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"SOHCAHTOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite side over hypotenuse, ...

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

The Lie derivative of a spinor psi is defined by L_Xpsi(x)=lim_(t->0)(psi^~_t(x)-psi(x))/t, where psi^~_t is the image of psi by a one-parameter group of isometries with X ...

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

A strong pseudo-Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is symmetric and for which, at each m in M, the map v_m|->g_m(v_m,·) is an ...

A strong Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a strong pseudo-Riemannian metric and positive definite. In a very precise way, the ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

The order n of an algebraic surface is the order of the polynomial defining a surface, which can be geometrically interpreted as the maximum number of points in which a line ...

A surface with boundary is a topological space obtained by identifying edges and vertices of a set of triangles according to all the requirements of a surface except that ...

A swirl is a generic word to describe a function having arcs which double back around each other. The plots above correspond to the function f(r,theta)=sin(6cosr-ntheta) for ...