93 Fun Facts About Pi Math

Which ratio in a circle defines the mathematical constant π?

Circumference to diameter is the ratio π, and it is the same for every circle: anything round, from a coin to a Ferris wheel, is a little over three times as far around as it is across.

Which Welsh mathematician first used the symbol π for the circle constant, in a 1706 textbook?

William Jones introduced π in his 1706 Synopsis Palmariorum Matheseos, a beginners' book built from his teaching notes, but the symbol only caught on after Leonhard Euler took it up in the 1730s.

Which ancient Greek approximated pi using inscribed and circumscribed polygons?

Archimedes trapped π between two bounds by drawing hexagons inside and outside a circle, then doubling their sides four times until he was working with 96-sided polygons.

Which book describes a great round basin as ten cubits across and thirty cubits around?

The Bible's First Book of Kings gives these round figures for the great cast-metal 'Sea' of Solomon's Temple, figures that work out to a π of exactly 3.

In The Simpsons, who silences a rowdy science conference by shouting that pi is exactly three?

Professor Frink shouts it because nothing else will quieten the hall: the claim that π has a neat, exact value is so wrong that the scientists gasp and the noise stops.

Which US state's lower house unanimously passed a bill in 1897 that would have legislated a wrong value of π?

Indiana's House first sent the bill to its Committee on Canals, then passed it 67–0; a Purdue professor who was visiting to lobby for funding coached the senators, and they shelved it.

Whose name usually goes with π/4 = 1 − 1/3 + 1/5 − ..., an infinite series also found by Madhava?

Leibniz found the series in 1673, two years after James Gregory and more than two centuries after Madhava's school in India; it converges so slowly that 500,000 terms give only five correct decimals.

Which 18th-century French naturalist posed the needle-dropping probability problem that can be used to estimate π?

Comte de Buffon asked how often a needle dropped on a ruled floor lands across a line; for a needle as long as the gap between lines the chance is 2/π, so counting crossings gives an estimate of π.

The Chudnovsky brothers computed billions of digits of π on a supercomputer they built in their apartment in which US city?

New York: the Soviet-born brothers assembled the machine from mail-order parts in Gregory Chudnovsky's Manhattan apartment, and it passed two billion digits in the early 1990s.

Which famous named equation, e^(iπ) + 1 = 0, links the five constants e, i, π, 1 and 0?

Euler's identity is Euler's formula e^(ix) = cos x + i sin x evaluated at x = π: since cos π = −1 and sin π = 0, e^(iπ) equals −1, and adding 1 gives 0.

In 1991 Dave Boll noticed the digits of π emerging from iteration counts at the 'neck' of which famous fractal?

The Mandelbrot set hides π at its neck: test points 0.1, 0.01 and 0.001 above the pinch at −0.75 take 33, 315 and 3,143 steps to escape, creeping toward the digits of π.

A clay tablet from 1900–1600 BCE implying π = 25/8 comes from which ancient civilization?

Babylonian scribes' 25/8 is 3.125, within one percent of π and a clear step up from the round value of 3 that other ancient texts settled for.

Which Chinese mathematician gave the fraction 355/113 for π around 480 AD, unmatched for centuries?

Zu Chongzhi pinned π between 3.1415926 and 3.1415927, but the Zhui Shu, the book in which he explained his method, was later lost, so nobody knows exactly how he did it.

Which mathematician first proved in the 1760s that π is irrational, using a continued fraction for the tangent function?

Johann Heinrich Lambert showed that the tangent of every rational number except 0 is irrational; since the tangent of π/4 is exactly 1, π/4 cannot be rational, and neither can π.

Where were Ludolph van Ceulen's 35 decimals of π, his life's work, engraved?

On his tombstone in Leiden: the original stone was later lost and a replica was unveiled in 2000, and German speakers long called π the Ludolphine number after him.

What is the formula for the area of a circle?

The area of a circle is πr²; a disk of radius 1 has area π ≈ 3.14159, and doubling the radius quadruples the area, since the formula scales with r².

What is the formula for the volume of a sphere?

The volume of a sphere is (4/3)πr³, exactly two-thirds of the cylinder that just encloses it, and the very same two-thirds ratio turns out to hold for the two shapes' total surface areas.

