Here are 50 facts from FunFact's “Maths & logic” topic, all checked. Each one cites its source (mathshistory.st-andrews.ac.uk, fr.wikipedia.org, mathworld.wolfram.com…) and the date it was checked. This topic is part of FunFact Premium.
Euler’s formula (vertices − edges + faces = 2) requires this as soon as three faces meet at every vertex.
The classic ball is a truncated icosahedron: 12 pentagons, 20 hexagons, 60 vertices, 90 edges. The number of hexagons can vary (zero in a dodecahedron), but the number of pentagons never does.
Source: Science News — Bending a Soccer Ball · Checked on October 24, 2026
The plus and minus symbols were originally used to measure wine or goods.
Merchants marked barrels with vertical or horizontal strokes to show a surplus or shortage of goods, giving rise to the arithmetic symbols.
Source: Oxford Mathematical History — Plus and Minus · Checked on October 24, 2026
The Modulor starts from a standard man 1.83 m (6 ft) tall: his height divided by the height of his navel (1.13 m, or 3 ft 8 in) gives 1.619.
Conceived by Le Corbusier in the mid-20th century, this “measure-man” was meant to standardize housing: ceiling heights, doors and stairs are set to his proportions. A real example of deliberate use of the golden ratio in architecture.
Source: Le Méridional — Culture Sud : la Cité Radieuse, l'œuvre d'art que l'on habite · Checked on October 24, 2026
It appeared in the 16th century.
Mathematicians first wrote “r” for root, and the letter then turned into this sign.
Source: MacTutor History of Mathematics — Mathematical Symbols · Checked on October 24, 2026
The Jesuit Joachim Bouvet, writing from Beijing in 1701, told him that the hexagrams of the I Ching (Yi Jing) match his system: sequences of 0s and 1s.
Each hexagram is made of six lines, solid or broken, which can be read as six binary digits. Leibniz saw in this a proof of the universality of his system. Three centuries later, binary is the basis of every computer.
Source: Wikipédia · Checked on October 24, 2026
This is the isoperimetric inequality: for a given surface area, no shape contains more volume than a sphere.
The surface tension of the soap film tries to shrink its surface to a minimum, so the bubble becomes spherical. In a plane, it is the disk that has the maximum area for a given perimeter.
Source: Université de Berkeley (Soap bubbles and isoperimetric problems) · Checked on October 24, 2026
The proof was given by the Russian Evgraf Fedorov in 1891, then by George Pólya in 1924.
Friezes, tilings, fabrics or mosaics like those of the Alhambra: any pattern that repeats in two directions belongs to one of these 17 “wallpaper groups.” It is a complete classification of the possible symmetries.
Source: EscherMath — Wallpaper Patterns · Checked on October 24, 2026
At 130 km/h, 100 km takes 46 minutes; at 110 km/h, just under 55 minutes. The gap is a little over 8 minutes.
Time = distance ÷ speed: 100 ÷ 130 h ≈ 46 min 9 s, 100 ÷ 110 h ≈ 54 min 33 s. Since air resistance grows with the square of speed, you use noticeably less fuel at 110 than at 130 km/h.
Source: Europe 1 — Temps de trajets, pollution... 110 km/h sur autoroute, ça change quoi ? · Checked on October 24, 2026
The number of possible arrangements of a 52-card deck is beyond imagination.
A 52-card deck can be shuffled in 8 × 10⁶⁷ ways, an 8 followed by 67 zeros. The observable universe has about 10²² to 10²⁴ stars, and Earth has about 10⁵⁰ atoms. Example: a well-shuffled deck is very likely in an order that has never existed before.
Source: American Mathematical Society — Card Shuffling Odds · Checked on October 24, 2026
For a run of at least 6, the probability is still 81%. Long runs are normal in true randomness.
Statistics teachers ask their students to invent a sequence of 100 flips: it generally contains too few long runs, and the teacher spots the fake with high reliability (about 90% in one classroom experiment). True randomness is more irregular than we imagine.
Source: Wolfram Demonstrations (Consecutive Heads or Tails) · Checked on October 24, 2026
Whether it is 10 letters or 10,000, the result is nearly identical: 1/e ≈ 36.8%. Problem posed by Montmort in 1708.
The Frenchman Pierre Rémond de Montmort studied it in a card game, the “jeu du treize.” It is called the “problème des rencontres” or the derangement problem. Surprising result: the number of letters hardly changes anything.
Source: Wolfram MathWorld — Derangement · Checked on October 24, 2026
Cicadas of the genus Magicicada have cycles of 13 or 17 years depending on the species and emerge en masse, by the millions.
