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An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

A sinusoidal spiral is a curve of the form r^n=a^ncos(ntheta), (1) with n rational, which is not a true spiral. Sinusoidal spirals were first studied by Maclaurin. Special ...

The 2-cusped epicycloid is called a nephroid. The name nephroid means "kidney shaped" and was first used for the two-cusped epicycloid by Proctor in 1878 (MacTutor Archive). ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...

An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

The geometric mean is smaller than the arithmetic mean, (product_(i=1)^Nn_i)^(1/N)<=(sum_(i=1)^(N)n_i)/N, with equality in the cases (1) N=1 or (2) n_i=n_j for all i,j.

A mathematical object invented to solve irreducible congruences of the form F(x)=0 (mod p), where p is prime.

A sphere which acts as a model of a spherical (or ellipsoidal) celestial body, especially the Earth, and on which the outlines of continents, oceans, etc. are drawn.

A graded algebra over the integers Z. Cohomology of a space is a graded ring.