Pi gets all the fanfare, but other numbers also deserve their own math holidays

March 14 is celebrated as Pi Day because the date, when written as 3/14, corresponds to the start of the decimal expansion 3.14159… of the most famous mathematical constant.

By itself, pi is simply a number, one of countless others between 3 and 4. What makes it famous is that it’s embedded in every circle you see – the circumference is pi times the diameter – not to mention a range of other unrelated natural contexts, from the bell curve distribution to general relativity.

The real reason to celebrate Pi Day is that mathematics, which is a purely abstract subject, describes our universe so well. My book “The Big Bang of Numbers” explores how mathematics is remarkably rooted in our reality. Perhaps the most striking evidence comes from mathematical constants: those rare numbers, including pi, that stand out from the crowd by appearing so frequently – and often unexpectedly – ​​in natural phenomena and associated equations, that mathematicians like me exalt them with special names and symbols.

So what other mathematical constants are worth celebrating? Here are my suggestions to start filling out the rest of the calendar.

The golden ratio

For January, I call the golden ratio, phi. Two quantities are said to be in this ratio if dividing the larger by the smaller gives the same answer as dividing the sum of the two quantities by the larger. Phi is equal to 1.618…, and since there is no January 61, we could celebrate it on January 6.

First calculated by Euclid, this ratio was popularized by the Italian mathematician Luca Pacioli, who wrote a book in 1509 extravagantly extolling its aesthetic properties. It is assumed that Leonardo da Vinci, who drew 60 designs for this book, incorporated them into the dimensions of the Mona Lisa’s features, a choice that some believe is responsible for her beauty.

The first idea that phi exists in nature came from another Italian, Fibonacci, while he was studying how rabbits multiply. A common assumption in breeding was that each pair of rabbits fathers another pair each month. Start with a single pair of rabbits, and successive populations will then follow the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on – that is, they will be multiplied by a monthly “growth rate” of 2.

What Fibonacci observed, however, 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… instead. This is the famous sequence named after Fibonacci; note that each population turns out to be the sum of its two predecessors.

How does phi appear among all these excited bunnies? Well, as you progress through the sequence, you see that each number is approximately 1.6 times the previous one. In fact, this growth rate keeps getting closer to 1,618…. For example, 21 is about 1.615 times 13, and 34 is about 1.619 times 21. This means that rabbits are settling down to reproduce with a growth rate that is no longer 2, but is getting closer and closer to the golden ratio.

Real rabbits are unlikely to follow this rule exactly. On the one hand, they have the unfortunate tendency to be eaten by predators. But Fibonacci numbers – like 5, 8, 13 and so on – appear widely in nature, such as in the number of spirals one might see in a typical pine cone. And yes, phi itself also makes a few appearances, perhaps most notably in the way leaves arrange themselves around a stem to maximize exposure to sunlight.

The constant ‘e’

February offers another successful constant, the Euler number e, which is worth 2.718…. So mark next February 7 for the party.

To understand this, consider “doubling” growth again, but now in terms of the “population” of dollars in your bank account. Miraculously, your money in this example earns you 100% interest, compounded annually. Every dollar invested becomes $2 at the end of the year.

Let us assume, however, that the interest is compounded semi-annually. Then 50% of the interest is credited mid-year, giving you $1.50. You get the remaining 50% interest on that $1.50 at the end of the year, which equals $0.75, giving you $2.25 ($1.50 + $0.75). Your investment is therefore multiplied by 2.25 instead of 2.

What if a war broke out between the banks, each offering to compound the same 100% interest over shorter, more frequent intervals? Could the sky be the limit in terms of payment? The answer is no. You could increase your growth rate from 2 to around 2.718 – more precisely to e – but no more. Although you get more frequent credits, their returns gradually decrease.

In the late 17th century, the discovery of calculus led to a quantum leap in people’s ability to comprehend the universe. Mathematics could now analyze everything that changed – which extended its domain to most natural phenomena. The constant e is famous because of its iconic role in calculus: it turns out to be the most natural growth factor for tracking change. Therefore, it appears in the laws describing many natural processes – from population growth to radioactive decay.

Next on our calendar of mathematical constants would of course come pi for March. My candidate for April is Feigenbaum’s constant delta, which equals 4.669… and measures how quickly growth processes turn into chaos.

I will wait until my first batch achieves public holiday status before proceeding further – I will be happy to consider any candidates you wish to nominate.

This article is republished from The Conversation, an independent, nonprofit news organization that brings you trusted facts and analysis to help you make sense of our complex world. It was written by: Manil Suri, University of Maryland, Baltimore County

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Manil Suri does not work for, consult, own shares in, or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.