MathPlotAI Logo MathPlotAI

Constructing a Sphere

Constructing a Sphere
Loading the math board and drawing, please wait…
2016-03-11 01:30
VectorCoordinate GeometrySolid Geometry
This example demonstrates how to construct a sphere using GeoGebra. Key mathematical concepts include vectors and coordinate geometry. Commands such as Vector, Polygon, and Sequence are used to build the components of the sphere. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Vector(((1.1 * d) * W_x)) → u
  2. Vector(((1.1 * d) * W_y)) → v
  3. Vector(((1.1 * d) * W_z)) → w
  4. Polygon(((1.1 * d) * (W_x + W_y)), ((1.1 * d) * ((-W_x) + W_y)), ((1.1 * d) * ((-W_x) - W_y)), ((1.1 * d) * (W_x - W_y))) → poly1, g, h, i, j
  5. Sequence(CurveCartesian[x(((r * cos((0.157 * i))) * W_z) + ((r * sin((0.157 * i))) * ((cos((0.157 * j)) * W_x) + (sin((0.157 * j)) * W_y)))), y(((r * cos((0.157 * i))) * W_z) + ((r * sin((0.157 * i))) * ((cos((0.157 * j)) * W_x) + (sin((0.157 * j)) * W_y)))), i, 0, 20], j, 0, p) → list3
  6. Sequence(CurveCartesian[x(((sqrt(r^(2) - i^(2)) * cos((0.157 * j))) * W_x) + ((sqrt(r^(2) - i^(2)) * sin((0.157 * j))) * W_y) + (i * W_z)), y(((sqrt(r^(2) - i^(2)) * cos((0.157 * j))) * W_x) + ((sqrt(r^(2) - i^(2)) * sin((0.157 * j))) * W_y) + (i * W_z)), j, 0, p], i, 0, r, 1) → list1
  7. Sequence(CurveCartesian[x(((sqrt(r^(2) - i^(2)) * cos((0.157 * j))) * W_x) + ((sqrt(r^(2) - i^(2)) * sin((0.157 * j))) * W_y) - (i * W_z)), y(((sqrt(r^(2) - i^(2)) * cos((0.157 * j))) * W_x) + ((sqrt(r^(2) - i^(2)) * sin((0.157 * j))) * W_y) - (i * W_z)), j, 0, p], i, 0, r, 1) → list2

AI Drawing Prompt Reference

Draw a sphere by first creating three unit vectors u, v, and w, then constructing a quadrilateral poly1 using these vectors. Next, use a series of curves to draw the sphere's surface, including radial curves from the center to the sphere and latitude curves.
The prompt above was compiled from the original drawing commands and is for reference only.