One popular hypothesis: a prime cycle reduces encounters with predators or rival species on shorter cycles (2, 3, 4, 5 or 6 years). Biologists still debate it: it is a serious lead, not a certainty.
Source: Scientific Reports — Massospora cicadina fungal parasite of periodical cicadas · Checked on October 24, 2026
Red, green, blue: 256 × 256 × 256 = 16,777,216. White is (255, 255, 255), black is (0, 0, 0).
256 values correspond to 8 bits, one byte per primary color, hence the “24 bits” of “true color.” Web codes like #FF0000 are written in hexadecimal (base 16), where FF equals 255: that is pure red.
Source: Université Jean Monnet, Saint-Étienne — Master 2 SIG : La chaîne de traitement vidéo · Checked on October 24, 2026
No evidence links Einstein to this five-houses puzzle; it was published in Life International magazine in 1962.
The claim that “only 2% of people can solve it” is also a myth attached to it. You solve it with a grid and successive eliminations: pure logic, no genius required.
Source: Mensa — Mensans love logic puzzles, right? · Checked on October 24, 2026
Four equally likely cases: GG, GB, BG, BB (G = girl, B = boy). If you know there is at least one girl, BB drops out: 3 cases remain, and only one is GG.
It all depends on how you learned the information. If you know the older child is a girl, the probability that the younger one is one too is indeed 1 in 2. This puzzle was popularized by Martin Gardner in 1959.
Source: The New York Times — The psychology of getting suckered · Checked on October 24, 2026
Francis Galton observed it in 1886: children of very tall parents are, on average, a bit less tall than they are.
Daniel Kahneman tells of Israeli Air Force instructors who thought criticism led to improvement, because after a botched maneuver the next one was better. It was simply the return toward the average.
Source: University of Vermont — Regression to the Mean · Checked on October 24, 2026
It was receiving too many false solutions. In 1882, Lindemann proved that this problem is impossible.
Constructing, with a straightedge and compass, a square with the same area as a circle: the challenge dates back to antiquity. It is impossible because π is “transcendental.” The expression “trying to square the circle” has since meant taking on an unsolvable problem.
Source: Futura — Quadrature du cercle : pourquoi dit-on que c'est impossible ? · Checked on October 24, 2026
This claim is widely discredited: the façade’s proportions only land on 1.618 if you pick the measuring points as you please.
The golden ratio is about 1.618. The mathematician George Markowsky showed in 1992 that many “proofs” rely on measurements chosen after the fact. Nothing in ancient sources suggests the architects sought it.
Source: Cambridge Archaeological Journal — Did the Greeks Build According to the Golden Ratio? · Checked on October 24, 2026
A “percentage point” is the gap between two rates; a “percentage” is a relative change.
Likewise, a rate that goes from 3% to 2.4% falls by 0.6 points, or −20%. Mixing the two can make headlines say anything: “+100%” can describe a move from 0.1% to 0.2%.
Source: The Journalist's Resource — Percent change versus percentage-point change · Checked on October 24, 2026
Study by mathematicians Dave Bayer and Persi Diaconis (1992). With fewer than 5 shuffles, the order remains tied to the starting order.
This is the riffle shuffle (called the “American” shuffle in France): you cut the deck in two and interleave the halves. The more you shuffle, the closer the deck gets to a random order; with too few shuffles, traces of the original order remain.
Source: Science News — Disorder in the Deck · Checked on October 24, 2026
In “La Géométrie” (1637), he denotes unknowns with the last letters of the alphabet and constants with the first.
Before him, equations were often written out in sentences or with symbols specific to each author. This convention has remained universal. “Cartesian coordinates” also owe their name to Descartes, whose Latin name was Cartesius.
Source: MacTutor (University of St Andrews) — Earliest Uses of Symbols for Variables · Checked on October 24, 2026
The two French mathematicians were trying to work out how to fairly split the stakes of an interrupted game.
An exchange of letters between the French mathematicians Blaise Pascal and Pierre de Fermat laid the rigorous mathematical foundations for calculating risks and gains.
Source: MacTutor History of Mathematics — Probability Origins · Checked on October 24, 2026
The last leap second was on December 31, 2016. It is used to realign atomic time with the Earth's irregular rotation.
These added seconds have caused computer outages: in 2012, several websites crashed. In 2022, the General Conference on Weights and Measures decided to abandon them by 2035 at the latest; in October 2026, it moved the deadline up to May 20, 2027.
