I recently had the great fortune to dig through my grandfather's basement, where I came across the most astounding book: a small, incidental yellow paperback.
#45 • COLLEGE OUTLINE SERIES • $1.25
PLANE and SPHERICAL
TRIGONOMETRY
With Five-Place Tables
KEYED TO STANDARD TEXTBOOKS
The book was tantalizingly close to its release to the public domain, having been copyrighted last in 1954. More than fifty years ago, this was a new book. In fact, some math geek in Post-War America cherished this math book just as much as I cherish my copy of Riddle's Calculus and Analytic Geometry. I'd heard of Trigonometry, of course; but I had no clue what Spherical Trigonometry was. I didn't remember that in pre-calculus.
The preface of the book gives a quaint reminder of the era in which it was rendered.
"Five-place tables are furnished with this outline, and the principle of handling any table is explained."
Logarithm tables! In this world where the 800 MHz processor silently purring under my fingertips can calculate thousands of multiplications in a second, I had forgotten that once, in the dim past, such devices had not yet been conceived. A five-place table of logarithms... what a find!
"There are so many rules!" I said, skimming the pages. It lays out in black and white the beautiful symmetries of the trigonometric functions, yes, but there was a sweet simplicity in those trigonometry tables. They'd compressed them in every way possible, for good reason - it had every single trig function calculated for every minute between 0 and 90 degrees. I'd never seen anything like it before. How did they do this? With Taylor Series and sheer balls? Even then, evaluating polynomials out by hand sucks ass, even if you're doing it to an arbitrary precision.
Shocking, to me, were the things I had worked out in pre-calculus but was never taught. Here's a chapter on reference angles that looks suspiciously like an old note I had at the top of a page of notes, one winter long ago:
(any function of Θ) = ±(same function of α)
So they're called reference angles. Huh.
I began to think that these college students of ages past were a bit spoiled, having all the secrets of trigonometry laid out for them in nice tables with a note reading "The student should commit this to memory." I mean, sure, trig tables are hard to use until you get used to them, but they surely didn't have to learn silly things like phase shift...
/me turns the page and sees a section on addition and subtraction forumlae for tangent and cotangent.
Okay. You win. 24 formulae for trigonometric identities. I dug around for my precalc cheat sheet, and there were only 10 on it.
My inner mathematician is aroused, and I wish to subscribe to your newsletter....
And the book goes on, enticing me with sentiments of the old way, back when they didn't give partial credit for half-assed answers. Back when mathematics was a rigid ... err, nevermind. ^_^
All the knowledge in this book, of surveying and spherical geometry, projection and haversines, has been lost to my generation of mathematician. Doing math now is easier (computationally speaking) than it ever has been before. And with the computational perfection that the difference engine can exact, we've lost a love of precision that clearly used to govern our field. This book should have been Mathematics for the Ages.
Examination I. (Three Hours.)
Examination II. (Three Hours.)
Examination III. (Three Hours.)
Examination IV. (You will need no tables or book for this examination. Two Hours.)
I scored a 30% F on the first exam.
"The more I learn, the more I find that I have yet to learn."
Speling being on the top of that list. Thanks Wiccanpiper!