116 Fun Facts About Pi Day

What date is Pi Day celebrated each year?

Pi Day is March 14, written 3/14 in month-first notation to match pi's opening digits; July 22, written 22/7, is a separate approximation date favoured in day-first countries.

What are the first three digits of pi?

The expansion continues 3.14159265... and never repeats; a room in the Palais de la Découverte in Paris has 707 of its digits on the wall.

Pi is the ratio of a circle's circumference to its what?

Pi is a circle's circumference divided by its diameter, the same ratio for every circle; since the diameter is twice the radius, it also equals circumference over 2r.

What type of number is pi?

Pi is irrational: it cannot be written as a fraction of two integers, a fact first proved in the 1760s, so its decimal expansion never ends or repeats.

What is the formula for the circumference of a circle?

The circumference is 2πr: the diameter is twice the radius, and the distance around any circle is pi times its diameter.

What is the formula for the area of a circle?

The area of a circle is πr², where r is the radius. This fundamental formula connects pi to every circle's area.

Which famous physicist's birthday falls on Pi Day?

Albert Einstein was born in Ulm, Germany, on March 14, 1879, and Pi Day events in his adopted American home town double as his birthday party.

What food is traditionally eaten on Pi Day?

Pie is a homophone of pi and is itself a circle, so pies have headlined the menu since the first celebration in 1988; schools and museums often add pie-eating contests.

Which state legislature nearly passed an 1897 bill implying pi equals 3.2?

Indiana's House of Representatives passed the bill before the state Senate rejected it, so it never became law.

In what year was Pi Day first officially recognized by the U.S. House of Representatives?

On March 12, 2009 the U.S. House passed a non-binding resolution designating March 14 as National Pi Day; the first large-scale celebration had come in 1988, two decades earlier.

Who organized the first large-scale Pi Day celebration in 1988?

Larry Shaw, a physicist on the staff of the science museum where he worked, organised the first celebration on March 14, 1988 and was later nicknamed the 'Prince of Pi'.

At which museum was the first Pi Day celebration held?

The Exploratorium in San Francisco, where physicist Larry Shaw worked, held the first celebration on March 14, 1988, and later made Pi Day an annual event.

Which ancient Greek mathematician is famous for his method of approximating pi using polygons?

Archimedes inscribed and circumscribed regular polygons around a circle, doubling their sides step by step, and squeezed pi between the bounds 223/71 and 3 1/7.

What is the fourth digit after the decimal point in pi?

Pi runs 3.14159265..., so the digits after the point go 1-4-1-5-9-2-6-5.

How many degrees are there in π radians?

π radians equals 180 degrees: a full circle of 360° measures 2π radians, and one radian is the angle whose arc length equals the radius.

Which country writes dates month-first, the format that makes 3/14 Pi Day?

The United States writes dates month-first, so March 14 becomes 3/14; day-first countries such as the United Kingdom would write 14/3, which is why some mark July 22 (22/7) instead.

What does it mean that pi is a transcendental number?

A transcendental number is not the root of any polynomial with rational coefficients; e was shown to be transcendental in 1873 and pi followed in 1882, nine years later.

What ancient civilization used the approximation 3.125 for pi around 1900 BC?

The value 25/8 is implied on a clay tablet; the Egyptian Rhind Papyrus from about the same era treats pi as (16/9)², roughly 3.16.

On Pi Day 2015 at 9:26:53 AM, what did the date and time together spell out?

This 'Pi Instant' comes around once a century, and 2015 was billed as Super Pi Day because that year's date supplied five digits.

What is the practice of memorizing digits of pi called?

Piphilology, a play on 'pi' and 'philology', is the practice of memorising pi's digits; poems whose word lengths encode the digits are called piems.

Which Indian mathematician's c.1400 infinite series for pi predated Europe's by over two centuries?

Madhava of Sangamagrama, founder of the Kerala school, found the arctangent series for pi around 1400; Europe rediscovered it through James Gregory and Leibniz in the 1670s.

Which Swiss mathematician popularized π for the circle constant from 1736 onward?

Leonhard Euler adopted π in his 1736 Mechanica and, through his vast correspondence and his 1748 Introductio, spread the symbol across Europe until it was universal.

The ancient Greek who first trapped pi between polygons stopped at how many sides?

