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500 Digits of Pi.docxmtms2002-03-374a.pdfPi Formulas
DIAMETER = RADIUS x 2
CIRCUMFERENCE = π x DIAMETER
DIAMETER = CIRCUMFERENCE ÷ π
AREA OF A CIRCLE = π x (RADIUS)2
Top 25 Most Interesting Pi Facts
Top 25 Most Interesting Pi Facts
Pi is the most studied number in mathematics, and for good reason. The number pi is integral to our understanding of geometry. Pi has uses in physics, astronomy, and mathematics. Pi is used in architecture and construction as well, and has been a vital part of everything from arches and bridges to the Pyramids of Giza.
Here are 25 fascinating facts about pi:
Here are 25 fascinating facts about pi:
1. The symbol for Pi has been in use for over 250 years. The symbol was introduced by William Jones, an Anglo-Welsh philologist (someone who studies language) in 1706. The symbol was made popular by the mathematician Leonhard Euler.
2. Since the exact value of pi can never be calculated, we can never find the accurate area or circumference of a circle.
3. March 14 or 3/14 is celebrated as pi day because 3.14 are the first digits of pi. Math nerds around the world love celebrating this infinitely long, never-ending number.
4. The record for reciting the most number of decimal places of Pi was achieved by Rajveer Meena at VIT University, Vellore, India on 21 March 2015. He was able to recite 70,000 decimal places. To maintain the sanctity of the record, Rajveer wore a blindfold throughout the duration of his recall, which took an astonishing 10 hours! Can’t believe it? Well, here is the evidence.
5. Pi is actually a part of Egyptian mythology. People in Egypt believed that the pyramids of Giza were built on the principles of pi. The vertical height of the pyramids have the same relationship with the perimeter of their base as the relationship between a circle’s radius and its circumference. The pyramids are phenomenal structures and are one of the seven wonders of the world.
6. Physicist Larry Shaw started celebrating 14 March as Pi day at San Francisco’s Exploratorium science museum. There he is known as the Prince of Pi.
7. There is an entire language made from the number Pi. But how is that possible? Well, some people loved pi enough to invent a dialect based on it. In “Pi-lish” the number of letters in each word match the corresponding digit of pi. This first word has three letters, the second has one letter, the third has four letters, and so on. This language is more popular than you might think. Software engineer Michael Keith wrote an entire book, called Not a Wake in this language.
8. Pi wasn’t always known as pi. Before the 1700s, people referred to the number we know as pi as “the quantity which when the diameter is multiplied by it, yields the circumference”. Not surprisingly, people got tired of saying so much whenever they wanted to talk about Pi. The Welsh mathematician William Jones, a friend of Sir Isaac Newton, began using the symbol for pi in 1706.
9. We will never be able to find all the digits of pi because of its very definition as an irrational number. Babylonian civilization used the fraction 3 ⅛, the Chinese used the integer 3. By 1665, Isaac Newton calculated pi to 16 decimal places. Computers hadn’t been invented yet, so this was a pretty big deal. In the early 1700s Thomas Lagney calculated 127 decimal places of pi, reaching a new record. In the second half of the twentieth century, the number of digits of pi increased from about 2000 to 500,000 on the CDC 6600, one of the first computers ever made. This record was broken again in 2017 when a Swiss scientist computed more than 22 trillion digits of pi. The calculation took over a hundred days.
10. The usefulness of pi has been a matter of debate, although it is loved by a lot of math enthusiasts. Some believe that tau (which amounts to 2π) is a better suited to circle calculations. For instance, you can multiply tau with the radius of a to calculate its circumference more intuitively. Tau/4 also represents the angle of a quarter of a circle.
11. In the Exploratorium science museum, a circular parade happens every year on pi day. Each person participating holds one digit in the number pi. It wasn’t celebrated around the United States like it is now until Congress passed Resolution 224, which designated March 3rd as pi day. Congress hoped that celebrating pi day would cultivate a higher level of enthusiasm for math and science among American students.
12. The calculation of pi is a stress test for a computer. It works just like a digital cardiogram since it indicates the level of activity within the computer’s processor.
