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Constructing a Sectorial Prism

Constructing a Sectorial Prism
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2018-10-23 20:19
PolygonAngleVectorSolid GeometryGeometric Construction
This example demonstrates the construction of a sectorial prism by rotating a sector, showcasing its geometric properties and cross-section relationships. Key mathematical concepts include prism, sector, rotation, vector, angle, polygon construction, intersection calculation, etc. The construction utilizes GeoGebra commands and objects such as Intersect, Point, Surface, CircleSector, Angle, Polygon, Vector, Rotate, and Translate. It is suitable for high school solid geometry teaching, helping students understand the construction of rotational solids and spatial geometric relationships.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Surface((4 * cos(α)), (4 * sin(α)), h, α, 0°, (5 * π / 3), h, 0, 3) → a
  4. Point(xAxis) → D
  5. CircleSector(A, D, E) → c
  6. Angle(D, A, E) → α
  7. Polygon((0, 0, 0), (2, -3.5, 0), (2, -3.5, 3), (0, 0, 3)) → q1, f, g, h, i
  8. Vector((0, 0, 0), (0, 0, 3)) → u
  9. Rotate(q1, (-(60°)), i) → q1'
  10. Translate(c, u) → c'