Search Results for ""

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

The involute of the circle was first studied by Huygens when he was considering clocks without pendula for use on ships at sea. He used the circle involute in his first ...

The class of curve known as Dürer's conchoid appears in Dürer's work Instruction in Measurement with Compasses and Straight Edge (1525) and arose in investigations of ...

The pedal curve of an epicycloid x = (a+b)cost-b[((a+b)t)/b] (1) y = (a+b)sint-bsin[((a+b)t)/b] (2) with pedal point at the origin is x_p = 1/2(a+2b){cost-cos[((a+b)t)/b]} ...

The roulette traced by a point P attached to a circle of radius b rolling around the outside of a fixed circle of radius a. These curves were studied by Dürer (1525), ...

A strophoid of a circle with the pole O at the center of the circle and the fixed point P on the circumference of the circle. Freeth (1878, pp. 130 and 228) described this ...

For a rectangular hyperbola x = asect (1) y = atant (2) with inversion center at the origin, the inverse curve is x_i = (2kcost)/(a[3-cos(2t)]) (3) y_i = ...

The inner Soddy center (or inner Soddy point) is the center of the inner Soddy circle. It is equivalent to the equal detour point X_(175) (Kimberling 1994) and has equivalent ...

For a given curve C, consider the locus of the point P from where the tangents from P to C meet at a fixed given angle. This is called an isoptic curve of the given curve. ...

The limaçon trisectrix is a trisectrix that is a special case of the rose curve with n=1/3 (possibly with translation, rotation, and scaling). It was studied by Archimedes, ...