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March 14 is celebrated as Pi Day because the date, when written as 3\/14, matches the start of the decimal expansion 3.14159\u2026 of the most famous mathematical constant.<\/p>\n
By itself, pi is simply a number, one among countless others between 3 and 4. What makes it famous is that it\u2019s built into every circle you see \u2013 circumference equals pi times diameter \u2013 not to mention a range of other, unrelated contexts in nature, from the\u00a0bell curve<\/a>\u00a0distribution to\u00a0general relativity<\/a>.<\/p>\n The true reason to celebrate Pi Day is that mathematics, which is a purely abstract subject, turns out to describe our universe so well. My book \u201cThe Big Bang of Numbers<\/a>\u201d explores how remarkably hardwired into our reality math is. Perhaps the most striking evidence comes from mathematical constants: those rare numbers, including pi, that break out of the pack by appearing so frequently \u2013 and often, unexpectedly \u2013 in natural phenomena and related equations, that\u00a0mathematicians like me<\/a>\u00a0exalt them with special names and symbols.<\/p>\n So, what other\u00a0mathematical constants<\/a>\u00a0are worth celebrating? Here are my proposals to start filling out the rest of the calendar.<\/p>\n For January, I nominate the\u00a0Golden Ratio<\/a>, phi. Two quantities are said to be in this ratio if dividing the larger by the smaller quantity gives the same answer as dividing the sum of the two quantities by the larger quantity. Phi equals 1.618\u2026, and since there\u2019s no Jan. 61, we could celebrate it on Jan. 6.<\/p>\n First calculated by Euclid<\/a>, this ratio was popularized by Italian mathematician Luca Pacioli, who wrote a\u00a0book in 1509<\/a>\u00a0extravagantly extolling its aesthetic properties. Supposedly, Leonardo da Vinci, who drew 60 drawings for this book,\u00a0incorporated it into the dimensions of Mona Lisa\u2019s features<\/a>, a choice some claim is responsible for her beauty.<\/p>\n The vertical and horizontal measures of Mona Lisa\u2019s face fit the Golden Ratio. ‘The Big Bang of Numbers’<\/p><\/div>\n The first inkling that phi occurs in nature came from another Italian, Fibonacci, while\u00a0studying how rabbits multiply<\/a>. A common reproductive assumption was that each pair of rabbits begets another pair every month. Start with a single rabbit pair, and successive populations will then follow the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on \u2013 that is, get multiplied by a monthly \u201cgrowth ratio\u201d of 2.<\/p>\n What Fibonacci observed, though, was that rabbits spent the first cycle reaching sexual maturity and only began reproducing after that. A single pair now gives the new, slower progression 1, 1, 2, 3, 5, 8, 13, 21, 34\u2026 instead. This is the\u00a0famous sequence<\/a>\u00a0named after Fibonacci; notice that each population turns out to be the sum of its two predecessors.<\/p>\n Fibonacci\u2019s rabbits don\u2019t really double their population each generation \u2013 their growth ratio actually approaches the 1.618\u2026 of phi. ‘The Big Bang of Numbers’<\/p><\/div>\n How does phi show up amid all these randy rabbits? Well, progressing through the sequence, you see that each number is about 1.6 times the previous one. In fact, this growth ratio keeps getting closer and closer to 1.618\u2026. For instance, 21 equals about 1.615 times 13, and 34 equals about 1.619 times 21. This means the rabbits settle down to reproducing with a growth ratio that is no longer 2, but rather, gets closer and closer to the Golden Ratio.<\/p>\n The number of spirals in a pine cone is usually a Fibonacci number. ‘The Big Bang of Numbers’<\/p><\/div>\n Actual rabbits are unlikely to follow this rule precisely. For one, they have the unfortunate tendency to get eaten by predators. But the\u00a0Fibonacci numbers<\/a>\u00a0\u2013 like 5, 8, 13 and so on \u2013\u00a0show up extensively in nature<\/a>, like in the number of spirals you might see in a typical pine cone. And yes, phi itself makes a few appearances as well, perhaps most notably in the way\u00a0leaves arrange themselves around a stem<\/a>\u00a0to maximize exposure to sunlight.<\/p>\n February offers another blockbuster constant,\u00a0Euler\u2019s number e<\/a>, which has the value 2.718\u2026. So mark next Feb. 7 for the shindig.<\/p>\n To understand e, consider \u201cdoubling\u201d growth again, but now in terms of the \u201cpopulation\u201d of dollars in your bank account. By some miracle, your money in this example is earning you 100% interest, compounded each year. Each $1 invested becomes $2 at year\u2019s end.<\/p>\n Suppose, however, the interest is compounded semiannually. Then 50% of the interest is credited midyear, giving you $1.50. You get the remaining 50% interest on this $1.50 at the end of the year, which works out to $0.75, giving you $2.25 ($1.50 + $0.75). So your investment gets multiplied by 2.25, rather than 2.<\/p>\n What if a war broke out between banks, each offering to compound the same 100% interest over shorter and more frequent intervals? Would the sky be the limit in terms of your payout? The answer is no. You could raise your growth ratio from 2 to about 2.718 \u2013 more precisely, to e \u2013 but\u00a0no higher<\/a>. Although you get more frequent credits, they have progressively diminishing returns.<\/p>\n In the late 17th century, the\u00a0discovery of calculus<\/a>\u00a0led to a quantum leap in people\u2019s ability to grapple with the universe. Math could now analyze anything that changed \u2013 which extended its domain to most phenomena in nature. The constant e is famous because of its\u00a0iconic role in calculus<\/a>: It turns out to be the most natural growth factor to track change. Consequently, it shows up in laws describing many natural processes – from\u00a0population growth<\/a>\u00a0to\u00a0radioactive decay<\/a>.<\/p>\nThe Golden Ratio<\/strong><\/h4>\n
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The constant \u2018e\u2019<\/strong><\/h4>\n
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