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The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

A 32-sided polygon. The regular icosidodecagon is a constructible polygon, and the regular icosidodecahedron of side length 1 has inradius r, circumradius R, and area A r = ...

A 24-sided polygon. The regular icositetragon is constructible. For side length 1, the inradius r, circumradius R, and area A are given by r = 1/2(2+sqrt(2)+sqrt(3)+sqrt(6)) ...

Find the plane lamina of least area A which is capable of covering any plane figure of unit generalized diameter. A unit circle is too small, but a hexagon circumscribed on ...

When a pair of non-incident edges of a tetrahedron is chosen, the midpoints of the remaining 4 edges are the vertices of a planar parallelogram. Furthermore, the area of this ...

It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

The best known packings of equilateral triangles into an equilateral triangle are illustrated above for the first few cases (Friedman). The best known packings of equilateral ...

Consider a one-dimensional Hamiltonian map of the form H(p,q)=1/2p^2+V(q), (1) which satisfies Hamilton's equations q^. = (partialH)/(partialp) (2) p^. = ...