Which inverse trig function has Taylor series x − x³/3 + x⁵/5 − …?

arctan(x) has this series, and since arctan(1) = π/4, setting x = 1 turns it into a formula for π; feeding it small fractions instead converges far faster, which is how π was computed for over two centuries.

What is the run of six consecutive 9s starting at the 762nd decimal place of pi called?

The Feynman Point is named after physicist Richard Feynman, who is said to have wanted to memorise π up to those six 9s so that he could recite them and finish 'and so on', as if π were rational.

Pi Day began in 1988 at which San Francisco science museum?

The Exploratorium held the first Pi Day with fruit pies and a march around one of its circular spaces, the idea of staff physicist Larry Shaw, nicknamed the Prince of Pi.

Which physicist was born on 14 March 1879, a date now celebrated as Pi Day?

Albert Einstein was born in Ulm on 14 March 1879; Pi Day's founders only noticed the coincidence a few years in, then added a celebration of his life to the festivities.

Which famous physicist died on Pi Day, 14 March 2018?

Stephen Hawking was told at 21 that motor neurone disease left him about two years to live; he lived another 55, dying at 76 on Pi Day.

In 2019 UNESCO designated 14 March as the International Day of what?

Mathematics got its international day on 14 March because many countries already marked the date as Pi Day; the first edition, in 2020, took the theme 'Mathematics is Everywhere'.

Which fraction is celebrated on Pi Approximation Day?

22/7 is 22 July written day first; at about 3.1429 it is actually closer to π than the 3.14 that Pi Day itself celebrates.

The constant τ, championed as a replacement for π, equals what?

τ equals 2π, so one full turn is exactly τ radians and a quarter turn is simply a quarter of τ, which is the case its fans make against π.

If a rope around Earth's equator were lengthened by 6.3 metres, how high could the whole rope be lifted?

About 100 centimetres, a full metre: the gain in height depends only on the extra length, not on the size of the ball, so the same 6.3 metres would lift a rope around a tennis ball just as high.

Which university has often released its admissions decisions on Pi Day, a nod to its maths-loving applicants?

MIT has often timed its decisions for Pi Day, and in 2020 it posted them at 1:59 pm so that the date and time together spelled out the first six digits of π.

On 'Super Pi Day' 2015, which clock time completed the first ten digits of pi?

9:26:53 follows the date 3/14/15 to spell 3.141592653, the first ten digits of π, a line-up that month-first calendars see only once a century.

Asteroid 314159 is named after which maths communicator known for Pi Day challenges?

Matt Parker, the Stand-up Maths YouTuber, is known for Pi Day stunts in which he calculates π by hand; asteroid 314159 Mattparker, named in 2024, carries the constant's first six digits in its number.

The 314th day of a common year, an unofficial second Pi Day, falls in which month?

November: the first ten months of a common year hold 304 days, so day 314 is 10 November; in leap years the date slips to 9 November.

Which value of π did the notorious 1897 American 'pi bill' most famously imply?

3.2 follows from the bill's ratio 'as five-fourths to four', which works out to 16/5; for all its fame as the pi bill, its garbled text never once uses the word pi.

Which US body passed a resolution in 2009 backing the designation of a national Pi Day?

The House of Representatives backed the day in March 2009, in a resolution that also urged schools to use it to teach pupils about π and get them interested in the subject.

π sets the rhythm of which simple device, whose period is 2π√(L/g) for length L and gravity g?

A pendulum's small swings are timed by its length and gravity alone, not by the weight on the end, which is what made it the heart of accurate clocks.

Rajveer Meena wore what throughout his Guinness-record recital of 70,000 digits of π in 2015?

A blindfold stayed on for the whole recital of nearly ten hours; Japan's Akira Haraguchi had recited 100,000 digits in 2006, but Guinness did not certify that feat, so the official record stayed far below it.

Who set a European record in 2004 by reciting 22,514 digits of π?

Daniel Tammet recited them at Oxford's Museum of the History of Science on Pi Day 2004, setting a European record and raising money for an epilepsy charity.

Kate Bush's song 'π', in which she sings the digits, appears on which 2005 album?

Aerial, Kate Bush's 2005 double album, includes 'π', a song about a man obsessed with the number, in which she sings dozens of its decimal places but omits a run of digits in the middle.

In the mnemonic 'How I want a drink, alcoholic of course', each word's count of what gives a digit of π?

