersection points and the chosen points with line segments, creating a composite figure of triangles, octahedron, circles, centroids, midpoints, and segments.
The prompt above was compiled from the original drawing commands and is for reference only.