11 - Parting Shorts

Summary

Ibn Qurra

Here is a multiple-choice question on the history of mathematics. The dates of birth and death of the Arab mathematician Thabit Ibn Qurra, who translated and commented on Greek higher mathematics, are

(A) 826–901 (B) 833–902 (C) 836–901 (D) 836–911 (E) All of the above.

The correct answer is (E). See Al Abdullah Al-Daffa', The Muslim contribution to mathematics (Humanities Press, 1977). The dates (A)–(D) are given, respectively, on pages 44, 13, 59, and 86.

Reading a calculator display

Sandra Z. Keith of St. Cloud State University in Minnesota writes:

A student differentiating f(x) = cos²x obtained the answer f′(x) = 2 cosx⁻ sin x, which I graded wrong, with my typical lecture on parentheses errors in the margin. When he protested that his answer was the same as mine, I challenged him to plug in numbers on his calculator. Punching the “negative” button on his calculator, he did not need to register a multiplication; the graphics display on his calculator, a TI-85 (or a TI-81), uses this format, the minus sign at a higher level, to denote 2cosx(−sinx), a language he had incorporated into his written work.

Infallibility of a symbolic manipulation program

Dean Clark of the University of Rhode Island in Kingston notes that Theorist is a highly and justifiably acclaimed manipulation program that uses a propositional calculus thought to be incapable of producing incorrect conclusions if the initial premises are correct.