He started from hexagons and doubled four times (6, 12, 24, 48, 96) to bound pi between 223/71 and 22/7.

What famous unsolved problem was proven impossible by the transcendence of pi?

A compass-and-straightedge construction can only produce algebraic lengths, so a square matching a circle's area is out of reach.

The "tau movement" argues that which number should replace pi as the fundamental circle constant?

Michael Hartl's 2010 Tau Manifesto argues that the ratio of circumference to radius, one full turn, is the more natural constant.

What is Euler's identity, often called the most beautiful equation in mathematics?

e^(iπ) + 1 = 0 links e, i, π, 1 and 0 in one line and is a special case of Euler's formula; a 1990 poll of Mathematical Intelligencer readers named it the most beautiful theorem in mathematics.

In 1949 John von Neumann's team spent 70 hours computing 2,037 digits of pi on which computer?

ENIAC, the Army's electronic computer at Aberdeen Proving Ground, produced 2,037 digits in about 70 hours in 1949; that same year Wrench and Smith reached 1,120 digits with a desk calculator.

Which Indian mathematician produced pi formulas that converge extremely rapidly?

Srinivasa Ramanujan's 1914 paper gave series for 1/π that add roughly eight correct digits per term, anticipating the fast algorithms used for record computations decades later.

Which university has often timed its admissions decision letters to arrive on Pi Day?

MIT has released its undergraduate admissions decisions on March 14 for years; in 2015 they went online at 9:26 am, that year's 'pi minute'.

Which mathematician brothers' 1988 formula, adding about 14 digits per term, pushed pi past a billion digits?

David and Gregory Chudnovsky built their 1988 algorithm on Ramanujan's series; it carried them past one billion digits in 1989 and drove the 100-trillion-digit computation of 2022.

The Comte de Buffon's 18th-century pi-estimating probability problem involves dropping what onto parallel strips?

In Buffon's needle problem a needle of length L dropped onto strips of width D crosses a line with probability 2L/(πD), so counting crossings estimates pi.

In statistics, where does pi show up in connection with the normal distribution?

The area under the basic bell curve e^(−x²) equals √π, which is why the density needs a 1/√(2π) factor to total one.

Who is credited with the first proof, in the 1760s, that pi cannot be written as a ratio of two integers?

Johann Heinrich Lambert showed in the 1760s that the tangent of any non-zero rational number is irrational; since tan(π/4) = 1 is rational, π/4 and hence π cannot be a fraction.

In 1882, who proved that pi is transcendental?

Ferdinand von Lindemann's 1882 proof extended Hermite's 1873 result that e is transcendental, and closed a construction problem the Greeks had left open for two millennia.

The Bailey-Borwein-Plouffe (BBP) formula, discovered in 1995, has what remarkable property?

Simon Plouffe found it in 1995; the PiHex project later used a variant to show that the quadrillionth binary digit of pi is 0.

What is the Feynman point in the digits of pi?

The joke is to recite pi to that point and finish 'nine nine nine nine nine nine and so on'; the earliest known version is in Douglas Hofstadter's 1985 book, and Feynman may never have said it.

How many decimal places of pi does NASA's JPL use for its most exacting navigation?

JPL's interplanetary navigation uses pi to 15 decimal places, 3.141592653589793; even the circumference of the observable universe needs only about 40 digits to be accurate to a hydrogen atom.

Which Chinese mathematician calculated pi to 7 decimal places in the 5th century AD?

Zu Chongzhi bounded pi between 3.1415926 and 3.1415927 in the 5th century, a precision unmatched for about 800 years; he also gave the fraction later known as milü.

Which fraction, known in China as milü, approximates pi to six decimal places?

355/113 comes out at about 3.1415929, matching pi to six decimal places; no fraction with a denominator of four digits or fewer gets closer.

Which English mathematician found in 1656 that π/2 equals the infinite product (2/1)(2/3)(4/3)(4/5)…?

John Wallis published the product in his 1656 Arithmetica Infinitorum; it was one of the first infinite products ever written down and is known as the Wallis product.

In Life of Pi, what is the main character's full first name, which he shortens to Pi?

Piscine Molitor Patel was named after a Paris swimming pool; after schoolmates turned it into 'Pissing' he rebranded himself as Pi.

