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The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

The technique of extracting the content from geometric (tensor) equations by working in component notation and rearranging indices as required. Index gymnastics is a ...

An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

The initial side of an angle theta drawn in angle standard position is the side lying on the positive x-axis. In general, viewing an angle as the amount of rotation about the ...

For a given curve C, consider the locus of the point P from where the tangents from P to C meet at a fixed given angle. This is called an isoptic curve of the given curve. ...

For an algebraic curve, the total number of groups of a g_N^r consisting in a point of multiplicity k_1, one of multiplicity k_2, ..., one of multiplicity k_rho, where sumk_i ...

A Jordan curve is a plane curve which is topologically equivalent to (a homeomorphic image of) the unit circle, i.e., it is simple and closed. It is not known if every Jordan ...

A curve also known as Gutschoven's curve which was first studied by G. van Gutschoven around 1662 (MacTutor Archive). It was also studied by Newton and, some years later, by ...

If any set of points is displaced by X^idx_i where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector. ...