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The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...

The upper central series of a group G is the sequence of groups (each term normal in the term following it) 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... that is constructed in the ...

The sphere with respect to which inverse points are computed (i.e., with respect to which geometrical inversion is performed). For example, the cyclides are inversions in a ...

The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a ...

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...

The pedal curve of an astroid x = acos^3t (1) y = asin^3t (2) with pedal point at the center is the quadrifolium x_p = acostsin^2t (3) y_p = acos^2tsint. (4)

The pedal curve of circle involute f = cost+tsint (1) g = sint-tcost (2) with the center as the pedal point is the Archimedes' spiral x = tsint (3) y = -tcost. (4)

The inverse curve of the cochleoid r=(sintheta)/theta (1) with inversion center at the origin and inversion radius k is the quadratrix of Hippias. x = ktcottheta (2) y = kt. ...

A chord which is a normal at each end. A centrosymmetric set K subset R^d has d double normals through the center (Croft et al. 1991). For a curve of constant width, all ...

The inverse curve of a sinusoidal spiral r=a^(1/n)[cos(nt)]^(1/n) with inversion center at the origin and inversion radius k is another sinusoidal spiral ...