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Net of a Pyramid by cemccourseware

Net of a Pyramid by cemccourseware
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2018-10-07 10:15
VectorSolid GeometryGeometric Construction
This example demonstrates the net of a pyramid. Key mathematical concepts include the structure of a pyramid in solid geometry. Using GeoGebra commands such as Intersect, Sequence, and Segment, the net of a pyramid can be constructed. Suitable for high school students studying solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Sequence(Rotate[(0, Apothem + SlantHeight), (i * α), A], i, 0, n) → NetEndPoints
  3. Sequence(Vector[Rotate[A + (0, 1, 0), (i * α), A] - A], i, 0, n - 1) → ApothemVectors
  4. Sequence((Element[ApothemVectors, i] * (Apothem + (SlantHeight * cos((k * θ))))) + (((0, 0, 1) * SlantHeight) * sin((k * θ))), i, 1, n) → apexSegments
  5. Sequence(Rotate[(0, radiusBase), (i * α) - α / 2, A], i, 0, n) → baseEndPoints
  6. Sequence(Polygon[Element[apexSegments, i], Element[baseEndPoints, i], Element[baseEndPoints, i + 1]], i, 1, n) → pyramidSegments
  7. Sequence(Polygon[Element[NetEndPoints, i], Element[baseEndPoints, i], Element[baseEndPoints, i + 1]], i, 1, n) → netSegments
  8. Segment((0, 0), (0, Apothem)) → apothemLineNet
  9. Segment((0, 0, 0), (0, 0, Height)) → HeightLine3D
  10. LaTeX("\text{\textbf{Question: }How do the number of sides in the base of a regular right pyramid, the\\height of the pyramid, and the apothem of the base relate to the net of the pyramid?}") → MainInstruc
  11. LaTeX("\text{\textbf{Instructions: }Move the sliders to change the number of sides in the base, the apothem,\\and the height. Move the Open-Closed slider to open and close the pyramid.}") → SpecInstruc
  12. Vector((15, 5), (1, Apothem / 2)) → apothemArrowNet
  13. LaTeX("Apothem") → apothemArrowLabelNet
  14. Vector((11, 4), (1, Apothem / 2)) → apothemArrow3D
  15. LaTeX("Apothem") → apothemArrowLabel3D
  16. LaTeX("Height") → heightArrowLabel3D
  17. Vector((6, 4, 10), (0.5, 0, Height)) → heightArrow3D

AI Drawing Prompt Reference

Draw an interactive regular pyramid with a regular polygon base and its net, including both 3D pyramid view and 2D net view. The graphics should show: a regular n-sided polygon base (adjustable n), with the pyramid apex extending upward from the base center, forming n isosceles triangles as lateral faces, the slant height as the perpendicular distance from base center to each lateral edge, and the height as the vertical distance from apex to base. The net should display the lateral faces arranged in a fan pattern around the central base polygon. Include sliders to control the number of base sides, slant height, and opening-closing degree, allowing smooth transition between net and closed pyramid states.
The prompt above was compiled from the original drawing commands and is for reference only.