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Two groups G and H are said to be isoclinic if there are isomorphisms G/Z(G)->H/Z(H) and G^'->H^', where Z(G) is the group center of the group, which identify the two ...

The inverse curve of the logarithmic spiral r=e^(atheta) with inversion center at the origin and inversion radius k is the logarithmic spiral r=ke^(-atheta).

A group G such that the quotient group G/Z(G), where Z(G) is the group center of G, is Abelian. An equivalent condition is that the commutator subgroup G^' is contained in ...

Given the center of a circle, divide the circle into four equal arcs using a compass alone (a Mascheroni construction).

A perspective collineation with center O and axis o is a collineation which leaves all lines through O and points of o invariant. Every perspective collineation is a ...

The inversion of a ring torus. If the inversion center lies on the torus, then the ring cyclide degenerates to a parabolic ring cyclide.

The inversion of a spindle torus. If the inversion center lies on the torus, then the spindle cyclide degenerates to a parabolic spindle cyclide.

A fractal composed of repeated copies of a pentagram or other polygon. The above figure shows a generalization to different offsets from the center.

The resultant of the vectors represented by the three radii from the center of a triangle's circumcircle to its polygon vertices is the segment extending from 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 ...