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Search Results for “conchoid”

By Phil Todd
Nicomeded Conchoid Apparatus
This illustrates the apparatus used to draw Nicomedes Conchoid. The conchoid was used by Nicomedes in a geometric construction for extracting a cube root.

Tags: Conchoid, nicomedes

By Phil Todd
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

By Phil Todd
Nicomedes Conchoid Clock
This device is illustrated in Eustocius Commentaries on Archimedes (well.. not the clock part of it, I admit.)

Tags: clock, conchoid, nicomedes

By admin
Circle Conchoid
Given a curve and a point (the pole) a conchoid is formed by offsetting the curve by a fixed distance along a line through the pole.  Imagine that the purple points are fixed on the hands, but free to slide in the circular groove, while the hands are forced to pass through the red point.  You can drag the red point and see how the conchoid varies.

Tags: clock

By admin
Nicomedes Conchoid
Nicomedes Conchoid is described in Eutocius' commentaries of Archimedes' book on Spheres and Cylinders.  Archimedes glibly describes finding two mean proportionals (equivalent to extracting a cube root).  Eutocius describes a dozen more or less slippery ways of doing this.  One involves a drawing apparatus invented by Nicomedes, on which this clock is based.  Drag the red point to vary the curve.

Tags: clock

By Phil Todd
Nicomedes Construction for Cube Root
Nicomedes Conchoid is a curve generated by a device involving two sliding joints. It can be used in this construction for two mean proportionals (which is Greek for finding a cube root). See if you can use it to extract cube roots of rational numbers.

Tags: Nicomedes, conchoid, construction

By Phil Todd
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

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