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Signed Distance and Gradient of Circle

Signed Distance and Gradient of Circle
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2020-10-11 18:55
CircleVectorCalculusGeometric Construction
This example demonstrates how to visualize the signed distance and gradient of a circle using geometric construction. Key mathematical concepts include vector analysis, differential geometry, and distance functions. The construction involves GeoGebra commands such as Point, UnitVector, Vector, Length to create the circle's parametric equation and gradient calculation. Suitable for high school students or college undergraduates learning analytic geometry and calculus fundamentals.

GeoGebra Commands & Parameters

  1. Point({(yg * yg) + radius, radius + yg}) → xp
  2. Point({(xp * t)}) → pp
  3. UnitVector(pp - xp) → c
  4. Vector((0, 0), (delX, delY)) → gradPhi
  5. Length(xp) → fg

AI Drawing Prompt Reference

Draw a circle and show the vectors from the center to points on the circumference. These vectors represent the distance, and points on the circumference are maxima of the distance function. Construct by first determining the center and radius, then calculating vectors from the center to points on the circumference, and finally showing how these vectors change to represent distance and gradient.
The prompt above was compiled from the original drawing commands and is for reference only.