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The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

Applying the stellation process to the icosahedron gives 20+30+60+20+60+120+12+30+60+60 cells of 11 different shapes and sizes (including the icosahedron itself). The ...

An isosceles tetrahedron is a nonregular tetrahedron in which each pair of opposite polyhedron edges are equal, i.e., a^'=a, b^'=b, and c^'=c, so that all triangular faces ...

The intersection of two lines L_1 and L_2 in two dimensions with, L_1 containing the points (x_1,y_1) and (x_2,y_2), and L_2 containing the points (x_3,y_3) and (x_4,y_4), is ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...