Letters: How, I, want, a, drink have 3, 1, 4, 1 and 5 of them, and the full line, credited to the physicist James Jeans, runs on to fifteen digits.

In which Alfred Hitchcock spy thriller is the symbol π the secret sign of an East German escape network?

Torn Curtain (1966) sends Paul Newman's physicist to East Germany, where he scratches π in the dirt with his foot to identify himself to the underground network that goes by that name.

Which World's Fair city opened a science museum in 1937 with a 'pi room' showing William Shanks's 707 digits?

Paris's Palais de la Découverte inscribed the 707 digits around a circular room in 1937; when Shanks's hand calculation was later found faulty, the wall had to be corrected.

Which digit is the last of the ten to appear in π's decimals, not showing up until the 32nd place?

Zero is the late arrival: every other digit turns up within the first thirteen decimal places, but the first 0 has to wait until place 32.

D. F. Ferguson found the error in Shanks's 707 digits of π using what?

Desk calculator: a mechanical one was enough to show that Shanks's digits went wrong after the 527th; within a few years electronic computers took over the record chase for good.

How did the German prodigy Zacharias Dase compute 200 decimals of π in 1844, a two-month task?

Mental arithmetic was Dase's stage act: he once multiplied two eight-digit numbers in his head in 54 seconds.

Which Englishman first computed 100 digits of π, in 1706?

John Machin's formula converged so fast that it took him past 100 digits; it was printed in the same 1706 book that first used the symbol π, and variants of it set record after record for two centuries.

Newton computed 15 digits of π around 1666 and said he was what to admit how far he'd carried it?

Newton wrote 'I am ashamed to tell you to how many figures I carried these computations, having no other business at the time'; he worked at Woolsthorpe during the 1665–66 plague years.

Which English mathematician, who also introduced the ∞ symbol, published a famous infinite product for π/2 in the 1650s?

John Wallis reached the product (2/1)(2/3)(4/3)(4/5)… by bold interpolation rather than proof, a method not regarded as rigorous, yet the result is exactly right.

François Viète's 1593 formula for 2/π is built from an infinite product of nested what?

Square roots nested inside square roots make up Viète's product, the first formula in Europe to capture an infinite process; its author also broke Spanish ciphers for the French crown.

Euler computed 20 digits of π with a fast-converging formula of his own in how long?

One hour was all Euler needed for 20 digits, using a two-term formula of his own; decades later, in 1844, a record of 200 digits still took two months of work.

Euler showed that 1 + 1/4 + 1/9 + 1/16 + ... sums to what?

The sum is π²/6, about 1.644934; Euler announced it in 1735 at age 28, solving a problem that had defeated the Bernoullis and other leading mathematicians for decades.

The Basel problem, solved by Euler, is named after a city in which country?

Basel is in Switzerland; the problem carries its name because the city was home to the Bernoulli family, who attacked it without success, and to Euler, who was born there in 1707 and solved it.

Two random whole numbers have a 6/π² chance, about 61%, of being what?

Coprime means sharing no common factor, so a fraction built from two random whole numbers is already in lowest terms about three times in five.

In his 1727 essay on the properties of air, Euler used the symbol π for which value?

6.28 was Euler's π in 1727, twice the value we use; he switched to 3.14 in the 1730s, and his influence made that choice stick.

Which fraction did Ptolemy use for π in the Almagest, a value of about 3.1417?

377/120 is thought to come from treating the circle as a 360-sided polygon and reading the chord of one degree from Ptolemy's own table, an early use of trigonometry to pin down π.

Which solid has a volume of exactly one-third πr²h, a third of the cylinder that encloses it?

A cone holds exactly a third of the cylinder with the same base and height, so three cone-shaped cups of water fill the matching can to the brim.

Which unit of solid angle, the three-dimensional cousin of the radian, makes a whole sphere a simple multiple of π?

The steradian measures how much of your surroundings something covers; the whole sky around you comes to four times π of them, about 12.57, just as a full circle of directions is twice π radians.

Jamshid al-Kashi's 1424 record (about 16 decimal digits) was worked out in which numeral system?

Sexagesimal (base 60) was how al-Kashi worked: he computed 2π to nine base-60 places from a polygon, then translated the result into sixteen decimals, a record that stood for well over a century.

Madhava of Sangamagrama, who found series for π around 1400, founded which school of maths?

