Squaring the Circle Is No Piece of Pi
Math lovers celebrate today (3/14) as Pi Day, in honor of the irrational number pi. Pi is the most recognized mathematical constant in the world. Scholars often consider Pi the most important and intriguing number in all of mathematics.
Pi Day is also Albert Einstein’s birthday, along with the birthdays of Apollo 8 Commander Frank Borman, Astronomer Giovanni Schiaparelli, and last-man-on-the-moon Gene Cernan.
Here are some interesting facts about the irrational and transcendental number:
1. Pi is the most recognized mathematical constant in the world. Scholars often consider Pi the most important and intriguing number in all of mathematics.
2. Pi is the 16th letter of the Greek alphabet just as p is the 16th of our alphabet.
3. The way a river meanders is described by its sinuosity; the length of its winding path divided by the distance from the source to the ocean as measured in a straight line. Strange as it may be, the average river has a sinuosity of around 3.14.
4. Pi is known as an irrational number because it can’t be written as a ratio or simple fraction; while 22/7 is close, it is not exact. It is also a transcendental number, meaning that it is not algebraic – it is not a root of a non-constant polynomial equation with rational coefficients.
5. Scientists in Carl Sagan’s novel Contact are able to unravel enough of pi to find hidden messages from the creators of the human race, allowing humans to access deeper levels of universal awareness.
6. The letter π is the first letter of the Greek word “periphery” and “perimeter.” The symbol π in mathematics represents the ratio of a circle’s circumference to its diameter. In other words, π is the number of times a circle’s diameter will fit around its circumference.
7. Egyptologists and followers of mysticism have been fascinated for centuries by the fact that the Great Pyramid at Giza seems to approximate pi. The vertical height of the pyramid has the same relationship to the perimeter of its base as the radius of a circle has to its circumference.
8. The first 144 digits of pi add up to 666, the Number of the Beast in the Book of Revelation.
9. William Shanks (1812-1882) calculated the first 707 digits of pi. He made a mistake after the 527th place and all the following digits were wrong.
10. The value of pi has now been calculated to more than two trillion digits.
11. As an irrational and transcendental number, pi will continue infinitely without repetition or pattern; it has been calculated to more than 1 trillion digits beyond its decimal point. This makes number enthusiasts very excited. While mere math mortals know pi as 3.14159, some super pi zealots memorize the value of pi to tens of thousands of digits. According to the Pi World Ranking List, Chao Lu holds the world record with his recital of 67,890 digits.
12. Albert Einstein was born on Pi Day: March 14, 1879.
13. In the OJ Simpson trial in 1995, doubts were raised about the reliability of one witness when he got the value of pi wrong.
14. A mysterious 2008 crop circle in Britain shows a coded image representing the first 10 digits of pi.
15. In 2002, a Japanese scientist found 1.24 trillion digits of pi using a powerful computer called the Hitachi SR 8000, breaking all previous records.
16. Pi is the secret code in Alfred Hitchcock’s Torn Curtain and in The Net starring Sandra Bullock.
17. Since there are 360 degrees in a circle and pi is intimately connected with the circle, some mathematicians were delighted to discover that the number 360 is at the 359th digit position of pi.
18. Umberto Eco’s famed book Foucault’s Pendulum associates the mysterious pendulum in the novel with the intrigue of pi.
19. The “squaring the circle” method of understanding pi has fascinated mathematicians because traditionally the circle represents the infinite, immeasurable, and even spiritual world while the square represents the manifest, measurable, and comprehensive world.
20. The first million decimal places of pi consist of 99,959 zeros, 99,758 1s, 100,026 2s, 100,229 3s, 100,230 4s, 100,359 5s, 99,548 6s, 99,800 7s, 99,985 8s, and 100,106 9s.
21. Pi was first rigorously calculated by one of the greatest mathematicians of the ancient world, Archimedes of Syracuse (287-212 B.C.). Archimedes was so engrossed in his work that he did not notice that Roman soldiers had taken the Greek city of Syracuse. When a Roman soldier approached him, he yelled in Greek “Do not touch my circles!” The Roman soldier simply cut off his head and went on his business.
22. A refined value of pi was obtained by the Chinese much earlier than in the West. The Chinese had two advantages over most of the world: they used decimal notations and they used a symbol for zero. European mathematicians would not use a symbolic zero until the late Middle Ages through contact with Indian and Arabic thinkers.
23. Al-Khwarizmi, who lived in Baghdad around A.D. 800, worked on a value of pi calculated to four digits: 3.1416. The term “algorithm” derives from his name, and his text Kitab al-Jabr wal-Muqabala (The Book of Completion Concerning Calculating by Transposition and Reduction) gives us the word “algebra” (from al-Jabr, which means “completion” or “restoration”).
24. William Jones (1675-1749) introduced the symbol “π” in the 1706, and it was later popularized by Leonhard Euler (1707-1783) in 1737
25. Leonardo da Vinci (1452-1519) and artist Albrecht Durer (1471-1528) both briefly worked on “squaring the circle,” or approximating pi.
26. There are no occurrences of the sequence 123456 in the first million digits of pi—but of the eight 12345s that do occur, three are followed by another 5. The sequence 012345 occurs twice and, in both cases, it is followed by another 5.
27. Some scholars claim that humans are programmed to find patterns in the world because it’s the only way we can give meaning to the world and ourselves. Hence, the obsessive search to find patterns in π.
28. In the seventeenth century, pi was freed from the circle and applied also to curves, such as arches and hypocycloids, when it was found that their areas could also be expressed in terms of pi. In the twentieth century, pi has been used in many areas, such as number theory, probability, and chaos theory.
29. John Donne’s (1572-1631) poem “Upon the Translations of the Psalms by Sir Philip Sidney, and the Countess of Pembroke, His Sister” condemns attempts to find an exact value of pi, or to “square a circle,” which Donne views as an attempt to rationalize God:
Eternal God—for whom who ever dare
Seek new expressions, do the circle square,
And thrust into straight corners of poor wit
Thee, who art cornerless and infinite—
30. Many mathematicians claim that it is more correct to say that a circle has an infinite number of corners than to view a circle as being cornerless.
Sources: express.co.uk | livescience.com | www.networkworld.com |