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The rotation operator can be derived from examining an infinitesimal rotation (d/(dt))_(space)=(d/(dt))_(body)+omegax, where d/dt is the time derivative, omega is the angular ...

If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, ...

The 20 Cayley lines generated by a hexagon inscribed in a conic section pass four at a time though 15 points known as Salmon points (Wells 1991). There is a dual relationship ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

Write down the positive integers in row one, cross out every k_1th number, and write the partial sums of the remaining numbers in the row below. Now cross off every k_2th ...

A stellation is said to be fully supported if all its included cells are supported, i.e., if all its bottom faces are covered by their adjacent cells. In other words, every ...

The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...

A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

Eliminate each knot crossing by connecting each of the strands coming into the crossing to the adjacent strand leaving the crossing. The resulting strands no longer cross but ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...