The Kerala school of south-west India grew up around Madhava, whose infinite series took π past ten digits some two centuries before European mathematicians found the same series.

Stirling's approximation, whose formula contains √(2πn), estimates which rapidly growing numbers?

Factorials such as 100! are painful to multiply out, but Stirling's formula lands within one percent even at n = 10, with π turning up in a problem that has no circle in sight.

Ludolph van Ceulen taught maths and which sport in Delft and Leiden?

Van Ceulen ran fencing schools in Delft and Leiden alongside his mathematics teaching; in 1600 he became one of the first teachers at Leiden's Duytsche Mathematique, an engineering school taught in Dutch rather than Latin.

In number theory the symbol π(x) has nothing to do with circles; what does it count up to x?

Prime numbers up to x are what π(x) counts, so π(10) is 4, for 2, 3, 5 and 7; primes look random, yet π(x) stays remarkably close to x divided by the natural logarithm of x.

Which is larger, e raised to the power π or π raised to the power e?

The number e^π is about 23.14 and π^e about 22.46; e always wins such contests, because the x-th root of x is largest when x equals e.

Hippocrates of Chios managed to square which shape bounded by circular arcs?

A lune is a crescent bounded by two circular arcs; Hippocrates showed that one such crescent has exactly the area of a triangle, the first curved figure ever matched to a straight-edged one.

Proving π transcendental in 1882 settled which ancient compass-and-straightedge problem?

Squaring the circle means building a square with exactly a circle's area using only compass and straightedge; Lindemann's 1882 proof showed it cannot be done, which is why the phrase now stands for attempting the impossible.

The 1882 proof that π is transcendental mirrored whose 1873 proof that e is?

Charles Hermite proved e transcendental in 1873 but never took on π himself, though he had done most of the hard work; nine years later Ferdinand von Lindemann finished the job with similar methods.

Adrien-Marie Legendre proved in 1794 that which number is also irrational?

π squared being irrational says more than π being irrational: it rules out π being √10, say, or the root of any other fraction; whether π times e or π to the power π is irrational is still unknown.

Which unproven statement would settle whether π and e are algebraically independent?

Schanuel's conjecture, a sweeping claim about the transcendence of exponentials, would imply that π and e are algebraically independent; as things stand it is not even known whether π + e is irrational.

π is widely conjectured, but not yet proved, to be which kind of number?

A normal number has every string of digits turning up equally often in every base; π's digits have passed every statistical test for it, yet a proof remains elusive.

One analytic definition makes π twice the smallest positive zero of which function?

Cosine's smallest positive zero is π/2, so π is twice it; equivalently π is the smallest positive zero of sine, a definition that avoids integrals for arc length.

Which 1949 computer was the first to calculate more than 2,000 digits of π?

ENIAC took 70 hours in September 1949 to produce 2,037 digits, nearly doubling in a single run the 1,120 digits that had been the record earlier that year.

Bill Gosper computed a record 17 million digits of π in 1985 using a 1914 series by which mathematician?

Srinivasa Ramanujan published the series in 1914; it converges far faster than the formulas that had dominated π records for two centuries, and Gosper was the first to use it for a record.

Which brothers' 1980s algorithms quadruple, then quintuple, the correct digits of π at every step?

The Borwein brothers, Jonathan and Peter, left the Brent–Salamin method behind: it doubles the correct digits at each step, so one step of their fourfold algorithm does the work of two.

The Brent–Salamin algorithm for π is also named after Legendre and which German mathematician of the same era?

Carl Friedrich Gauss's work on the arithmetic–geometric mean lay behind the method that Richard Brent and Eugene Salamin each published in the 1970s; it doubles the number of correct digits at every step.

Just 25 iterations of the AGM-based Brent–Salamin algorithm yield how many correct digits of π?

Since each iteration doubles the correct digits, 25 iterations of Brent–Salamin give about 45 million; its heavy memory use is why records rely on the Chudnovsky series instead.

Estimating π by scattering random points over a square is a classic example of which method, named after a casino?

Monte Carlo methods were named in the 1940s after the Monaco casino where a relative of the mathematician Stanisław Ulam liked to gamble; like roulette, they get answers from repeated random trials.

The 1995 BBP formula extracts a lone digit of π without the earlier ones, but only in which system?