13. Givenchy sells a men’s cologne with the name ‘Pi’. The company markets this product as capable of enhancing the attractiveness of intelligent and visionary men.
14. The number pi is not just an important part of conversations among mathematicians or students. In the famous O.J. Simpson trial, the defense attorney and FBI agent’s argument revolved around the value of pi. The FBI agent’s findings in the case weren’t accurate because he used pi inaccurately.
15. The number pi was so alluring, even in the 16th century, that Dutch-German mathematician Ludolph van Ceulen spent most of his life calculating the first 36 digits of pi. It is said that the first 36 numbers were engraved on his tombstone, which is now lost.
16. William Shanks, a British mathematician, worked manually to find the digits of pi in 1873. He spent many years trying to calculate the pi digits by hand and found the first 707 digits. Unfortunately, the 527th digit he found was wrong, which made all the following digits wrong as well.
17. In the year 1888, an Indiana country doctor claimed that he learnt the exact measure of a circle through supernatural means. He believed in his “supernatural” knowledge so much that he filed a proposal to pass a bill in the Indiana legislature so that he could copyright his genius findings. However, there was a math professor in the legislature who showed the fellow how his proposed bill would result in a wrong value of pi.
18. The number pi is literally infinitely long. But the number 123456 doesn’t appear anywhere in the first million digits of pi. It is a bit shocking because if a million digits of pi don’t have the sequence 124356, it definitely is the most unique number.
19. Chinese people were far ahead of the West in finding the digits of pi. Why? Chinese mathematicians were ahead in the pi game because of two reasons: they had decimal notations and they had a symbol for the number zero. It wasn’t until the late middle ages that European mathematicians started using the number zero. At that time, European mathematicians partnered with Arab and Indian minds to bring the symbol of zero into their system.
20. In ancient times, mathematicians used a unique method to calculate pi. They would add more and more sides to a polygon so that its area approached the area of a circle. Archimedes, the most famous Greek mathematician and inventor, used a polygon with 96 sides. Many other mathematicians also used this polygon-method to compute the infinitely long number pi. In China, a mathematician used over 3,000 sides in a polygon to arrive at the value 3.14159. Another mathematician used about 25,000 sides to calculate pi.
21. Many mathematicians believe that it is more accurate to say that a circle has infinite corners than it is to say that it has none. It is only reasonable to assume that the infinite number of corners in a circle correlates to the infinite number of digits of pi.
22. The number pi is very effective when you used in calculations For instance, rounding the number pi to just 9 digits after the decimal and use it to calculate earth’s circumference yield incredibly accurate results. For every 25,000 miles, the number pi will only err to 1/4th of an inch.
23. Even today, people are racing to calculate more digits of pi in a never ending competition. In the year 2010, a Japanese engineer and an American computer wizard broke the record for the most number of pi digits by calculating up to 5 trillion digits of pi. The amazing part is that they didn’t use any supercomputers. They just used desktop computers, 20 external hard disks, and their brilliant minds.
24. The Greek letter π is the first letter of the word periphery and perimeter. And as we all know, pi is the ratio of a circle’s “periphery” to its diameter.
25. Interestingly, some of the most famous scientists in the world have a connection to pi day. Albert Einstein was born on March 14th, 1879. Stephen Hawking died on March 15th, 2018 at the age of 76.
Curious Pi Facts
Curious Pi Facts
“This value, represented by the symbol π (pi), has puzzled mathematicians for nearly four thousand years, generating more interest, consuming more brainpower, and filling more waste baskets with discarded theories than any other single number…you will never find an exact value for π.” David Blatner The Joy of π...
π Humankind’s fascination with pi vastly transcends practical need. “Ten decimals are sufficient to give the circumference of the earth to the fraction of an inch [if earth were a perfect circle which it is not], and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful telescope.” Simon Newcomb quoted in Mathematics and the Imagination by Edward Kasner and James Newman.
π Pi’s symbol is the 16th letter of the Greek alphabet (π).
π The first time the symbol π (16th letter of the Greek alphabet) was used to denote pi was in William Jone’s Symopsis Palmariorum Matheseos published in 1706.
