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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 matrices A, X, B, and C satisfy AX-XB=C, then [I X; 0 I][A C; 0 B][I -X; 0 I]=[A 0; 0 B], where I is the identity matrix.

An n-route is defined as a walk of length n with specified initial point in which no line succeeds itself.

Rubik's group is the group corresponding to possible rotations of a Rubik's Cube. There are six possible rotations, each corresponding to a generator of the group, and the ...

The Rudvalis group is the sporadic group Ru of order |Ru| = 145926144000 (1) = 2^(14)·3^3·5^3·7·13·29. (2) It is implemented in the Wolfram Language as RudvalisGroupRu[].

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

The divisibility test that an integer is divisible by 9 iff the sum of its digits is divisible by 9.

A negative number multiplied by another negative number gives a positive number.

A straightedge with markings to indicate distances. Although geometric constructions are sometimes said to be performed with a ruler and compass, the term straightedge is ...

One of the straight lines sweeping out a ruled surface. The rulings on a ruled surface are asymptotic curves.