GXWeb Strophoid (3)

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GXWeb Constructing the Oblique Strophoid (3)

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About the Strophoid (from Wolfram MathWorld)

A strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the pole). In the special case where C is a line, A lies on C, and O is not on C, then the curve is called an oblique strophoid. If, in addition, OA is perpendicular to C then the curve is called a right strophoid, or simply strophoid by some authors. The right strophoid is also called the logocyclic curve or foliate.

$a = A(x)$

0 6.0082 6

$\theta$

0 0.82742 6.2832

App generated by GXWeb

This simpler oblique strophoid curve is the locus of points B (and D) where

$\angle OAB = \theta$

NOTE: this strophoid is RIGHT when point F = (0,0).

Cartesian equation: $y^2=x^2 \cdot \frac{a-x}{a+x}$

Parametric equation: $x(t)=a^2 \cdot \frac{a^2-t^2}{a^2+t^2}$ $y(t)=t \cdot \frac{t^2-a^2}{t^2+a^2}$

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©2020 Compass Learning Technologies ← Live Mathematics on the Web ← GXWeb Curve Construction Collection ← GXWeb Strophoid (3)