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Smiley Construction by Ed Ankrom

Smiley Construction by Ed Ankrom
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2016-07-23 00:07
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Project 2Modeling Parabolas using GeoGebraUs
This example demonstrates how to construct a smiley face using GeoGebra, integrating special points, addition, hyperbolas, tangent functions, and circumcircles. Key math concepts include special points, hyperbolas, tangent functions, circumcircle, and addition operations. Construction highlights involve GeoGebra commands like Tangent and Circumcircle, with objects such as a, c, b, d, A, B, f, g, p, h, q, r, s, C, D. Suitable for high school mathematics teaching, showcasing the integration of analytical geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Numeric a(1.55)
  2. Numeric c(0.25)
  3. Numeric b(3.4)
  4. y = (a * x^(2)) + (b * x) + c
  5. Point A(-4.49, -1.77)
  6. Point B(6.85, -1.77)
  7. x = 0
  8. y = 0
  9. p(x) = If[-0.1 ≤ x ≤ 0.1, 5]
  10. h(x) = If[-0.1 ≤ x ≤ 0.1, 4]
  11. q(x) = If[-0.1 ≤ x ≤ 0.1, 3]
  12. r(x) = If[-0.1 ≤ x ≤ 0.1, 2]
  13. s(x) = If[-0.1 ≤ x ≤ 0.1, 1]
  14. Point C(-2.71, -3.47)
  15. Point D(8.63, -3.47)
  16. t(x) = If[-0.1 ≤ x ≤ 0.1, 7]
  17. f_1(x) = If[-0.1 ≤ x ≤ 0.1, 6]
  18. x = 7
  19. e(x, y) = If[-0.1 ≤ y ≤ 0.1, 6]
  20. x = 1
  21. x = 2
  22. x = 3
  23. x = 4
  24. x = 5
  25. x = 6
  26. x = -1
  27. x = -2
  28. p_1(x) = If[-0.1 ≤ x ≤ 0.1, -1]

AI Drawing Prompt Reference

Draw a smiley face consisting of a parabola, two parallel lines, a circle, and several special points. The parabola passes through points (-4.49, -1.77) and (6.85, -1.77), the circle passes through points (-2.71, -3.47) and (8.63, -3.47), and the parallel lines are at x=0 and y=0, with special points near the axes to form a smiley outline.
The prompt above was compiled from the original drawing commands and is for reference only.