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" For example, one time we were putting some numbers into a formula, and got to 48 squared. I reach for the Marchant calculator, and he says, “That’s 2,300.” I begin to push the buttons, and he says, “If you want it exactly, it’s 2,304.” The machine says 2,304. “Gee! That’s pretty remarkable!” I say. “Don’t you know how to square numbers near 50?” he says. “You square 50—that’s 2,500—and subtract 100 times the difference of your number from 50 (in this case it’s 2), so you have 2,300. If you want the correction, square the difference and add it on. That makes 2,304. "
― Steven H. Strogatz , The Joy of x: A Guided Tour of Math, from One to Infinity
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" This explanation was long in coming. It required more than fifty years of insights into quantum theory, and was proposed in 1957 by the physicists John Bardeen, Leon Cooper, and Robert Schrieffer. Its most surprising innovation is the idea that electrons can form pairs. Normally we would expect electrons to repel each other, since they are all negatively charged. The pairing mechanism is indirect. The interaction between the electrons is mediated by the lattice of positively charged ions. (Earlier, we referred to these ions as atoms. But since they are freely sharing some of their conduction electrons, they are positively charged and so should be called ions. Their positive charge is the key to the pairing mechanism.) When an electron moves through the lattice, it pulls the lattice toward it slightly, because of its opposite charge. That deformation creates a region of space with a tiny excess of positive charge, which tends to attract a second electron toward it. In that indirect sense, the two electrons are linked. "
― Steven H. Strogatz , Sync: The Emerging Science of Spontaneous Order