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3D Heart

3D Heart
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2016-01-03 20:21
VectorSolid GeometryParametric EquationGraphing
This example demonstrates how to create a 3D heart shape using mathematical commands in GeoGebra. It involves core concepts like solid geometry, vector operations, and parametric equations. Key construction elements include commands like Surface, Point, and Vector, along with objects a, A, B, C, D, E, F, G, u, b. Suitable for high school and above students learning 3D geometry and spatial visualization, or for mathematical visualization education.

GeoGebra Commands & Parameters

  1. Surface((((((4 * cos(v)) * sin(abs(u))^(abs(u))) * cos(u)) * cos(v)) * 1.6), ((((4 * cos(v)) * sin(abs(u))^(abs(u))) * sin(u)) * cos(v)), (2 * sin(v)), u, -3.141592653589793, 3.141592653589793, v, -1.5707963267948966, 1.5707963267948966) → a
  2. Point(zAxis) → A
  3. Point(xAxis) → B
  4. Point(zAxis) → C
  5. Point(yAxis) → D
  6. Point(yAxis) → E
  7. Vector(F, G) → u

AI Drawing Prompt Reference

Draw a 3D heart shape using parametric equations to define its surface. First, draw the heart surface with u ranging from -π to π and v from -π/2 to π/2. Then create two points A and C on the z-axis, point B on the x-axis, and points D and E on the y-axis. Finally, define the vector u from F to G.
The prompt above was compiled from the original drawing commands and is for reference only.