Search Results for ""

The polar curve r=1+2cos(2theta) (1) that can be used for angle trisection. It was devised by Ceva in 1699, who termed it the cycloidum anomalarum (Loomis 1968, p. 29). It ...

Amazingly, the catacaustic of the deltoid when the rays are parallel in any direction is an astroid. In particular, for a deltoid with parametric equations x = 2cost+cos(2t) ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

The involute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_i = ...

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.

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 ...

Given an acute angle in a right triangle, the adjacent side is the leg of the triangle from which the angle to the hypotenuse is measured. Lengths of adjacent and opposite ...

Extend the symmedians of a triangle DeltaA_1A_2A_3 to meet the circumcircle at P_1, P_2, P_3. Then the symmedian point K of DeltaA_1A_2A_3 is also the symmedian point of ...

Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...