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Model the St Louis Arch

Model the St Louis Arch
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2016-11-03 02:17
FunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Explore the Graphs of Quadratic Functions
This example demonstrates the geometric modeling of the St Louis Arch, involving concepts like ellipses, unit circles, rational numbers, and multiplication. Key GeoGebra commands/objects used include a (width), h (height), k (center), c (focal distance), B (ellipse point), A, C (control points), and pic1 (image). Suitable for high school mathematics education, focusing on analytical geometry and function graphing.

GeoGebra Commands & Parameters

  1. Numeric a(1)
  2. Numeric h(0)
  3. Numeric k(0)
  4. c(x) = (a * (x - h)^(2)) + k
  5. Point B(11.3072, -1.448)
  6. Point A(-2.18, -0.96)
  7. Point C(6.82, -0.96)

AI Drawing Prompt Reference

Model the St Louis Arch by setting the width to 1 and height to 0 with the center at (0,0). Calculate the focal distance c using the ellipse formula, then draw the ellipse based on the given control points (-2.18, -0.96), (6.82, -0.96), and (11.3072, -1.448). Finally, construct the arch shape using these points and the ellipse.
The prompt above was compiled from the original drawing commands and is for reference only.