> Now I will go on with my own experience as a youngster in mathematics. Another thing that my father told me--and I can't quite explain it, because it was more an emotion than a telling--was that the ratio of the circumference to the diameter of all circles was always the same, no matter what the size. That didn't seem to me too unobvious, but the ratio had some marvelous property. That was a wonderful number, a deep number, pi. There was a mystery about this number that I didn't quite understand as a youth, but this was a great thing, and the result was that I looked for pi everywhere.
When I was learning later in school how to make the decimals for fractions, and how to make 3 1/8, 1 wrote 3.125 and, thinking I recognized a friend, wrote that it equals pi, the ratio of circumference to diameter of a circle. The teacher corrected it to 3.1416.
I illustrate these things to show an influence. The idea that there is a mystery, that there is a wonder about the number was important to me--not what the number was. Very much later, when I was doing experiments in the laboratory--I mean my own home laboratory, fiddling around--no, excuse me, I didn't do experiments, I never did; I just fiddled around. Gradually, through books and manuals, I began to discover there were formulas applicable to electricity in relating the current and resistance, and so on. One day, looking at the formulas in some book or other, I discovered a formula for the frequency of a resonant circuit, which was f = 1/2 pi LC, where L is the inductance and C the capacitance of the... circle? You laugh, but I was very serious then. Pi was a thing with circles, and here is pi coming out of an electric circuit. Where was the circle? Do those of you who laughed know how that comes about?
I have to love the thing. I have to look for it. I have to think about it. And then I realized, of course, that the coils are made in circles. About a half year later, I found another book which gave the inductance of round coils and square coils, and there were other pi's in those formulas. I began to think about it again, and I realized that the pi did not come from the circular coils. I understand it better now; but in my heart I still don't know where that circle is, where that pi comes from.
When I was learning later in school how to make the decimals for fractions, and how to make 3 1/8, 1 wrote 3.125 and, thinking I recognized a friend, wrote that it equals pi, the ratio of circumference to diameter of a circle. The teacher corrected it to 3.1416.
I illustrate these things to show an influence. The idea that there is a mystery, that there is a wonder about the number was important to me--not what the number was. Very much later, when I was doing experiments in the laboratory--I mean my own home laboratory, fiddling around--no, excuse me, I didn't do experiments, I never did; I just fiddled around. Gradually, through books and manuals, I began to discover there were formulas applicable to electricity in relating the current and resistance, and so on. One day, looking at the formulas in some book or other, I discovered a formula for the frequency of a resonant circuit, which was f = 1/2 pi LC, where L is the inductance and C the capacitance of the... circle? You laugh, but I was very serious then. Pi was a thing with circles, and here is pi coming out of an electric circuit. Where was the circle? Do those of you who laughed know how that comes about?
I have to love the thing. I have to look for it. I have to think about it. And then I realized, of course, that the coils are made in circles. About a half year later, I found another book which gave the inductance of round coils and square coils, and there were other pi's in those formulas. I began to think about it again, and I realized that the pi did not come from the circular coils. I understand it better now; but in my heart I still don't know where that circle is, where that pi comes from.
-Richard Feynman
"What is Science?"
1966 Lecture
http://www.fotuva.org/feynman/what_is_science.html