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## Friday, March 14, 2014

### No Pi Day in Singapore

 Number Photos ibbly.com

Because of the way Singaporeans write their dates (DD/MM/YYYY), celebrating Pi Day with school students in Singapore is a mere calendrical impossibility. At best, Singaporeans' celebration of Pi Day could be likened to Americans' celebration of the Abacus Day in the United States.

At a time when so much is written about the merits of Singapore math, it's just frustrating that Singapore students and teachers aren't able to commemorate the most popular constant in mathematics on March 14. However, in Singapore, we haven't let calendrical concerns prevent us from indulging ourselves in some extra-mathematical activities, peeping at some hidden pi treasures from yesteryear.

For us, the diehard supporters, let's look at a dozen irrational or transcendental musings on Pi.

1. Pi in the Sky—The Digits of Pi Eternally Linked!

The German mathematician Ludolph van Ceulen (1540-1610) spent much of his life calculating the decimal expansion of pi. The professor at the University of Leiden determined pi to 35 decimal places. When he died in 1610, the numbers 288 were carved on his tombstone (now lost) in St. Peter's churchyard, at Leyden—in the 33rd, 34th, and 35th decimal places of pi.

 Ludolph van Ceulen died of exhaustion after deriving 35 decimal places of pi, which are engraved on his tombstone. proofmathisbeautiful.tumblr.com

2. A Pi Bill—To Pi or Not to Pi

Over the centuries, mathematical cranks, particularly the circle squarers, had submitted proofs of pi related to different values.
 To pi or not to pi: Changing pi to 3.2  FP54U3YGZSNYZFC.LARGE.jpg

The notorious Edwin Goodwin (1828-1902) who believed that a square and a circle of the same perimeter had the same area, was unique in getting so many values of pi: 4, 3.555556. 3.3333333, ..., 3.2, 2,56. His attempt to legislate a legal value of pi of 4 exemplifies that irrational forces are present, ready to shake up the ivory towers.

My birth dates are at positions 3,749,507 and 25,864,351. And my mobile numbers start at positions 308,617,971 in pi. Where do you occur in pi? It's never too late to test the power of your computer in searching for your IC number or phone numbers in the decimal expansion of pi—claim your "digital imprint," and immortalize it!

4. Tattooing Pi

 blogs.discovermagazine.com

Are you so much in love with the beauty of Pi that you're prepared to get a tattoo of it on some inconspicuous parts of your body?

5. The Bible Encoded in Pi

When coded in numeric form, every text in the world can be stored. Besides the biblical value of pi being equal to 3, as deduced from 1 Kings 7:23 and II Chronicles 4:2—which describes a round "sea" (large bowl) made of metal, 10 cubits in diameter and 30 cubits in circumference—could the Bible, with an estimated 10⁷ digits occur in the digits of pi? Or, at least, could some of the 66 books of the Holy Scriptures be encoded in it? Or, what about some Shakespeare's plays

For young readers, what about the frequency of your favorite digit, or "lucky number," appearing within the first million or billon places of pi?

6. Pi Digits for Sale

 https://www.scienceteecher.com/Pi-T-shirts/

If random numbers are a multi-million business, would it unethical to commercialize the digits of pi in future, although up to now they have been used primarily for scientific purposes?

7. Meta-Pi: Does π Contain π Itself?

Does pi contain itself, or at least finite sequences of it? After all, some numerologists claimed that the decimal expansion of pi contains the secrets of the universe. For instance, Dr. Matrix, the renowned numerologist and the darling of number perverts, noted that "Pi conveys the entire history of the human race."

8. Pi Quickies, Trickies, and Toughies

The beauty, ubiquity, and utility of pi has blessed recreational mathematicians with a number of mathematical quickiestrickies, and toughies.

What are the next numbers in the following sequence? 3, 1, 4, 1, 5, ...

Show that there exists precisely one set of three single-digit positive integers a, b, c such that π/4 = tan¹ 1/a + tan¹ 1/b + tan¹ 1/c[a = 2, b = 5, c = 8]

What is the probability that a coin tossed an even number of times will land an equal number of times on its head and on its tail?

What is the probability that two numbers, p and q, chosen at random be relatively prime? (6/π²)

Prove that pi is irrational.

Which is larger? eπ or πe

9. Contact with ET
 Did the pi-aliens do that?

In the short story Contact by Carl Sagan, an extraterrestrial tells a woman on Earth that pi contains an important message for us in encrypted form.

By using zeros and ones in the decimal representation of pi, we can send meaningful messages to beings or aliens from other galaxies.

10. Pi Mnemonics and Haikus in Chinese and Malay

For the majority of us who aren't blessed with a sharp memory, creating mnemonic devices that will allow us to more easily memorize the digits of pi is a less-stressful mental exercise. Besides, long after we've forgotten our school math, composing meaningful mnemonics could help us remember, say, the first twenty-five digits of pi until we breathe our last breath.

Other than remembering mnemonics in English, such as "May I have a large container of coffee?," why not compose some in other languages and dialects? And some pi-kus (pi-haikus) as well?

π = 3.14 and John 3:16

So close, yet so far
Rational and eternal
The union is null.

11. Pi on Mars and Venus
Is the value of pi different on other planets, or in other galaxies, if the curvature of space, or multi-dimensionality, is taken into account? At least, from a philosophical standpoint, could pi take on different values, just like the sum of the interior angles of a triangle needn't always be 180 degrees?

12. Non-Euclidean Geometry and Pi

In Euclidean and non-Euclidean geometries, the ratio of the circumference, C, of a circle to its diameter, d, depends on the type of geometry. In other words, depending on the geometric milieu, can we then say that the value of pi varies?

Euclidean geometry: C/dπ

Lobachevskian geometry: C/d > π

Riemannian geometry: C/d < π

Pi-fully yours

References

Berggren, L., Borwein, J. & Borwein, P. (2000). Pi: A source book (2nd ed.). Springer.

Gardner, M. (1985). The Magic Numbers of Dr. Matrix. New York, Dorset Press.

Posamentier, A. S. & Lehmann, I. (2004). Pi: A biography of the world's most mysterious number. New York: Prometheus Books.

Yan, K. C. (2013). 17 theomatical haikus for math educators. Yan's One Minute Math Blog, May 18, 2013.

Yan, K. C. (2009). Geometrical quickies & trickiesSingapore: GLM Pte Ltd.

© Yan Kow Cheong, March 14, 2014.