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Net of Pyramid

Net of Pyramid
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2020-04-15 21:11
PolygonVectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the net of a pyramid and its fundamental properties. It involves core mathematical concepts such as polygons, triangles, vectors, coordinate geometry, and solid geometry. The construction utilizes GeoGebra commands and objects like Sequence, Polygon, Line, Point, Segment, Vector, LineBisector, Intersect, UnitVector, and Circle as outlined in the construction summary. It is suitable for high school students learning solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[A, ((360 * ° / n) * k), O], k, 0, n - 1, 1) → Vertices
  2. Polygon(Vertices) → Polygon
  3. Line(O, zAxis) → a
  4. Point(a) → V
  5. Segment(O, V) → Height
  6. Segment(A, V) → SlantEdge
  7. Vector((0, 0, 1)) → Z
  8. LineBisector(Element[Vertices, 1], Element[Vertices, 2]) → ReferencePerpendicularBisector
  9. Intersect(ReferencePerpendicularBisector, Line[Element[Vertices, 1], Element[Vertices, 2]]) → ReferenceIntersectionPoint
  10. Vector(O, ReferenceIntersectionPoint) → ReferenceVector
  11. UnitVector(ReferenceVector) → ReferenceUnitVector
  12. Sequence(Vector[Rotate[ReferenceUnitVector, ((360 * ° / n) * k), O]], k, 0, n - 1, 1) → ReferenceAllUnitVector
  13. Circle(Element[Vertices, 1], SlantEdge) → c
  14. Circle(Element[Vertices, 2], SlantEdge) → d
  15. Intersect(c, d) → B, C, ,
  16. Segment(O, C) → FlattenLength
  17. Sequence(O + ((FlattenLength * cos(angle)) * Element[ReferenceAllUnitVector, k]) + ((Height * sin(angle)) * Z), k, 1, n, 1) → AllVertices
  18. Polygon(Element[Vertices, 1], Element[AllVertices, 1], Element[Vertices, 2]) → poly1, b, e, f
  19. Polygon(Element[Vertices, 2], Element[AllVertices, 2], Element[Vertices, 3]) → poly2, g, h, i
  20. Sequence(Polygon[Element[Vertices, k], Element[AllVertices, k], Element[Vertices, k + 1]], k, 1, n - 1, 1) → AllTriangles
  21. Polygon(Element[Vertices, n], Element[AllVertices, n], Element[Vertices, 1]) → FinalTriangle, j, k, l

AI Drawing Prompt Reference

Draw the net of a pyramid, including the base polygon and triangular faces. Start by drawing the base polygon, then draw a height line from the apex to the center of the base. Next, draw circles centered at the base center with radii equal to the slant edges, intersecting at points that become the vertices of the triangular faces. Finally, connect these triangular faces to the base polygon to form the complete net.
The prompt above was compiled from the original drawing commands and is for reference only.