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Orthoptic of a closed Fermat curve

Orthoptic of a closed Fermat curve
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2019-09-24 15:59
CalculusDerivativeParametric EquationGeometric ConstructionLocus
This example demonstrates the construction and properties of the orthoptic curve of a closed Fermat curve. Key mathematical concepts include derivatives, geometric constructions, locus, and parametric equations. The construction utilizes GeoGebra commands such as Tangent, Segment, OrthogonalLine, Intersect, Angle, and Locus. Suitable for high school and above mathematics learners to understand curve geometry and calculus applications.

GeoGebra Commands & Parameters

  1. Tangent(A, c) → f
  2. Segment(O, A) → g
  3. OrthogonalLine(O, g) → h
  4. Intersect(c, h) → B, C
  5. Tangent(C, c) → i
  6. Angle(f, i) → α
  7. Intersect(f, i) → D
  8. Locus(D, t) → loc1

AI Drawing Prompt Reference

Draw a closed Fermat curve and construct its orthoptic curve. First, draw the Fermat curve. Then, choose any point A on the curve and draw the tangent line f at point A. Next, draw a line segment from the origin O to point A, and construct the perpendicular line h to OA, which intersects the Fermat curve at points B and C. Draw the tangent line i at point C, calculate the angle α between f and i, and find their intersection point D. Finally, construct the locus curve loc1 with D as the locus point and t as the parameter.
The prompt above was compiled from the original drawing commands and is for reference only.