Underwood Dudley

A budget of trisections

My intention in publishing is to enable those who have been puzzled by one or two discoverers to see how they look in a lump. The only question is, has the selection been farily made? To this my answer is, that no selection at all has been made. The books are, without exception, those which I have in my own library; and I have taken all—I mean all of the kind: Heaven forbid that I should be supposed to have no other books! (Budget, vol. 1, p. 7.)

Two-Year Magazine Subscription Rates

When a magazine incites you to subscribe to it, you are often given the choice of signing up for one year or two. The cost of the second year is usually less than that of the first. How do magazines decide on how much the discount for the second year should be? Is a mathematical model at work? A simple model could take into account the interest rate, i, that the magazine could earn on money paid in advance, the cost, c, of obtaining a subscription, and the probability, p, that a one-year subscriber will renew. If we let s denote the single-year subscription rate and t the two-year rate, then the present value of a two-year subscription is t c while the present value of two successive one-year subscriptions is

Characteristics of Trisectors

The feeling which tempts persons to his problem is that which, in romance, made it impossible for a knight to pass a castle which belonged to a giant or an enchanter. I once gave a lecture on the subject: a gentleman who was introduced to it by what I said remarked, loud enough to be heard by all around, “Only prove to me that it is impossible, and I will set about it this very evening.”

Non-Euclidean Constructions

Always write in your books. You may be a silly person—for though your reading my book is rather a contrary presumption, yet it is not conclusive—and your observations may be silly or irrevelant, but you cannot tell what use they may be of long after you are gone where Budgeteers cease from troubling. (Budget, vol. 2, p. 265.)