What is the sum of the infinite series 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...?

The Leibniz series sums to π/4; it converges painfully slowly, but Jonathan Borwein and Mark Limber used Euler-number acceleration to squeeze 5,263 decimal places out of it.

Which tech company's employee set the 2019 record for most digits of pi (31.4 trillion)?

In 2019, Emma Haruka Iwao, a Google employee, calculated pi to 31,415,926,535,897 digits (31.4 trillion) using Google Cloud, breaking the previous record. The number of digits itself starts with 314159..., matching pi's digits.

Which James Jeans sentence encodes the opening digits of pi in its word lengths?

How(3) I(1) want(4) a(1) drink(5) alcoholic(9) of(2) course(6) gives 3.1415926; such poems are known as piems.

Which famous scientist died on Pi Day in 2018?

Stephen Hawking's ashes were interred in Westminster Abbey between the graves of Isaac Newton and Charles Darwin.

What did the Basel problem, solved by Euler in 1734, ask for?

Euler showed the sum is π²/6, about 1.6449, unexpectedly tying pi to the integers; the problem is named for his home town, where the Bernoullis had failed to crack it.

July 22, written 22/7 in day/month format, is celebrated as which unofficial maths holiday?

Pi Approximation Day marks 22/7, a fraction accurate to two decimal places that dates back to Archimedes; it is most popular where dates are written day first.

The Palais de la Découverte's pi room originally showed 707 digits copied from whose flawed 1873 calculation?

William Shanks published 707 digits in 1873, but a slip partway through made his last 180 wrong; the error was detected by desk calculator in the 1940s and the wall was corrected in 1949.

What record did Rajveer Meena set in 2015, taking nearly 10 hours while blindfolded?

Akira Haraguchi claimed 100,000 digits in 2006, but Guinness never verified it.

Which UN body designated Pi Day as the International Day of Mathematics in 2019?

UNESCO's 40th General Conference proclaimed March 14 the International Day of Mathematics in November 2019; the first observance followed on March 14, 2020.

What did the staff and public do at the first Exploratorium Pi Day in 1988?

Larry Shaw, who organised it, worked at the museum as a physicist.

Which house resolution recognised March 14, 2009, as National Pi Day?

H. Res. 224, sponsored by Bart Gordon of Tennessee, passed the House 391–10 on March 12, 2009; as a simple resolution it was non-binding.

Which pastry chef's pie starred in Google's 30th-anniversary Pi Day Doodle in 2018?

Dominique Ansel, inventor of the Cronut, baked the salted caramel apple pie in Google's 2018 Doodle marking 30 years of Pi Day; the company's first Pi Day Doodle had come in 2010.

Which whole month did some people observe as 'Pi Month'?

March 2014, written 3/14, matched pi's first three digits, so enthusiasts dubbed the whole month Pi Month; the following year's 3/14/15 was billed as Super Pi Day.

What is the volume of a sphere of radius r?

A sphere's volume is 4/3πr³; Archimedes found it by showing a sphere fills exactly two-thirds of its circumscribing cylinder, while 4πr² is the surface area.

At what time of day has MIT usually posted its Pi Day admissions decisions?

MIT usually posts at 6:28 pm Eastern, which it calls 'Tau Time' because 6.28 is tau, pi's rival constant; the 2015 Super Pi Day release came at 9:26 am instead.

Which New Jersey town combines Pi Day with an Einstein look-alike contest?

Princeton holds an Einstein look-alike contest as part of its Pi Day festivities; Einstein lived in the town for over 20 years while at the Institute for Advanced Study.

How many digits of pi did Matt Parker's team calculate by hand over six days in 2024?

An asteroid, 314159 Mattparker, was named in his honour that August.

What is the probability that two randomly chosen integers share no common factor?

Two random integers are coprime with probability 6/π², about 61 percent; it is the reciprocal of Euler's Basel sum 1 + 1/4 + 1/9 + … = π²/6.

Which November date is the 314th day of a common year?

November 10 is the 314th day of a common year, which is why some celebrate it as a second pi date; in leap years the 314th day moves back to November 9.

Tau Day celebrants jokingly suggest eating what?

Because tau is 2π, Tau Day on June 28 comes with the slogan 'twice the pi(e)': celebrants claim the right to eat twice as much pie as on Pi Day.

