"Ричард Фейнман. Surely You're Joking, Mr. Feynman!/Вы, конечно, шутите, мистер Фейнман! (англ.)" - читать интересную книгу автора

better and better, and I eventually got to be the head of the team. So I
learned to do algebra very quickly, and it came in handy in college. When we
had a problem in calculus, I was very quick to see where it was going and to
do the algebra - fast.
Another thing I did in high school was to invent problems and theorems.
I mean, if I were doing any mathematical thing at all, I would find some
practical example for which it would be useful. I invented a set of
right-triangle problems. But instead of giving the lengths of two of the
sides to find the third, I gave the difference of the two sides. A typical
example was: There's a flagpole, and there's a rope that comes down from the
top. When you hold the rope straight down, it's three feet longer than the
pole, and when you pull the rope out tight, it's five feet from the base of
the pole. How high is the pole?
I developed some equations for solving problems like that, and as a
result I noticed some connection - perhaps it was sin^2 + cos^2 = 1 - that
reminded me of trigonometry. Now, a few years earlier, perhaps when I was
eleven or twelve, I had read a book on trigonometry that I had checked out
from the library, but the book was by now long gone. I remembered only that
trigonometry had something to do with relations between sines and cosines.
So I began to work out all the relations by drawing triangles, and each one
I proved, by myself. I also calculated the sine, cosine, and tangent of
every five degrees, starting with the sine of five degrees as given, by
addition and half-angle formulas that I had worked out.
A few years later, when we studied trigonometry in school, I still had
my notes and I saw that my demonstrations were often different from those in
the book. Sometimes, for a thing where I didn't notice a simple way to do
it, I went all over the place till I got it. Other times, my way was most
clever - the standard demonstration in the book was much more complicated!
So sometimes I had 'em beat, and sometimes it was the other way around.
While I was doing all this trigonometry, I didn't like the symbols for
sine, cosine, tangent, and so on. To me, "sin f" looked like s times i times
n times f! So I invented another symbol, like a square root sign, that was a
sigma with a long arm sticking out of it, and I put the f underneath. For
the tangent it was a tau with the top of the tau extended, and for the
cosine I made a kind of gamma, but it looked a little bit like the square
root sign.
Now the inverse sine was the same sigma, but left-to-right reflected so
that it started with the horizontal line with the value underneath, and then
the sigma. That was the inverse sine, NOT sin^-1 f - that was crazy! They
had that in books! To me, sin^-1 meant 1/sine, the reciprocal. So my symbols
were better.
I didn't like f(x) - that looked to me like f times x. I also didn't
like dy/dx - you have a tendency to cancel the d's - so I made a different
sign, something like an sign. For logarithms it was a big L extended to
the right, with the thing you take the log of inside, and so on.
I thought my symbols were just as good, if not better, than the regular
symbols - it doesn't make any difference what symbols you use - but I
discovered later that it does make a difference. Once when I was explaining
something to another kid in high school, without thinking I started to make
these symbols, and he said, "What the hell are those?" I realized then that