[March 14 (3/14) is officially Pi Day. Pi gets all the fanfare,
but other numbers also deserve their own math holidays. ]
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PI DAY! AND OTHER NUMBERS THAT DESERVE A HOLIDAY  
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Manil Suri
March 8, 2023
The Conversation
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_ March 14 (3/14) is officially Pi Day. Pi gets all the fanfare, but
other numbers also deserve their own math holidays. _

"Chambered Nautilus Shell - detail. A nautilus shell is an example of
a logarithmic spiral , by jitze (CC BY 2.0)

 

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

By itself, pi is simply a number, one among countless others between 3
and 4. What makes it famous is that it’s built into every circle you
see – circumference equals pi times diameter – not to mention a
range of other, unrelated contexts in nature, from the bell curve
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to general relativity
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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 “The Big Bang of Numbers
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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 – and often,
unexpectedly – in natural phenomena and related equations, that
mathematicians like me [[link removed]] exalt them with
special names and symbols.

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

The Golden Ratio

For January, I nominate the Golden Ratio
[[link removed]], 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…, and since
there’s no Jan. 61, we could celebrate it on Jan. 6.

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

[a rectangle over Mona Lisa's face labels the vertical and horizontal
ratio]
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The vertical and horizontal measures of Mona Lisa’s face fit the
Golden Ratio. 'The Big Bang of Numbers'
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The first inkling that phi occurs in nature came from another Italian,
Fibonacci, while studying how rabbits multiply
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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 – that is, get multiplied by a monthly “growth
ratio” of 2.

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… instead. This is the famous sequence
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Fibonacci; notice that each population turns out to be the sum of its
two predecessors.

[diagram of how many rabbits you'll have month by month]
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Fibonacci’s rabbits don’t really double their population each
generation – their growth ratio actually approaches the 1.618… of
phi. 'The Big Bang of Numbers'
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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…. 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.

['petals' on the base of a pine cone spiral outward from the center in
13 lines]
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The number of spirals in a pine cone is usually a Fibonacci number.
'The Big Bang of Numbers' [[link removed]]

Actual rabbits are unlikely to follow this rule precisely. For one,
they have the unfortunate tendency to get eaten by predators. But the
Fibonacci numbers
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13 and so on – show up extensively in nature
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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
leaves arrange themselves around a stem
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sunlight.

The constant ‘e’

February offers another blockbuster constant, Euler’s number e
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Feb. 7 for the shindig.

To understand e, consider “doubling” growth again, but now in
terms of the “population” 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’s end.

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.

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 – more precisely, to e
– but no higher
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Although you get more frequent credits, they have progressively
diminishing returns.

In the late 17th century, the discovery of calculus
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quantum leap in people’s ability to grapple with the universe. Math
could now analyze anything that changed – which extended its domain
to most phenomena in nature. The constant e is famous because of its
iconic role in calculus [[link removed]]: It
turns out to be the most natural growth factor to track change.
Consequently, it shows up in laws describing many natural processes -
from population growth
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to radioactive decay [[link removed]].

The constant e is a big part of calculus – and turns up in all kinds
of natural phenomena.

Next on our calendar of mathematical constants would come pi, of
course, for March. My nominee for April is Feigenbaum’s constant
delta [[link removed]], which
equals 4.669… and measures how quickly growth processes spin off
into chaos.

I’ll wait for my first batch to achieve official holiday status
before going any further – happy to consider any candidates you want
to nominate [[link removed]].[The Conversation]

Manil Suri [[link removed]],
Professor of Mathematics and Statistics, _University of Maryland,
Baltimore County
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This article is republished from The Conversation
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the original article
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* mathematics
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* Science
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* pi day
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