Who most notably proposed in 2010 that tau should replace pi?

Michael Hartl published The Tau Manifesto on June 28, 2010, building on Bob Palais's 2001 essay 'π Is Wrong!'; he argues the circumference-to-radius ratio makes formulas simpler.

Which physicist founded the Exploratorium in 1969?

Frank Oppenheimer, younger brother of J. Robert Oppenheimer and a Manhattan Project veteran, opened the Exploratorium in San Francisco's Palace of Fine Arts in 1969.

Which Welsh mathematician first used the symbol π for the circle ratio, in 1706?

William Jones introduced π for the ratio in his 1706 beginners' book Synopsis Palmariorum Matheseos; Euler's later adoption made the symbol universal.

The 1706 adoption of π followed earlier abbreviations of which Greek word?

π abbreviated periphery, Greek periphereia: William Oughtred wrote π/δ for the periphery-to-diameter ratio in 1647, six decades before π alone came to mean the constant.

The Welsh mathematician who popularised π was a close friend of Halley and which other giant?

He later edited and published many of Newton's manuscripts.

Which celebrated mental calculator computed 200 decimal places of pi in 1844?

Zacharias Dase, a famed calculating prodigy, worked out 200 decimal places of pi in about two months in 1844 using an arctangent formula supplied by L. K. Schulz von Strassnitzky.

In which physical law does the constant 1/(4πε₀) appear?

Coulomb's law gives the force between two charges as q₁q₂/(4πε₀r²); the 4π reflects the surface area of a sphere, 4πr², over which the field spreads.

What value for pi does the Rhind Papyrus's area rule imply, to two decimals?

256/81 comes to 3.1605..., so 3.16, an error of less than one percent against the true value.

Which scribe wrote the Rhind Mathematical Papyrus?

The scribe Ahmes wrote the papyrus around 1550 BC, stating that he copied it from an older text made in the reign of King Nimaatre, that is Amenemhat III.

Around 150 AD, which scientist gave 3.1416 for pi in the Almagest?

Ptolemy used 3;8,30 in sexagesimal, about 3.1416, in the Almagest; he may have taken the value from Archimedes or Apollonius of Perga.

Which Cao Wei mathematician built a 3,072-sided polygon around 265 AD to get 3.1416?

Liu Hui, commenting on the Nine Chapters in 263 AD, used a 3,072-sided polygon to reach 3.1416; his iterative algorithm could reach any required accuracy.

Liu Hui expressed pi as which fraction, admitting it was 'a bit small'?

Liu Hui gave 157/50, which is 3.14, calling it slightly too small but good enough for practical use; his more refined value was 3927/1250, or 3.1416.

Which Indian astronomer used 3.1416 in the Aryabhatiya of 499 AD?

Aryabhata's Aryabhatiya of 499 AD gives the circumference of a circle of diameter 20,000 as 62,832, which works out to 3.1416.

Persian astronomer Jamshid al-Kashi's 1424 pi record used roughly how many decimal digits?

Al-Kashi computed 2π to nine sexagesimal places in 1424, equivalent to 16 decimal digits, using a polygon of 3 × 2²⁸ sides; the record stood about 180 years.

Which French mathematician reached nine digits of pi in 1579 with a huge polygon?

In 1593 he published Viète's formula, an infinite product for pi.

Ludolph van Ceulen, who reached 35 digits, taught mathematics and what else?

He opened a fencing school in Leiden in 1594 before becoming a professor there.

Which English mathematician gave a continued fraction for 4/π in the 1650s?

William Brouncker, first president of the Royal Society, turned Wallis's product into the continued fraction 4/π = 1 + 1²/(2 + 3²/(2 + 5²/(2 + …))), which Wallis printed in his Arithmetica Infinitorum.

Which 1706 formula let John Machin compute 100 digits of pi?

John Machin's formula π/4 = 4 arctan(1/5) − arctan(1/239) converges fast enough that he reached 100 digits in 1706; Machin-like arctangent formulae set pi records for 250 years.

William Shanks calculated 607 digits of pi in 1853 but erred at which digit?

Shanks's error began at the 528th decimal place, so the tail of his 1853 figures and his whole 1873 extension were wrong; D. F. Ferguson exposed it with a desk calculator in the mid-1940s.

