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In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

From the feet H_A, H_B, and H_C of each altitude of a triangle DeltaABC, draw lines (H_AP_A,H_AQ_A), (H_BP_B,H_BQ_B), (H_CP_C,H_CQ_C) perpendicular to the adjacent sides, as ...

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...

A cubic curve is an algebraic curve of curve order 3. An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in ...

There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

A knot diagram which has alternating under- and overcrossings as the knot projection is traversed. The first knot which does not have an alternating diagram has 8 crossings.

Given the direct sum of additive Abelian groups A direct sum B, A and B are called direct summands. The map i_1:A-->A direct sum B defined by i(a)=a direct sum 0 is called ...

The real projective plane with elliptic metric where the distance between two points P and Q is defined as the radian angle between the projection of the points on the ...