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The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

The bifolium is a folium with b=0. The bifolium is a quartic curve and is given by the implicit equation is (x^2+y^2)^2=4axy^2 (1) and the polar equation ...

B^^ = T^^xN^^ (1) = (r^'xr^(''))/(|r^'xr^('')|), (2) where the unit tangent vector T and unit "principal" normal vector N are defined by T^^ = (r^'(s))/(|r^'(s)|) (3) N^^ = ...

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 ...

A circular sector is a wedge obtained by taking a portion of a disk with central angle theta<pi radians (180 degrees), illustrated above as the shaded region. A sector with ...

The cornoid is the curve illustrated above given by the parametric equations x = acost(1-2sin^2t) (1) y = asint(1+2cos^2t), (2) where a>0. It is a sextic algebraic curve with ...

A curve whose centrode revolves about a fixed axis with constant angle and speed when the curve is traversed with unit speed. The tangent indicatrix of a curve of constant ...

The Dürer folium is a special case of the rose curve with n=1. It is therefore also an epitrochoid. It has polar equation r=asin(theta/2) (1) and can be written as a ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the first fundamental form is the inner product of tangent vectors, ...