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Archytas Curve by Georg Wengler

Archytas Curve by Georg Wengler
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2017-06-14 01:44
TrigonometryCoordinate GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the construction of the Archytas curve, which involves trigonometry and coordinate geometry. Using the Surface and CurveCartesian commands, the curve can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Surface(a / 2 + (a / 2 * cos(u)), (a / 2 * sin(u)), (a * v), u, 0, (2 * π), v, -4, 4) → b
  2. CurveCartesian((a * cos(t)^(2)), ((a * cos(t)) * sin(t)), (a * sqrt(((1 - cos(t)) * cos(t)))), t, ((-π)) / 2, π / 2) → k_1
  3. CurveCartesian((a * cos(t)^(2)), ((a * cos(t)) * sin(t)), ((-a) * sqrt(((1 - cos(t)) * cos(t)))), t, ((-π)) / 2, π / 2) → k_2