Daniel Ferguson's 1946 approximation of 620 digits was the best achieved without what?

Wrench and Smith reached 1,120 digits in 1949 using a desk calculator.

The Madhava-Leibniz series was independently rediscovered by James Gregory in which year?

James Gregory found the arctangent series in 1671, in a letter to John Collins; Leibniz reached the π/4 special case in 1673, over two centuries after the Kerala school.

Around 1500, Nilakantha Somayaji presented a pi series in which form?

Nilakantha Somayaji set the series in Sanskrit verse in his Tantrasamgraha of about 1500; Indian astronomical texts were composed in metre to aid memorisation, and the Kerala school's Malayalam prose came later.

Whose 1837 result showed constructible lengths must solve certain polynomial equations?

Pierre Wantzel showed in 1837 that a constructible length must satisfy a polynomial whose degree is a power of two, settling angle trisection and cube doubling; the circle followed in 1882.

The 1882 theorem proving pi transcendental also establishes the transcendence of which constant?

Lindemann's theorem says e^α is transcendental for any non-zero algebraic α; α = 1 makes e transcendental, and α = iπ would contradict e^(iπ) = −1 unless π is transcendental too.

Which two mathematicians independently published fast iterative pi algorithms in 1975-76?

Eugene Salamin and Richard Brent independently published the arithmetic-geometric mean algorithm in 1975–76; it doubles the correct digits each step and rests on work Gauss did around 1800.

The Borwein brothers' 1987 algorithm multiplies the number of correct digits by how much per step?

The Borweins' 1987 quintic algorithm multiplies the correct digits by five each iteration; their earlier quartic algorithm quadrupled them, and both descend from Ramanujan's modular equations.

Which two men reached 10 trillion digits of pi in 2011?

Shigeru Kondo and Alexander Yee reached 10 trillion digits in October 2011 on Kondo's home-built machine in Japan, using Yee's y-cruncher program and the Chudnovsky formula.

The program y-cruncher was originally written to compute what?

Alexander Yee wrote y-cruncher to compute the Euler-Mascheroni constant, gamma, whose Greek letter resembles a 'y'; from the 5-trillion-digit run of 2010 it became the standard engine for pi records.

How many days did Emma Haruka Iwao's 2019 record pi calculation take?

Iwao's run took 121 days on 25 Google Cloud virtual machines and consumed about 170 terabytes of storage; it was the first pi record set on a public cloud service.

Who broke Iwao's 2019 record in 2020 with 50 trillion digits?

Timothy Mullican computed 50 trillion digits in January 2020 on second-hand server hardware over 303 days; Iwao reclaimed the record in 2022 with 100 trillion.

Akira Haraguchi's unofficial 2006 record was reciting how many digits of pi?

Akira Haraguchi recited 100,000 digits over 16 hours on 3–4 October 2006 in Kisarazu, pausing every two hours for onigiri; Guinness declined to ratify the claim.

Which memory technique has been used to memorise pi to 67,890 digits?

Another trick is spotting patterns, such as the year 1971 in the first fifty digits.

Which computer first carried pi past one million digits, in 1973?

Jean Guilloud and Martin Bouyer passed one million digits in 1973 on a CDC 7600 in Paris, in just under a day of machine time; the digits were published as a 400-page book.

Mike Keith's book Not A Wake, written in Pilish, encodes how many digits of pi?

Not A Wake (2010) runs to 10,000 words, each encoding one digit; Keith's earlier story 'Cadaeic Cadenza' covered 3,835 digits and a 740-digit poem came before it.

In Basic Pilish, a ten-letter word represents which digit?

A ten-letter word stands for 0, since n letters give the digit n only below ten; Standard Pilish also lets words over ten letters stand for two digits.

Which Poe poem did Mike Keith retell in Pilish, opening 'Poe, E.'?

It opens 'Poe, E. Near a Raven', encoding 3.14159 in the word lengths.

Which musician wrote a 2004 song that is a mnemonic for the first 50 digits of pi?

Andrew Huang's 2004 song uses its lyrics as a mnemonic for the first 50 digits of pi; he extended it to 100 digits in 2013 as 'Pi Mnemonic Song'.

On which album does Kate Bush sing pi to its 78th decimal place?

