[2128]. I take from a biographical dictionary the first five names of poets, with their ages at death. They are
Aagard, died at 48.
Abeille, “ “ 76.
Abulola, “ “ 84.
Abunowas, “ “ 48.
Accords, “ “ 45.
These five ages have the following characters in common:—
1. The difference of the two digits composing the number divided by three, leaves a remainder of one.
2. The first digit raised to the power indicated by the second, and then divided by three, leaves a remainder of one.
3. The sum of the prime factors of each age, including one as a prime factor, is divisible by three.—Peirce, C. S.
A Theory of Probable Inference; Studies in Logic (Boston, 1883), p. 163.
[2129]. In view of the fact that the offered prize [for the solution of the problem of Fermat’s Greater Theorem] is about $25,000 and that lack of marginal space in his copy of Diophantus was the reason given by Fermat for not communicating his proof, one might be tempted to wish that one could send credit for a dime back through the ages to Fermat and thus secure this coveted prize, if it actually existed. This might, however, result more seriously than one would at first suppose; for if Fermat had bought on credit a dime’s worth of paper even during the year of his death, 1665, and if this bill had been drawing compound interest at the rate of six per cent, since that time, the bill would now amount to more than seven times as much as the prize.—Miller, G. A.
Some Thoughts on Modern Mathematical Research; Science, Vol. 35 (1912), p. 881.
[2130]. If the Indians hadn’t spent the $24. In 1626 Peter Minuit, first governor of New Netherland, purchased Manhattan Island from the Indians for about $24. The rate of interest on money is higher in new countries, and gradually decreases as wealth accumulates. Within the present generation the legal rate in the state has fallen from 7% to 6%. Assume for simplicity a uniform rate of 7% from 1626 to the present, and suppose that the Indians had put their $24 at interest at that rate (banking facilities in New York being always taken for granted!) and had added the interest to the principal yearly. What would be the amount now, after 280 years? 24 × (1.07)280 = more than 4,042,000,000.