How Math Explains the World.pdf
and he and physicists Boris Podolsky and Nathan Rosen devised, in 1935, a thought experiment, known as the EPR experiment,^10 th ...
Wobegon. Axial spin is another example of conjugate variables—it is im- possible to simultaneously determine the spin of a photo ...
tion from traveling faster than light, what is happening here is that the probability wave has collapsed instantly throughout th ...
J. Bronowski, The Ascent of Man (Boston: Little, Brown, 1973), p. 336. See http:// en .wikipedia .org/ wiki/ Schr %C3 %B6dinger ...
Section II The Incomplete To olb ox ...
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4 Impossible Constructions The Brotherhood It was a powerful secret society of men bound together by common be- liefs in religio ...
The Greeks actually constructed both numerical and geometrical proofs of this fact—the numerical proof was based on the concept ...
plague lasted for almost four years, and killed a third of the Athenian population. Only recently have we discovered through DNA ...
mathematician, has gone before. Menaechmus is credited with the dis- covery of the hyperbola and parabola,^5 which are two of th ...
as others.”^7 It seems that even in ancient Greece, they felt that another name for the runner-up is “loser.” Other problems in ...
regular polygons with three, four, and six sides, and there is a slightly more complex construction for a regular polygon with f ...
When he was nineteen years old, Gauss supplied a straightedge-and- compass construction for the regular heptadecagon—the polygon ...
constructable numbers. Simple trigonometry showed that the sine and cosine of a 20-degree angle were not constructable numbers.^ ...
straightedge-and-compass construction. To this day Lindemann gets the credit, although much of the earlier work was done by the ...
regular polygons revealed a surprising connection between geometry and an interesting class of prime numbers. Indeed, this is on ...
we have seen, the world according to quantum mechanics consists of a collection of whole numbers of basic units—mass, energy, le ...
but with a detailed analysis of the error in the “proof.” And guess who got to perform that analysis? Junior faculty members—lik ...
One of the great benefits of living in the Information Age is the extraordinary amount of classic material that is available on ...
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