π Egyptian scribe Ahmes’ “Rhind Papyrus” implies a pi ratio of 3.16049 over 3,650 years ago – within one percent of the true value – and it is the first know reference to pi.
π A number of ancient Greeks, including Archimedes of Syracuse, offered values for pi starting about 2,500 years ago.
π China’s Ch’ang Hong implied a pi ratio of 3.162 about 1,800 years ago.
π 1,500 years ago Chinese astronomer Tsu Ch’ungchih and his son, Tsu Keng-chih deduced that pi is approximately 3.1415929 – astoundingly they were within 8-millionths of 1 percent difference from the now-accepted value for pi.
π Also around 1,500 years ago in India, mathematician Aryabhata approximated pi at 3.1416.
π In 1579 French lawyer and mathematician Francois Viète for the first time described pi using an infinite product, one of the first steps in the evolution of mathematics toward trigonometry and calculus.
π German mathematician Ludolf van Ceulen spent most of his adult life calculating pi to 35 decimals by the time of his death in 1610 – legend says his pi value was engraved on his tombstone in St. Peter’s church in Leyden, Germany. The tombstone has since been lost and there is no report if it was round or rectangular in shape.
π Leonardo da Vinci (1452-1519) developed a novel way to measure the area of a circle using the rotation of wheel half the thickness of its radius.
π By 1699, Englishman Abraham Sharp found 72 decimals of pi.
π By 1873, Englishman William Shanks calculated pi to 707 digits. “The accomplishment was hailed throughout the civilized world as the unveiling of a great mathematical truth,” according to Joy of Pi by David Blatner. (Shanks had made a mistake after the 527th place, making all subsequent numbers wrong -- an error that was not discovered until 72 years later!)
π In 1947 English mathematician D.F. Ferguson was believed to be first to use a mechanical calculator to compute pi. He computed pi to 808 digits. In 1948, Levi Smith and John Wrench found the 1,000th digit of pi. Crude calculators of the era could only compute one or two additional digits per day.
π In 1948 in Aberdeen, Maryland, George Reitwiesner, John von Neumann and N.C. Metropolis used one of the earliest computers, ENIAC, to compute pi to 2,037 digits. The ENIAC had 19,000 vacuum tubes and hundreds of thousands of transistors and capacitors. It could compute an additional pi digit every two minutes.
π In 1958, an IBM 704 computer calculated the first 707 digits of pi in 40 seconds – a feat that had taken a year on the ENIAC computer a decade earlier, and had taken mathematician William Shanks a major portion of his adult lifetime to do by hand. In 1973, Jean Guilloud and M. Bouyer found the one millionth digit of pi (which happens to be 1). In 1982, pi was calculated past the eight millionth digit in Japan. By 1995, David and Gregory Chudnovsky had computed pi to the one billionth digit.
π “Computing pi is the ultimate stress test for a computer – a kind of digital cardiogram.” Islands of Truth by Ivars Peterson.
π On October 4, 2006, Akria Haraguchi, a 60 year old Japanese mental health counselor who lives near Tokyo, recited pi to 100,000 decimal places from memory. It took him fourteen and a half hours. Haraguchi is seeking to be listed in the Guinness Book of Records which at the time, listed Hiroyuki Goto also of Japan, as the record holder having recited 42,195 pi decimal places from memory in February of 1995.
π In April, 1995, the Reuters wire service reported that a twelve-year-old Chinese boy, Zhang Zhuo, recited the value of pi to 4,000 decimal places from memory. It took him twenty-five minutes. This is probably a world record for a pre-teen.
π Many believe that the North American record is held by Gaurav Raja. In 2006 he recited 10,980 digits of pi. At the time, he was a junior in high school in Roanoke, Virginia, and among other recognition, he appeared on the Today Show.
π “Since there are 360 degrees in a circle and pi is intimately connected with the circle, we eagerly look at the 360th digit. Again we are rewarded with a most remarkable fact. At [the 359th digit] we find 360. Thus 360 is ‘centered’ over [the 360th digit].” The Magic of Pi, Monte Zerger.
π “You can determine your hat size by measuring the circumference of your head, then divide by pi, and round off to the nearest one-eighth inch.” The Joy of Pi, David Blatner.
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