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The Dottie number is the name given by Kaplan (2007) to the unique real root of cosx=x (namely, the unique real fixed point of the cosine function), which is 0.739085... ...

The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

The pedal curve for an n-cusped hypocycloid x = a((n-1)cost+cos[(n-1)t])/n (1) y = a((n-1)sint-sin[(n-1)t])/n (2) with pedal point at the origin is the curve x_p = ...

The inner Vecten circle is the circumcircle of the inner Vecten triangle. It has center at Kimberling center X_(642), which is the complement of the inner Vecten point ...

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

The straight line on which all points at infinity lie. The line at infinity is central line L_6 (Kimberling 1998, p. 150), and has trilinear equation aalpha+bbeta+cgamma=0, ...

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

The MacBeath triangle DeltaX_AX_BX_C (a term coined here for the first time), is the triangle whose vertices are the contact points of the MacBeath inconic with the reference ...