After a few days of half-heartedly solving problems with complex numbers expressed in rectangular or trigonometric unit-circle forms, I have finally reached a self-determined terminus for basic trigonometry. This is somewhat overdue, according to my Friendly Mathematicians, but I wanted to make sure that I didn't miss anything. I wanted to know that I could at least recognize one form or another so that when I encountered them in my next mathematical section, I could go back to my references and find it. Well then, that's enough for now.

I can't say I found trigonometry thrilling, the way algebra sometimes was. There's nothing like a polynomial pileup to make a mathematical aspirant feel as if I was riding an amusement park ride. Geometry was less thrilling, because at least the first-year work I did wasn't intensely challenging. It was endless mental origami, folding and matching and folding again and matching and proving. Trigonometry, emerging from geometry, added more numbers to it, and plotted a three-dimensional landscape filled with lighthouses, ladders, cast shadows, and seaside panoramas. But once I progressed into trigonometric identities and equations, I bogged down in a seemingly endless proliferation of interlocking relationships that gave me no information about anything except themselves. No doubt I will be glad someday that I did this (or maybe not!) and I will probably encounter something like it again soon enough.

So for now I bid farewell to the terse Brits with their story problems about coastal landmarks, fishing boats, observation towers, and memories of warfare. I also leave, for now, Schaum's red-backed book and its sparkling prose. (Example from Schaum's: "Whenever sin X is between 0 and 1, it is possible to find angles in quadrants I and II that satisfy the value of sin X and could be angles in a triangle. The first-quadrant angle is always a solution but the second-quadrant angle is a solution only when its sum with the given angle is less than 180 degrees.") And I bid a grateful good riddance to the often baffling Barron's text with its Ruritanian fantasy characters, who I hope find better employment in fantasyland than teaching algebra and trigonometry.

I will be going onward to Logarithms, which I will learn from a variety of sources, including my vintage 1958 college algebra text, which merits an entire Electron essay all by itself. Meanwhile, this Electron Blog will be taking about a week off while the Electron writer makes a trip to the "home place" in New England.

Cicadas: the party's almost over

Electron readers may be sick of hearing about the 17-year cicadas here, but I find them so fascinating that I can't help paying attention to them and writing about them. The weather has heated up, so the cicadas who are still in action are making noise again. The howler species seems to have finished, so we are left with the sustained buzzers and the clickers, who go pz-pz-pz-pz-pz and sound, in the words of one cicada text, like a lawn sprinkler. As I drove through the leafy suburban neighborhoods today, I passed through areas of high noise and less noise and no noise, as I passed by populated trees and less populated areas. The cicadas have pruned many of the ends of the branches off deciduous trees, as they pierce the new stems to lay their eggs. So everywhere in this Mid-Atlantic area you can see the drooping, dried ends of cicada-pruned branches. Stopping by a noisy tree, I was fascinated to hear that the buzzing chorus rose and fell rhythmically in volume, cycling in about a few seconds from louder to softer. Were they all co-ordinating their amplitude? Were the cicadas following a sine wave? If so, how did they know to do this? No doubt there is an explanation, though it probably doesn't involve a tuxedoed Jiminy Cricket conducting the Cicada Philharmonic.

Alas, all the adult Cicadas here will be dead by the end of the month, leaving their eggs to hatch a few weeks later. The areas under trees are littered with winged carcasses, which are soon eaten by birds and other insects. I hope that enough of their young survive to bury themselves in the earth and emerge en masse again in 2021, by which time the Electron, and the Internet, will probably be beamed directly into your brain through bio-electromagnetic implants. (What a horrifying prospect.)

I'll be spending the next week or so in cicada-free New England, and will return in due time after the Summer Solstice.

Posted at 2:08 am | link