70 Fun Facts About Math and Science

Pi, about 3.14159, is the ratio of a circle's circumference to which of its measurements?

Because it is irrational, its decimal expansion never ends and never repeats; by the 2020s computers had calculated it to trillions of digits.

In the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, what number comes next?

Each term is the sum of the two before it, and the pattern shows up in sunflower seed heads, pine cones and the spirals of a nautilus shell.

The Pythagorean theorem says the square on which side equals the sum of the squares on the other two?

The classic 3-4-5 triangle is the simplest whole-number example: 9 plus 16 equals 25.

The interior angles of any triangle always add up to how many degrees?

That is only true on a flat surface; draw a triangle on a sphere, like the Earth, and the angles add up to more.

A googol is 10 raised to which power?

The name was coined by a nine-year-old, mathematician Edward Kasner's nephew, and later inspired the misspelled name of a certain search engine.

A Möbius strip is a famous example of what kind of surface?

You can make one by giving a paper strip a half twist and taping the ends; an ant walking along it would cover both "sides" without ever crossing an edge.

After 358 years of failed attempts, who finally proved Fermat's Last Theorem in 1994?

Fermat had scribbled in a book margin that he had a marvellous proof that the margin was too small to contain; the eventual proof ran to over 100 pages.

Per the theorem proved by computer in 1976, at most how many colours does any map need so neighbours differ?

It was the first major theorem proved with the help of a computer, and some mathematicians at the time refused to accept a proof no human could check by hand.

Which 17th-century English mathematician first used the sideways-eight infinity symbol?

The shape is sometimes called a lemniscate, from the Latin for "decorated with ribbons".

In Roman numerals, what number does the letter M represent?

The system uses just seven letters in total, and there is no symbol for zero.

In Roman numerals, what number does MCM stand for?

A smaller numeral placed before a larger one is subtracted, which is why the letters for 100 and 1000 side by side make 900.

The binary number system used by computers writes every number using only which two symbols?

In binary the number ten is written 1010, and each digit is called a bit, short for binary digit.

Ada Lovelace's algorithm, called the first computer program, was written for which Babbage machine?

Her notes computed Bernoulli numbers, and she was the first to see that such a machine could do more than crunch numbers.

A perfect number equals the sum of its proper divisors. What is the smallest one?

The next one is 28, and nobody has ever found an odd perfect number, or proved that none exists.

Euclid, the "father of geometry", is chiefly known for which treatise?

Written around 300 BC, it was used as a standard textbook for more than two thousand years.

Which mathematician was honoured after his death with a medal calling him the "Prince of Mathematicians"?

As a schoolboy he reportedly summed the numbers 1 to 100 in seconds by pairing them into 50 pairs of 101.

Hypatia, the celebrated ancient philosopher and mathematician, lived and taught in which city?

She was murdered by a mob in 415 AD, and her death is often treated as a symbol of the end of classical learning.

1729 is the smallest number expressible as the sum of two of what, in two different ways?

G. H. Hardy had arrived by taxi number 1729 and called it dull; Ramanujan instantly saw it as 1³ + 12³ and 9³ + 10³.

Katherine Johnson, whose calculations were critical to early US crewed spaceflights, worked for which organisation?

John Glenn reportedly asked for her to check the computer's numbers by hand before he would fly his 1962 orbital mission.

What is the square root of 2, to three decimal places?

It is the length of the diagonal of a square with sides of 1, and legend says the Pythagoreans were horrified to discover it cannot be written as a fraction.

A gross is a group of how many items?

It is a dozen dozens, and a "great gross" is a dozen of those: 1,728.

Goldbach's conjecture, still unproven, says every even number greater than 2 is the sum of two of what?

It has been checked by computer for every even number up to four quintillion, yet no one has proved it holds for all of them.

What is the smallest prime number?

It is also the only even prime, since every other even number can be divided by two.

Which Swiss mathematician introduced much of modern notation, including the concept of a function?

He kept producing roughly a paper a week even after going almost completely blind, dictating his work to assistants.

In which year was Isaac Newton's Principia first published?

Edmond Halley, of comet fame, paid for the printing himself after the Royal Society ran out of money.

Albert Einstein won the 1921 Nobel Prize in Physics for which discovery?

The prize citation pointedly did not mention relativity, which was still considered too controversial by parts of the committee.

Who was the first person to win a Nobel Prize twice?

Her two prizes were in different sciences, physics in 1903 and chemistry in 1911, a feat no one else has matched.

By 2010, how many entries on the periodic table were known, completing its first seven rows?

Only about 94 of them occur naturally on Earth; the rest have been made in laboratories, often lasting a fraction of a second.

Which is the lightest and most abundant chemical element in the universe?

It makes up about three quarters of all normal matter, and stars like the Sun shine by fusing it into heavier atoms.

Which element has the chemical symbol Au?

The symbol comes from the Latin word aurum, and the metal is so soft that a single gram can be beaten into a sheet a square metre wide.

The speed of light in a vacuum is roughly how many kilometres per second?

At that speed light from the Sun still takes about eight minutes to reach Earth.

DNA is a polymer whose two chains coil around each other to form what shape?

Stretched out, the DNA in a single human cell would be about two metres long.

Absolute zero, the lowest possible temperature, is equivalent to what on the Celsius scale?

Scientists have cooled atoms to within a billionth of a degree of it, but it can never be reached exactly.

Penicillin was discovered in 1928 by which Scottish physician?

He noticed it by accident when mould contaminated a dish of bacteria he had left out while on holiday.

Edward Jenner created the world's first vaccine, protecting against which disease?

The word vaccine comes from vacca, Latin for cow, because his method used material from cowpox sores.

Dry air is about 78% which gas?

Oxygen is only about a fifth of the air, and argon, a gas most people never think about, comes third at almost 1%.

