Search Results for ""

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 conchoid of de Sluze is the cubic curve first constructed by René de Sluze in 1662. It is given by the implicit equation (x-1)(x^2+y^2)=ax^2, (1) or the polar equation ...

Let T be a central triangle and let U(T) be its unary cofactor triangle. Then T and U(T) are perspective, and their perspector is called the eigencenter of T. Let the A-, B-, ...

The evolute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_e = (a^2-b^2)/acos^3t (3) y_e = (b^2-a^2)/bsin^3t. ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

Let J_A, J_B, and J_C be the vertices of the outer Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

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 ...

"The" Griffiths point Gr is the fixed point in Griffiths' theorem. Given four points on a circle and a line through the center of the circle, the four corresponding Griffiths ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...