MathPlotAI Logo MathPlotAI

Sphere Investigation

Sphere Investigation
Loading the math board and drawing, please wait…
2016-12-17 00:57
TrigonometryCoordinate GeometrySolid GeometryCalculusOptimization
In collections CCSS High School: Geometry (Circle equations) CCSS High School: Geometry Circle Equations
This example dynamically illustrates the equation of a sphere in 3D space, covering core math concepts like sphere equations, surfaces, arithmetic operations, optimization problems, perimeter, differential equations, and the unit circle. It utilizes GeoGebra commands/objects such as OrthogonalLine, Intersect, Polygon, PointIn, Sphere, Circle, Angle, Dilate, Segment, and Distance. Suitable for high school students and math enthusiasts studying solid geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. OrthogonalLine(C, xOyPlane) → g
  2. Intersect(g, xOyPlane) → D
  3. Intersect(f, h) → B
  4. Polygon(A, B, D) → poly1, d, a_1, b
  5. PointIn(poly1) → E
  6. Sphere(E, C) → c
  7. Circle(E, Distance[A, C], xOyPlane) → k
  8. Angle(D, B, E) → α
  9. Dilate(A, If[0 < i ≤ 1, 1 - i, 0], B) → A'
  10. Segment(E, A') → j
  11. Dilate(B, If[1 < i ≤ 2, 2 - i, 0], D) → B'
  12. Segment(B, B') → l
  13. Dilate(D, If[2 < i ≤ 3, 3 - i, 0], A) → D'
  14. Segment(D, D') → m
  15. Dilate(D, If[3.5 < i ≤ 4.5, 4.5 - i, 0], C) → D'_1
  16. Segment(D, D'_1) → n
  17. Angle(C, D, E) → β
  18. Dilate(C, If[4.5 < i ≤ 5.5, 5.5 - i, 0], A) → C'
  19. Segment(C, C') → p
  20. Polygon(A, D, C) → poly2, c_1, a_2, d_1
  21. Distance(A, A') → distanceAA'
  22. Distance(A', B') → distanceA'B'

AI Drawing Prompt Reference

Illustrate a sphere in 3D space and its relationship with the coordinate plane. Construct geometric structures like points, lines, polygons, and circles related to the sphere, including a perpendicular line from the center, intersection points, and a polygon. Perform scaling and connecting operations on these elements to form multiple line segments and new polygons, ultimately demonstrating mathematical concepts such as the sphere's equation, surface, and optimization problems.
The prompt above was compiled from the original drawing commands and is for reference only.