Halley's Comet returns to the inner Solar System roughly every how many years?

It last passed in 1986 and is due back in 2061, so most people get at most one or two chances to see it.

Which Russian chemist formulated the periodic law and an early periodic table?

He left gaps for elements not yet discovered and correctly predicted the properties of gallium and germanium before anyone found them.

Gregor Mendel, founder of modern genetics, worked out his laws of inheritance by breeding which plant?

He was an Augustinian friar and grew about 28,000 plants in the monastery garden over eight years.

In which 1859 book did Charles Darwin publish his theory of evolution?

The first printing of 1,250 copies sold out on the day it was published.

Nikola Tesla is best known for contributions to which kind of electricity supply system?

His system won the so-called War of the Currents against Thomas Edison's rival approach and became the standard for household power grids.

Using an improved telescope he built himself, Galileo observed the four largest moons of which planet?

Those four moons, Io, Europa, Ganymede and Callisto, are still called the Galilean moons in his honour.

DNA pioneer Rosalind Franklin was an expert in which technique?

Her famous image, Photo 51, was shown to James Watson without her knowledge and helped him and Francis Crick build their model.

Oxygen is the third most abundant element in the universe. Which element is the second most abundant?

On Earth it is the most abundant element in the crust by mass, largely locked up in rocks and water.

What is the atomic number of carbon?

Its six protons let it form four bonds at once, which is why it is the backbone of every known form of life.

What is the longest bone in the human body?

It is also the strongest, and it can support up to about 30 times the weight of an adult.

Insulin was first isolated in 1921 by Frederick Banting and Charles Best at a university in which city?

Within a year it was being used to treat diabetic patients, and Banting shared the 1923 Nobel Prize, becoming its youngest medicine laureate.

Anders Celsius, who proposed his temperature scale in 1742, was from which country?

His original scale ran the other way, with 0 as boiling and 100 as freezing; it was flipped after his death.

The Richter scale for measuring earthquake strength was presented by Charles Richter in which year?

Each whole number step on the scale means about 32 times more energy released.

Which massless particle can only ever move at the speed of light?

Every beam of light is a stream of them, and a bright bulb emits around a billion billion every second.

The neutron was discovered in 1932 by which physicist?

The discovery came less than a decade before it made nuclear fission, and the atomic bomb, possible.

Measurements of the universe's expansion put its age at roughly how many years?

Earth, by comparison, is only about 4.5 billion years old, so the universe had already existed for nine billion years before our planet formed.

Olympus Mons, the largest known volcano in the Solar System, is found on which planet?

It rises about 22 km, nearly two and a half times the height of Everest, and its base would cover most of France.

What is the point on the ground directly above where an earthquake begins called?

The rupture itself can start tens or even hundreds of kilometres underground.

On the Mohs hardness scale, which mineral scores the maximum 10?

The scale is not evenly spaced: the jump from 9 to 10 is about four times greater than the jump from 8 to 9.

The Avogadro constant is approximately 6.022 times 10 to which power?

Chemists celebrate Mole Day on 23 October, from 6:02 am to 6:02 pm, in its honour.

Around when did Euclid demonstrate that there are infinitely many prime numbers?

Since 1951 every record-size prime has been found by computer, many through the Great Internet Mersenne Prime Search.

What shapes sat atop the tomb of Archimedes, as described by Cicero, marking his proudest result?

He had shown a sphere has two-thirds the volume and surface area of its circumscribing cylinder.

What nickname did the Roman general Marcellus give Archimedes, whose war machines defended Syracuse?

Briareus was a hundred-handed giant; Marcellus had ordered Archimedes spared, and was angered when a soldier killed him anyway.

In which year did William Thomson, later Lord Kelvin, propose an absolute temperature scale?

The kelvin was formally added to the SI in 1954; in the early 20th century the scale was often called the 'absolute Celsius' scale.

Which human tissue component contains no mitochondria at all?

A liver cell, by contrast, may hold more than 2,000; the organelle's own bacterium-like genome supports the endosymbiotic theory.

What is the approximate speed of sound in air at 20 °C?

That is about 767 mph; Newton's Principia underestimated it at 979 feet per second, about 15% too low, by ignoring temperature fluctuations in the wave.

Sound travels faster through which of these gases?

Sound moves faster in low-molecular-weight gases like helium than in heavy ones like xenon; for a given ideal gas only temperature, not pressure, matters.

What tied with Euler's identity as 'greatest equation ever' in a 2004 Physics World poll?

A 1990 Mathematical Intelligencer poll had already named Euler's identity the most beautiful theorem in mathematics.

In which 1748 work did Euler first publish the formula from which his famous identity follows?

The identity links five fundamental constants using addition, multiplication and exponentiation exactly once each.

Where in India does an AD 876 stone inscription show the first certain symbol for zero?

The Bakhshali manuscript uses a black dot for zero; the word itself reached English via Italian from Arabic ṣifr, meaning empty.

Which Mesoamerican people may have invented the Long Count calendar's zero, before the Maya?

The eight earliest Long Count dates were found outside the Maya homeland; the Maya later used a shell-shaped glyph for zero.

By what name is Pascal's binomial array known in China, after a 13th-century mathematician?

Jia Xian had described it in the 11th century; Pascal's own treatise on it was published posthumously in 1665.

Who illustrated Pacioli's 1509 Divina proportione and called the golden ratio the 'sectio aurea'?

Pacioli's book, largely plagiarised from Piero della Francesca, gave the ratio its 'divine proportion' name; Euclid had called it the extreme and mean ratio.

The golden ratio is the ratio of a regular pentagon's diagonal to which other length?

That is why it appears in constructing the dodecahedron and icosahedron; its value is (1+√5)/2, about 1.618.