MathPlotAI Logo MathPlotAI

Viviani Curve by wuguoning (2)

Viviani Curve by wuguoning (2)
Loading the math board and drawing, please wait…
2020-03-05 16:53
VectorSolid GeometryParametric EquationGeometric Construction
This example demonstrates the construction and properties of the Viviani Curve, formed by the intersection of a sphere and a cylinder in 3D space. Key mathematical concepts include solid geometry, vector operations, parametric equations, and spatial geometric relationships. The construction utilizes GeoGebra commands and objects such as Cylinder, Sphere, CurveCartesian, Point, Intersect, and Vector as outlined in the construction summary. Suitable for high school students and above studying spatial geometry, vectors, and parametric equations, as well as for mathematical competitions or enrichment purposes.

GeoGebra Commands & Parameters

  1. Cylinder((r / 2, 0, -1.25), (r / 2, 0, 1.25), r / 2) → c1, g, h, i
  2. Sphere((0, 0, 0), r) → a
  3. CurveCartesian((r / 2 * (1 + cos(t))), (r / 2 * sin(t)), (r * sin((0.5 * t))), t, -6.28319, 6.28319) → b
  4. Point(b) → A
  5. Intersect(xAxis, zAxis) → B
  6. Vector(B, A) → u

AI Drawing Prompt Reference

Draw a cylinder with radius r, base center at the origin, and height 2.5, then draw a sphere with radius r and center at the origin. Use parametric equations to draw the Viviani curve, which is the intersection of the cylinder and sphere. Finally, find the intersection of the x-axis and z-axis, and draw a vector from this point to a point on the curve.
The prompt above was compiled from the original drawing commands and is for reference only.