Aerial (2005) includes the song 'π', in which Bush sings the digits to the 78th decimal place and then jumps to the 101st through 137th.

Which Purdue professor happened to be present and helped sink the Indiana pi bill?

Clarence Abiathar Waldo, a Purdue mathematics professor in town over the university's budget, briefed the senators; the Senate then postponed the bill indefinitely on February 12, 1897.

Which Indiana Senate body initially reported the pi bill favourably?

The Senate's Committee on Temperance reported the bill favourably; on the floor Senator Orrin Hubbell mocked it, complaining that the Senate was wasting $250 a day on such frivolity.

By what vote did the Indiana House pass its 1897 pi bill?

The Indiana House passed House Bill 246 unanimously, 67–0, on February 6, 1897; it died in the Senate six days later after Purdue's C. A. Waldo briefed the senators.

Which Italian mathematician's 1901 Buffon's needle experiment is a textbook case of confirmation bias?

Mario Lazzarini's 1901 experiment reported 3,408 needle tosses yielding exactly 355/113; statisticians later showed the needle length and toss count were chosen to land on that known value.

Lazzarini chose needles with what length relative to the strip width?

Lazzarini used needles 5/6 as long as the strip width: with 3,408 tosses and 1,808 crossings, 2 × (5/6) × 3408/1808 works out to exactly 355/113.

Which Polish mathematician conceptualised the Monte Carlo method used to estimate pi?

Stanisław Ulam conceived the Monte Carlo method in 1946 while convalescing and playing solitaire; Nicholas Metropolis named it after the Monaco casino where Ulam's uncle liked to gamble.

Ulam invented the modern Monte Carlo method while working where in the late 1940s?

Ulam was at Los Alamos National Laboratory, working on nuclear weapons, when he conceived the method in 1946; the first Monte Carlo neutron simulations were then run on ENIAC.

Yann Martel's Life of Pi won which literary award the year after its 2001 publication?

Life of Pi won the 2002 Man Booker Prize; its castaway Pi Patel spends 227 days at sea with the tiger Richard Parker, a count that echoes the approximation 22/7.

Which solid has volume equal to one third of πr²h?

A cone's volume is 1/3πr²h, exactly one third of the cylinder with the same base and height, a fact Archimedes credited to Democritus and Eudoxus.

Gelfond's constant, e raised to the power π, is approximately what?

Gelfond's constant e^π ≈ 23.1407 was proved transcendental by Aleksandr Gelfond in 1934; by coincidence e^π − π comes out at 19.999, tantalisingly close to 20.

Which director's 1998 debut, Pi, won the Directing Award at Sundance?

Darren Aronofsky's Pi (1998) won the Directing Award at Sundance; shot in high-contrast black and white, it follows number theorist Max Cohen in his Chinatown apartment.

Which pair computed 100,000 digits of pi on an IBM 7090 in 1961?

Daniel Shanks and John Wrench computed 100,265 digits on an IBM 7090 in July 1961 in under nine hours of machine time, using two Machin-like arctangent formulae to cross-check.

Which physical law, containing pi, limits how well a function can be localised in space and frequency?

The Heisenberg uncertainty principle, Δx·Δp ≥ h/(4π), is the physical form of the Fourier trade-off: the more sharply a function is localised in position, the more spread its frequencies.

Which Japanese mathematician's statistical tests found pi's digits consistent with normality?

Yasumasa Kanada's University of Tokyo team ran statistical tests on its 1.24-trillion-digit computation of 2002 and found the digits consistent with normality; he set several records between 1995 and 2002.

Which base-16 digits open pi?

In base 16 pi begins 3.243F6A8885A3…, the string also familiar from the Blowfish cipher's tables; hexadecimal digit-extraction formulae are used to check new decimal records.

Cadaeic Cadenza mimics 'The Raven', 'Jabberwocky', Hamlet and the lyrics of which prog-rock band?

It also imitates 'The Raven', 'Jabberwocky', Prufrock, the Rubaiyat and Hamlet.

What was the title of Ludolph van Ceulen's 1596 book giving 20 decimals of pi?

Van den Circkel ('On the Circle', 1596) gave pi to 20 decimals; van Ceulen later reached 35, the figure engraved on his tombstone in Leiden's Pieterskerk.