Riders in the Geometrical Sky
Math books from 100+ years ago contain many quaint terms, the best known being "vulgar fractions" and "promiscuous examples." As a mathematics teacher, I would have been hard pressed to discuss such in a classroom...without a snicker or two...or even a complaint from a parent.
Another "olde" term is a "geometrical rider." I even have a book with that title. Anyone know what a rider is...in the geometrical sense?
Basically, a rider is defined to be an exercise of a known proposition or proven theorem. That is, the theorem or proposition has been taught and the rider gives the student further experience exploring it.
As Richard Proctor's "olde" book First Step in Geometry (1887) claims: "It generally happens that the difficulty of a deduction is greatly diminished when it is given in this way, for we know in what direction to seek a solution." That is the same today...only now students know to just look at the page number and title for the section...and they know what to do.
Nonetheless, I like the terms "rider" and "vulgar fractions." It suggests the presence of "nonriders" (e.g. openended, nonstandard problems)and "refined fractions" (e.g. continued fractions.
