Is Pi Irrational Or Rational
What is pi?
Pi is a number that relates a circle'southward circumference to its diameter. Pi is an irrational number, which means that it is a real number that cannot be expressed past a elementary fraction. That'south because pi is what mathematicians call an "infinite decimal" — after the decimal indicate, the digits go on forever and ever.
Students are usually introduced to the number pi as having an approximate value of iii.14 or 3.14159. Though it is an irrational number, some people employ rational expressions, such as 22/7 or 333/106, to estimate pi. (These rational expressions are authentic only to a couple of decimal places.)
Mathematicians and math enthusiasts are interested in calculating pi to as many digits as possible. The record for reciting the nearly digits of pi belongs to Suresh Kumar Sharma of Bharat, who recited pi to 70,030 decimal places in 2015, according to the Pi World Ranking Listing (opens in new tab). Meanwhile, some computer programs have calculated the value of pi to an astounding 62.8 trillion digits, Live Science previously reported. Calculations like these are often unveiled on Pi Day, a pseudo-vacation that occurs every yr on March 14 (three/14).
Related: eleven numbers that are cooler than pi
What are the outset 100 digits of pi?
The commencement 100 digits of pi are:
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067
The website piday.org (opens in new tab) has pi listed to the first 1 million digits.
Where does pi come from?
Past definition, pi is the ratio of the circumference of a circumvolve to its diameter. In other words, pi equals the circumference divided by the bore (π = c/d). Conversely, the circumference of a circle is equal to pi times the bore (c = πd). No matter how big or pocket-size a circle is, pi will ever work out to exist the aforementioned number. Pi (π) is the 16th letter of the Greek alphabet and is used to represent the widely known mathematical constant.
Who invented pi?
Pi has been known for nigh 4,000 years and was discovered by the ancient Babylonians. A tablet dating to somewhere betwixt 1900 B.C. and 1680 B.C. establish pi to be iii.125, according to the Exploratorium in San Francisco (opens in new tab). People in aboriginal Egypt were making like discoveries, equally evidenced past the Rhind papyrus of 1650 B.C. In this document, the Egyptians calculated the area of a circle by a formula giving pi an approximate value of three.1605. There is even a biblical verse where it appears pi was approximated, co-ordinate to a correspondence published in 1999 in the journal Nature (opens in new tab):
And he made a molten sea, ten cubits from the ane brim to the other: information technology was round all about, and his height was 5 cubits: and a line of thirty cubits did compass it most. — I Kings 7:23 (Male monarch James Version)
One of the first calculations of pi was carried out past Greek mathematician Archimedes of Syracuse (287 B.C. to 212 B.C.), according to the Exploratorium (opens in new tab). Archimedes used the Pythagorean theorem to find the areas of 2 polygons. Archimedes approximated the expanse of a circle based on the area of a regular polygon inscribed within the circle and the expanse of a regular polygon within which the circle was confining. The polygons, every bit Archimedes mapped them, gave the upper and lower bounds for the expanse of a circle, and he approximated pi at between 3 i/7 and 3 ten/71.
Earlier, Chinese mathematician and astronomer Zu Chongzhi (429 B.C. to 501 B.C.) had calculated pi using a similar method, finding the value to exist 355/113. Unfortunately, Zu's book of writing has been lost, then piddling is known about his work or methods.
British mathematician William Jones was the first to begin using the symbol π to stand for pi, in 1706.
What is pi used for?
In basic mathematics, pi is used to discover the area and circumference of a circumvolve. Pi tin can exist used to find an expanse by multiplying the radius of the circle squared times pi. So, to find the surface area of a circle with a radius of three centimeters, the calculation would be π3^2 = 28.27 cm. Because circles announced commonly in nature and are frequently used in other mathematical equations, pi is all effectually us and is used constantly.
Pi has even trickled into the literary world. Pilish is a form of writing English in which the numbers of letters in successive words follow the digits of pi, according to author Mike Keith (opens in new tab). Keith used Pilish in his book "Non A Wake." Here is an case from the book: "Now I fall, a tired suburbian in liquid nether the trees, Drifting alongside forests simmering red in the twilight over Europe."
"At present" has three messages, "I" has i letter, "fall" has 4 letters, "a" has i letter of the alphabet, and then on.
This article was updated on Oct. xix, 2018, past Live Science senior writer Brandon Specktor. It was updated over again on March iii, 2022, by Live Science correspondent Adam Isle of man.
Boosted resources
- Learn more nearly pi, its history, and pregnant from piday.org (opens in new tab)
- Laugh (or groan) at these pi-related jokes and puns (opens in new tab) from the educational site The Nine Planets
Bibliography
Exploratorium. (northward.d.). A cursory history of pi. Retrieved March 3, 2022, from https://world wide web.exploratorium.edu/pi/history-of-pi (opens in new tab)
Keith, Thou. (2010). Not a wake. Vinculum Press. Retrieved March iii, 2022, from http://www.cadaeic.cyberspace/notawake.htm (opens in new tab)
Keith, M. (n.d.). Writing in Philish. Retrieved March iii, 2022, from http://www.cadaeic.net/pilish.htm (opens in new tab)
Mometrix Test Training. (northward.d.) one one thousand thousand digits of pi. Retrieved March 3, 2022, from https://www.piday.org/million (opens in new tab)
Peil, N. (1999). Biblical reply to cooking up pi. Nature 399(522). https://www.nature.com/articles/21064 (opens in new tab)
Pi World Ranking List. (n.d.). Retrieved March 3, 2022, from https://www.pi-world-ranking-listing.com/?page=lists&category=pi (opens in new tab)
The Nine Planets (2020, Oct viii). Hilarious pi jokes. https://nineplanets.org/pi-jokes/ (opens in new tab)
Is Pi Irrational Or Rational,
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