March 14, 2016

Celebrating All Things Pi on 3/14

by Bonnie Denmark

There’s no better time to celebrate the magic of mathematics than Pi Day, which of course is on 3/14. Called by some the geekiest day of the year, Pi Day (also Albert Einstein’s birthday) is a great excuse for number lovers of the world to rally around math’s favorite constant, pi (π), the ratio of a circle’s circumference to its diameter.

Let’s start with 3 pi basics:

  • Pi is a constant. This means that no matter what size the circle, the ratio of the circumference to its diameter is always the same.
  • Pi is an irrational number. It cannot be written as a simple fraction—or the ratio of two integers—so it cannot be calculated precisely.
  • Pi is a transcendental number. It cannot be calculated using basic algebraic operations such as roots and powers.

Here’s another point:

  • Because pi is irrational, it does not end or repeat after the decimal point. So far, pi has been calculated to 5 trillion digits, a record set in 2010 using a standard desktop PC. The endlessness of pi makes pi reciting contests a great sport. The latest record was set in 2006 when 60-year-old Japanese counselor Akira Haraguchi recited a full 100,000 digits after the decimal. It took him over 16 hours.

    The first thousand digits of pi (Tom Murphy)

Let’s look at 1 interesting perspective on Haraguchi’s remarkable achievement:

  • The numbers in pi seem endless and random, but it has not been proven that the digits actually are random. In his book Symmetry, University of Oxford professor Marcus du Sautoy claims that the ability to recite tens of thousands of digits “is the sign not of an amazing memory but rather of a mind sensitive to the symmetry and patterns threaded through the piece. Memory, both in the human brain and in computers, is connected very often with an ability to spot structure or connections which allow the hardware to store information in compressed form” (p. 254). Du Sautoy offers one string of 20 numbers in pi as an example: 12345543211234554321.

To round out our Pi Day list, here are 4 more tidbits:

  • Philosophers, astronomers, and mathematicians from Egypt, India, China, Greece, Rome, and other places around the world have pondered pi for thousands of years. The earliest written record of pi was discovered on a Babylonian clay tablet written in cuneiform (ca. 1900-1680 BCE).
  • To compute pi, many ancients used multi-sided polygons to approximate a circle. With this method, Greek mathematician and astronomer Archimedes (287-212 BCE) determined that pi was approximately 22/7, a fraction which is still used today for basic calculations involving pi.

    Pi can be estimated by computing the perimeters of circumscribed and inscribed polygons. (Wikimedia Commons)

  • Pi is used in architecture, space science, electromagnetism studies, DNA research, quantum mechanics, and probability theory, among other fields. Some believe pi was used in calculations for building the Great Pyramid of Giza (2560 BCE), as the distance around the base of the pyramid equals the circumference of a circle whose radius equals the height of the pyramid.

The Great Pyramid of Giza (Wikimedia Commons)

  • To demonstrate how the constant is used by scientists and engineers today, NASA’s Jet Propulsion Laboratory challenges students with pi-based math problems. One problem from last Pi Day asked students to calculate the number of times that Mars Rover Opportunity’s 25-centimeter diameter wheels had rotated when it reached a distance of 42.195 kilometers. (Find the answer here.)

So celebrate pi for the mystery of it, for the history of it, for the iconicity of it, or simply for the fun of it. Happy Pi Day!

 

LEARN MORE

See this year’s set of Pi in the Sky math problems from NASA’s Jet Propulsion Laboratory.

Read how pi is used in calculating sine waves and wave periods in our module Wave Mathematics: Trigonometic functions.

Read how NASA scientists use pi in Pi Day the NASA Way.

Learn more about pi and get ideas for how to celebrate Pi Day at http://www.piday.org/

 

PRINT SOURCES

Du Sautoy, Marcus. Symmetry: A Journey into the Patterns of Nature. Harper, 2008.

Skinner, Stephen. Scared Geometry: Deciphering the Code. Sterling, 2009.

Written by

Bonnie Denmark holds an MA in linguistics and teacher certification in English, ESL, and Spanish. She has devoted her professional life to educational and accessibility issues as a computational linguist, multimedia curriculum developer, educator, and writer. She has also worked nationally and internationally as a language instructor, educational technology consultant, and teacher trainer. Bonnie joined the Visionlearning team as a literacy specialist in 2011, assisting the project by developing comprehension aids for science modules and creating other STEM learning materials.

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