Humbert's Theorem
The Necessary and Sufficient condition that an algebraic curve has an algebraic Involute is that theArc Length is a two-valued algebraic function of the coordinates of the extremities. Furthermore, this functionis a Root of a Quadratic Equation whose Coefficients are rational functions of 
and 
.
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 195, 1959.
- Regular Sequence
- Regular Singularity
- Regular Singular Point
- Regular Surface
- Regular Triangle Center
- Regulus
- Reidemeister Moves
- Reidemeister's Theorem
- Reinhardt Domain
- Relation
- Relative Error
- Relative Extremum
- Relatively Prime
- Relative Maximum
- Relative Minimum
- Relaxation Methods
- Remainder
- Remainder Theorem
- Rembs' Surfaces
- Removable Crossing
- Removable Singularity
- Rencontres Number
- Rendezvous Values
- Repartition
- Repdigit