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Flower Function

Flower Function
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2020-03-03 06:01
FunctionSolid GeometryGeometric ConstructionGraphing
This example demonstrates the 3D surface plot of a flower function and its variations. Core math concepts include surface, area, function graphing, triangles, secant lines, and solid geometry. Construction involves commands like Surface, Line, Circle, Segment, and Sphere in GeoGebra. Suitable for high school and above students to understand complex function geometry and parameter effects.

GeoGebra Commands & Parameters

  1. Surface(x(A) + ((j * cos(i°)) * cos(((m * i))°)), y(A) + ((0.5 * (j - 1)) * cos(((m * i))°)^(2)), z(A) + ((j * sin(i°)) * cos(((m * i))°)), i, 0, 720, j, 0, 4) → a
  2. Surface(x(A) + ((j * cos(i°)) * cos(((m * i))°)), y(A) + ((0.5 * (j - 1)) * cos(((m * i))°)^(2)), z(A) + ((j * sin(i°)) * cos(((m * i))°)), i, 0, 720, j, 0, 2.5) → b
  3. Surface(x(A) + ((j * cos(i°)) * cos((((0.5 * m) * i))°)), y(A) + ((0.5 * (j - 1)) * cos((((0.5 * m) * i))°)^(2)) - 0.2, z(A) + ((j * sin(i°)) * cos((((0.5 * m) * i))°)), i, 0, 720, j, 0, 1.8) → c
  4. Line(A, yAxis) → f
  5. Circle(A + (0, 0.1, 0), 0.5, f) → d
  6. Segment(A, B_1) → g
  7. Sphere(A, 0.35) → e
  8. Surface(x(C) + (((0.5 * j) * cos(i°)) * cos(((m1 / 4 * i))°)), y(C) + ((0.5 * (j - 1)) * cos(((m1 / 4 * i))°)^(2)), z(C) + (((0.5 * j) * sin(i°)) * cos(((m1 / 4 * i))°)), i, 0, 720, j, 0, 4.8) → h