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Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

A number of attractive 6-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

An infinitesimal which is not the differential of an actual function and which cannot be expressed as dz=((partialz)/(partialx))_ydx+((partialz)/(partialy))_xdy, the way an ...

If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 ...

A line in the complex plane with slope +/-i. An isotropic line passes through either of the circular points at infinity. Isotropic lines are perpendicular to themselves.

A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...

The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.

Lemoine-Brocard geometry is that part of triangle geometry concerned with the Brocard points, Brocard triangles, etc. and with symmedians and symmedian points.

Lemoine geometry is that part of triangle geometry concerned with symmedians and symmedian points.

In the depiction of a row of identical columns parallel to the plane of a perspective drawing, the outer columns should appear wider even though they are farther away.