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The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

The inverse curve of the lituus is an Archimedean spiral with m=2, which is Fermat's spiral.

The catacaustic of a logarithmic spiral, where the origin is taken as the radiant point, is another logarithmic spiral. For an original spiral with parametric equations x = ...

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).

The pedal curve of a logarithmic spiral with parametric equation f = e^(at)cost (1) g = e^(at)sint (2) for a pedal point at the pole is an identical logarithmic spiral x = ...

The radial curve of the logarithmic spiral is another logarithmic spiral.

An equilateral parallelogram whose acute angles are 45 degrees. Sometimes, the restriction to 45 degrees is dropped, and it is required only that two opposite angles are ...

A major arc (right figure) is an arc of a circle having measure greater than or equal to 180 degrees (pi radians).

Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line ...

The dual of the rhombidodecadodecahedron U_(38) and Wenninger dual W_(76).