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For a semicubical parabola with parametric equations x = t^2 (1) y = at^3, (2) the involute is given by x_i = (t^2)/3-8/(27a^2) (3) y_i = -(4t)/(9a), (4) which is half a ...

The semimajor axis (also called the major semi-axis, major semiaxis, or major radius) of an ellipse (or related figure) is half its extent along the longer of the two ...

The semiminor axis (also called the minor semi-axis, minor semiaxis, or minor radius) of an ellipse (or related figure) is half its extent along the shorter of the two ...

An algebraic curve of degree six. Examples include the astroid, atriphtaloid, Cayley's sextic, cornoid, cycloid of Ceva, dumbbell curve, ellipse evolute, epicycloid, Freeth's ...

The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

Two triangles are similar if their triples of vertex angles are the same.

Two figures are homothetic if they are related by a dilation (a dilation is also known as a homothecy). This means that the connectors of corresponding points are concurrent ...

If a line L is the Simson line of a point P on the circumcircle of a triangle, then P is called the pole of L (Honsberger 1995, p. 128).

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 ...

The pedal curve of a sinusoidal spiral r=a[cos(nt)]^(1/n) with pedal point at the center is another sinusoidal spiral with polar equation r=a[cos(nt)]^(1+1/n). A few examples ...