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A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

A linkage with six rods which draws the inverse of a given curve. When a pencil is placed at P, the inverse is drawn at P^' (or vice versa). If a seventh rod (dashed) is ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

A phase portrait is a plot of multiple phase curves corresponding to different initial conditions in the same phase plane (Tabor 1989, p. 14). Phase portraits for simple ...

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

A hexomino is a 6-polyomino. There are 35 free hexominoes (illustrated above), 60 one-sided hexominoes, and 216 fixed hexominoes.

An octomino is an 8-polyomino. There are 369 free (illustrated above), 704 one-sided, and 2725 fixed octominoes.

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.