# Euclid's Muse

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# Search Results for “isotomic”

##### Ellipse Isotomic
The ellipse isotomic generated by point D is teh locus of the reflection of D in the tangents to the ellipse. What shape is the isotomic when D lies on one of the foci of the ellipse? Why?

Tags: isotomic, ellipse

##### Circle isotomic
The circle isotomic is the locus of the reflections of a given point in the tangents to the circle. It is easy to convince yourself that it is also the envelope of the circles whose centers lie on the circle and which pass through the given point. The given point is C.  Try dragging it outside the circle.

Tags: isotomic, curve, envelope, limacon

##### Circle isotomic and Conchoid
The circle isotomic with respect to P is the locus of the reflection of P in the tangents of the circle. The Conchoid is the locus of the points a given fixed distance from a point on the circle, and lying on a line through that point and P.

Tags: conchoid, circle, isotomic

##### Pascal's Limacon
Given a circle with center A and a point C, here are three related ways of constructing Pascal’s Limacon: It is the isotomic (look it up) of the circle with pole C. It is the conchoid (look it up) of a circle centered at A whose circumference passes through C. It is an epitrochoid (look it up) formed by a circle of equal radius rolling around the original. This app constitutes a visual proof of the above, and depends on the fact that the composition of reflections in two parallel lines is equivalent to a translation of twice the distance between the lines.

Tags: Pascal, Limacon, Epitrochoid, Conchoid, Isotomic, Pedal, reflection

##### Circle Envelope (Hyperbola)
The hyperbola has foci A and B. The family of circles whose center C lies on the hyperbola and which pass through the fixed point D defines an envelope curve. What does this envelope look like when D lies on A or B?

Tags: hyperbola, envelope, isotomic

##### Circle Envelope
The ellipse has foci A and B. The family of circles whose center C lies on an ellipse and which pass through a  fixed point D defines an envelope curve. (Press Show). What does the envelope look like when D lies on one of the foci of the ellipse.

Tags: ellipse, envelope, circle, isotomic