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Geometric Transformations and Parallelogram Demo

Geometric Transformations and Parallelogram Demo
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2016-06-15 06:20
Coordinate GeometryTransformationGeometric Construction
This example demonstrates constructing a parallelogram using points a, b, c, d and transforming the function f's graph. Core math concepts include geometric transformations (translation), properties of parallelograms, and function graph transformations. Construction highlights: uses Segment and Surface commands in GeoGebra with objects f, a, b, c, d, e, g, h, i, j, k, l. Suitable for high school mathematics teaching to understand the relationship between geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Segment((0, 0, -1.5), (0, 0, 1.5)) → f
  2. Surface(((0.5 * cos(t)) * sin(f)), ((0.5 * sin(t)) * sin(f)), 1.5 + (0.2 * cos(f)), t, 0, (2 * π), f, 0, π) → a
  3. Surface(1 + (cos(t) * sin(f)), ((0.3 * sin(t)) * sin(f)), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → b
  4. Surface((cos(60°) * (1 + (cos(t) * sin(f)))) - (sin(60°) * ((0.3 * sin(t)) * sin(f))), (sin(60°) * (1 + (cos(t) * sin(f)))) + (cos(60°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → c
  5. Surface((cos(120°) * (1 + (cos(t) * sin(f)))) - (sin(120°) * ((0.3 * sin(t)) * sin(f))), (sin(120°) * (1 + (cos(t) * sin(f)))) + (cos(120°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → d
  6. Surface((-(1 + (cos(t) * sin(f)))) - (0 * ((0.3 * sin(t)) * sin(f))), (0 * (1 + (cos(t) * sin(f)))) + (-(((0.3 * sin(t)) * sin(f)))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → e
  7. Surface((cos(240°) * (1 + (cos(t) * sin(f)))) - (sin(240°) * ((0.3 * sin(t)) * sin(f))), (sin(240°) * (1 + (cos(t) * sin(f)))) + (cos(240°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → g
  8. Surface((cos(300°) * (1 + (cos(t) * sin(f)))) - (sin(300°) * ((0.3 * sin(t)) * sin(f))), (sin(300°) * (1 + (cos(t) * sin(f)))) + (cos(300°) * ((0.3 * sin(t)) * sin(f))), 1.4 + (0.08 * cos(f)), t, 0, (2 * π), f, 0, π) → h
  9. Surface(1.2 + (1.2 * cos(f)), (sin(t) * sin(f)), -1 - (cos(t) * sin(f)), t, (5 / 6 * π), (7 / 6 * π), f, 0, π) → i
  10. Surface((cos(120°) * (1.2 + (1.2 * cos(f)))) - (sin(120°) * (sin(t) * sin(f))), (sin(120°) * (1.2 + (1.2 * cos(f)))) + (cos(120°) * (sin(t) * sin(f))), -1 - (cos(t) * sin(f)), t, (5 / 6 * π), (7 / 6 * π), f, 0, π) → j
  11. Surface((cos(240°) * (1.2 + (1.2 * cos(f)))) - (sin(240°) * (sin(t) * sin(f))), (sin(240°) * (1.2 + (1.2 * cos(f)))) + (cos(240°) * (sin(t) * sin(f))), -1 - (cos(t) * sin(f)), t, (5 / 6 * π), (7 / 6 * π), f, 0, π) → k
  12. Surface(((0.51 * cos(t)) * sin(f)), ((0.51 * sin(t)) * sin(f)), 1.5 + (0.21 * cos(f)), t, 0, (2 * π), f, (2 / 3 * π), π) → l

AI Drawing Prompt Reference

Draw a parallelogram using points a, b, c, and d as vertices. First, draw points a, b, c, and d, then use the translation of function f's graph to demonstrate geometric transformations. Start by drawing the graph of f, followed by a, b, c, d, e, g, h, i, j, k, and l, and finally show the transformation of the function graph through translation.
The prompt above was compiled from the original drawing commands and is for reference only.