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Adjustable Prism Extrusion: GM1-06-P2 Interactive Solid Geometry

Adjustable Prism Extrusion: GM1-06-P2 Interactive Solid Geometry
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2016-05-18 04:23
PolygonCoordinate GeometrySolid GeometryGeometric ConstructionSlider Animation
This example demonstrates an adjustable prism and its extrusion process, allowing users to dynamically change the height and base shape by dragging points or using sliders, thereby visualizing the construction of a 3D solid. Core mathematical concepts include the definition of a prism, relationships between bases and lateral faces, parallelism and perpendicularity in space, and coordinate/integer point labeling. The construction uses GeoGebra commands: Point, Polygon, LineBisector, Intersect, Segment, Prism, Circle, and Text. Key objects include vertices A, B, C, D, E, F, base polygon poly1, lateral faces such as faceABJheight, faceBCKJ, faceCDLK, faceDEML, faceEFNM, faceFHON, and the height segment. This is suitable for middle and high school solid geometry lessons, helping students understand prism composition, the effect of parameter changes on volume and surface area, and exploring coordinate geometry with integer points.

GeoGebra Commands & Parameters

  1. Point(Circle[A, sqrt(8 - (8 * cos((2 * π / Sides))))]) → B
  2. Polygon(A, B, Sides) → poly1, g, D, E, F, H_1, I, h, i, j, k, l, q, r, C
  3. LineBisector(h) → p
  4. Segment(A, B) → f
  5. LineBisector(f) → m
  6. Intersect(m, p) → G
  7. Segment((x(G), y(G), 0), (x(G), y(G), 5)) → centersegment
  8. Point(centersegment) → H
  9. Segment((x(A), y(A), 0.01), (x(A), y(A), z(H))) → s
  10. Point(s) → height
  11. Prism(poly1, height) → a, J, faceCDLK, faceDEML, faceEFNM, faceFHON, faceHIPO, faceAheightPI, faceheightJKLMNOP, edgeAheight, edgeBJ, edgeCK, K, edgeDL, edgeEM, edgeFN, edgeHO, edgeIP, edgeheightJ, edgeJK, edgeKL, edgeLM, edgeMN, L, edgeNO, edgeOP, edgeheightP, M, N, O, P, faceABJheight, faceBCKJ
  12. Circle(Q, 0.25) → RadioOutline1
  13. Circle(Q1, 0.25) → RadioOutline1_1
  14. Circle(Q2, 0.25) → RadioOutline1_2
  15. Circle(Q3, 0.25) → RadioOutline1_3
  16. Circle(Q4, 0.25) → RadioOutline1_4
  17. Circle(Q5, 0.25) → RadioOutline1_5
  18. Text("3 sides") → textside1
  19. Text("4 sides") → textside2
  20. Text("5 sides") → textside3
  21. Text("6 sides") → textside4
  22. Text("7 sides") → textside5
  23. Text("8 sides") → textside6
  24. Circle(Q, 0.2) → Radio1
  25. Circle(Q_1, 0.2) → Radio2
  26. Circle(Q_2, 0.2) → Radio3
  27. Circle(Q_3, 0.2) → Radio4
  28. Circle(Q_4, 0.2) → Radio5
  29. Circle(Q_5, 0.2) → Radio6

AI Drawing Prompt Reference

Draw an adjustable prism with changeable height and base shape. First, create a regular polygon as the base. Then, adjust the number of sides and size of the polygon by dragging points or using sliders. Next, generate the prism with the specified base and height, showing the lateral and top faces. Finally, add labels to indicate the relationships between the lateral and base faces.
The prompt above was compiled from the original drawing commands and is for reference only.