"Here's Looking at Euclid" [.]

[fiefoe]

The book gets less effective trying to explain the evolution of mathematics without going into enough proofs.

• A pilot’s slide rule is circular, is called a “whiz wheel,” and measures speed, distance, time, fuel consumption, temperature and air density.
• More than just an elegant piece of math, Piet Hein’s superellipse touched on a deeper human theme—the ever-present conflict in our surroundings between circles and straight lines.
• Franklin is also said to have invented another square in his forties. Over the course of a single evening, he composed an incredible 16 × 16 square which he claimed was “the most magically magical of any magic square ever made by any magician.”
• In fact, 17-clue Sudokus inspire something of a combinatorics cult.
• What Sam Loyd did with Get Off the Earth was to curve the geometrical vanish so it was in a circular form, and in place of lines put Chinese warriors.
• Demaine is now applying his theoretical work on hinged dissections to make robots that can transform from one shape into another through folding.
• It turns out that with a language, jugglers have been able to discover tricks that had eluded them for thousands of years.
• Consider that for a moment: Conway’s powertrain is such a lethal machine that it annihilates every number in the universe apart from 2592 and 24547284284866560000000000—two seemingly unrelated, fixed points in the never-ending expanse of numbers.
• A corollary of this result is that the harmonic series with only the terms including 314159 must add up to infinity.
• The Fibonacci recurrence algorithm of adding two consecutive terms in a sequence to make the next one is so powerful that whatever two numbers you start with, the ratio of consecutive terms always converges to phi.
• Many galaxies are in the shape of logarithmic spirals.
• It was weird to realize that in two dimensions the chance of a drunkard’s walking back into the lamppost was an absolute certainty, but it seems even weirder to think that a bee buzzing forever is very likely never to return home.
• If the coin is tossed infinitely many times, the most likely number of times he will swap sides is zero. The next most likely number is one, then two, three, and so on.
• Kelly tells you to bet the fraction of your bankroll determined by . In this case the edge is 10 percent and the odds are even (or 1 to 1), making equal to 10 percent. So, wager 10 per cent of the bankroll every bet.
• “Beat the Dealer was kind of the first quant book out there and it led fairly directly to quite a revolution,” said Thorp.
• Poincaré concluded that the baker hadn’t stopped his cheapskate, short-measure ways, but instead was giving Poincaré, the squeaky wheel, the largest loaf at hand, thus introducing bias in the distribution.
• If by looking at data from human populations you could detect reliable patterns, then it was only a small leap to realize that populations of, for example, atoms also behaved with predictable regularities.
• "cosmic order expressed by the [bell curve]... reigns with serenity and in complete self-effacement amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of unreason.”
• Imagine that each row of pins in the quincunx is a random variable that will create an error in measurement. Either it will add a small amount to the correct measurement or it will subtract a small amount.
• The more random errors we can introduce into measurement, the more likely it is that we will get a bell curve from the data—even if the phenomenon being measured is not normally distributed.
• It was only on reading about János’s results, which were published in 1831 as an appendix in a book by his father, Farkas, that Gauss revealed to anyone he had also considered the falsity of the parallel postulate.

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