Search Loci: Convergence:
Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a^2 - b^2 but was floored because the examiner unkindly asked for the factors of p^2 - q^2.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Using Historical Problems in the Middle School
Problems from Bonnycastle
Here are some problems used by Karen Dee Michalowicz of the Langley School. She reports that her students have enjoyed solving these and have created similar problems of their own. The problems that follow come from the 1807 London Edition of John Bonnycastle’s Introduction to Mensuration and Practical Geometry. Two problems are in rhyme. The third problem is one that would never be printed in a book today, because of its “political incorrectness.”
Ans. Bottom 14.44401, top 24.4002
Ans. 7.05 cubic inches.