Hexadecimal (base 16) digits fall straight out of the BBP formula because it is a sum of terms in powers of 1/16, so a digit far along can be found without working out the ones before it.

Rabinowitz and Wagon's 1995 method drips out digits of π one at a time; what is it called?

A spigot algorithm is named after a tap: digits drip out in order, one at a time, and once a digit has emerged the method never needs it again.

Which creator of FFmpeg and QEMU set a 2009 π record on a home PC, not a supercomputer?

Fabrice Bellard's desktop PC cost under 2,000 euros and needed 131 days to reach nearly 2.7 trillion digits, overtaking a record set four months earlier on a multi-million-euro supercomputer.

Emma Haruka Iwao set π records in 2019 and 2022 while working for which company?

Google's cloud did the work: Emma Haruka Iwao announced 31.4 trillion digits on Pi Day 2019, lost the record a year later, and took it back in 2022 with 100 trillion.

From 2010 to 2024, every record for digits of π was computed with which program?

Y-cruncher grew out of a big-number library that Alexander Yee started writing in high school; it has since carried the record from trillions of digits to hundreds of trillions.

In 1961 Daniel Shanks and John Wrench took π past 100,000 digits on a 7090 mainframe built by which company?

IBM's 7090 produced 100,265 digits in a single run, over 140 times the 707 that the Victorian amateur William Shanks had spent years working out by hand.

Roughly how many digits of π fix the observable universe's circumference to within one atom?

About 40 is all it takes: one standard reckoning says 39 digits and NASA's says 37 decimals, so the trillions of digits computed since are for sport and for testing computers, not for measuring anything.

Heisenberg's uncertainty principle states Δx·Δp is at least Planck's constant h divided by what?

The bound is h/4π: physicists usually write it as ħ/2, where ħ is Planck's constant divided by 2π, so π sits inside the most famous limit in quantum physics.

By Barbier's theorem, every curve of constant width w has what perimeter?

Barbier's theorem gives perimeter πw for every curve of constant width w, so a Reuleaux triangle, built from three arcs of radius w, is exactly as far around as a circle of diameter w.

In a square with an inscribed circle, random dots land inside the circle with what probability?

The circle covers π/4, about 0.785, of the square around it, so four times the share of dots that land inside gives an estimate of π, though one that homes in very slowly.

The area under the basic bell curve e^(−x²), over the whole real line, equals what?

√π is the area under the whole curve, which is why π turns up in the bell curve of statistics; the classic proof squares the integral and switches to polar coordinates, where a circle appears.

A right angle is exactly how many radians?

A right angle is π/2 radians because a full 360° turn is 2π radians, so 1° = π/180.

What is the surface area of a sphere of radius r?

The surface area is 4πr², the same as the curved side of a cylinder that just fits around it.

What is the area of an ellipse with semi-major axis a and semi-minor axis b?

The area is πab, which becomes the familiar circle formula when a and b are equal; the perimeter is far harder, with no exact formula in elementary terms at all.

Measurement of a Circle shows that a circle has the same area as which figure built from its radius and circumference?

A right triangle with the radius and the circumference as its two short sides: the ancient proof shows that the circle can be neither larger nor smaller than that triangle, so the two must be equal.

In which Carl Sagan novel is a message from the universe's creator hidden in the digits of π?

Contact ends with Ellie finding a circle of 0s and 1s buried deep in π's digits once they are written in base 11, a signature left by whoever built the universe.

In the 1967 Star Trek episode 'Wolf in the Fold', how is a possessed computer neutralized?

Spock orders the computer to compute π to the last digit, tying up the Redjac entity with an endless task since π never terminates or repeats; the episode aired in December 1967.

Which director made his feature debut with the 1998 thriller Pi?

Darren Aronofsky raised part of Pi's budget through $100 donations from friends and family, then won the Directing Award at Sundance; in the film a computer named Euclid spits out a mysterious 216-digit number.

Yann Martel's Life of Pi won which literary award in 2002?

Life of Pi won the 2002 Man Booker Prize; the novel had been turned down by at least five London publishers before Knopf Canada took it.

Which 1985 Douglas Hofstadter book first floated reciting π to the six 9s, then saying 'and so on!'?

Metamagical Themas collects Hofstadter's Scientific American columns; the title is an anagram of Mathematical Games, the Martin Gardner column it took over from.