Source: Paris Match Belgique — Cette grande mesure qui entrera en vigueur l'année prochaine change notre manière de mesurer le temps · Checked on October 24, 2026
Proven by Donald Knuth in 1976-1977: a strategy can win in 5 moves at most.
Invented in 1970 by Mordecai Meirowitz, the game consists of guessing a combination from hints telling you how many pegs are the right color in the right spot, or the right color in the wrong spot. Knuth's algorithm picks, at each guess, the move that eliminates the most possibilities.
Source: Wolfram MathWorld — Mastermind · Checked on October 24, 2026
They are Reuleaux heptagons: their width is identical in every direction, like that of a circle.
Thanks to this, a vending machine recognizes them whatever their orientation, like a round coin. The Reuleaux triangle, from the same family, resembles the rotor of the Wankel engine (whose sides are, however, a little flatter).
Source: Scientific American — British Objects of Constant Width · Checked on October 24, 2026
An edict by King Charles IX (known as the Edict of Roussillon, 1564) set the start of the year at January 1, applied in 1567. Before that, depending on the diocese, the year began at Christmas, on March 25, at Easter or on March 1.
Because Easter falls on a different date each year, some years lasted longer than others. For dates from January to April before 1567, historians must therefore specify which start of the year (“style”) is being used.
Source: Hérodote.net — 9 août 1564 : l'édit de Roussillon · Checked on October 24, 2026
A treatment can look less effective on average while being better in every group.
One medical treatment can seem less effective overall than another, yet prove superior in every demographic subgroup when the data are analyzed separately.
Source: American Statistician — Simpson's Paradox · Checked on October 24, 2026
His trick: 50 pairs of numbers that each add up to 101.
He paired 1 and 100, 2 and 99, 3 and 98… making 50 pairs of 101, so 5,050. The same trick gives the sum of the integers from 1 to n: n × (n+1) ÷ 2. The anecdote may be embellished, but the method is real.
Source: Mathematical Association of America — Gauss Anecdote · Checked on October 24, 2026
Wounded in a duel on May 30, 1832, he died the next day. His letter to his friend Auguste Chevalier, published as early as September 1832, was taken up by Liouville in 1846.
In it, Galois gave a criterion for knowing when an equation can be solved using radicals (square roots, cube roots…). Misunderstood in his lifetime, these ideas became “Galois theory,” a pillar of modern algebra.
Source: Encyclopedia.com — Evariste Galois · Checked on October 24, 2026
€100 → €150 → €75: you have lost 25%. To cancel a 50% increase, you need a 33.3% decrease.
A percentage is always calculated on the current value, not on the original one. The trap applies to prices, salaries or investments. Conversely, to cancel a 50% decrease, you need a 100% increase.
Source: Wikipédia (Pourcentage) · Checked on October 24, 2026
On a dry road, it takes about 14 m (46 ft) to stop once braking begins at 50 km/h (31 mph), and about 56 m (184 ft) at 100 km/h (62 mph), not counting reaction time.
The energy to be dissipated is proportional to the square of the speed. On top of that comes the distance covered during reaction time (about 14 m, or 46 ft, per second at 50 km/h). A crash at 50 km/h (31 mph) carries nearly three times as much energy than one at 30 km/h (19 mph).
Source: Wikipédia · Checked on October 24, 2026
From €10 to €40, you gain €30, which is 3 times the starting price, so +300%. Conversely, a decrease cannot exceed 100%.
The percentage increase counts only the increase, not the starting price: “+100%” means “multiplied by 2.” A 100% decrease leads to zero; there is no such thing as a 150% decrease.
Source: Math93 — Cours de 1re ES : les pourcentages · Checked on October 24, 2026
This is “God's number,” proven in 2010 with the help of computing time provided by Google (about 35 processor-years). One move = a quarter turn or half turn of one face (26 counting quarter turns only).
That doesn't mean it's easy: finding those 20 moves is very hard for a human, who in practice uses many more. The human world record is measured in seconds.
Source: cube20.org — God's Number is 26 in the Quarter Turn Metric · Checked on October 24, 2026
Even with one digit per Planck volume, the smallest conceivable unit of volume, it still wouldn't fit in the entire observable universe.
This number appears as an upper bound in a math problem by Ronald Graham (1970s) and once held the record for the largest number used in a proof. Its last digits, however, are known: it ends in ...2464195387.
Source: Rice University — Numbers Beyond Belief · Checked on October 24, 2026
In The Sand Reckoner (3rd century BC), he invents a notation to name numbers far larger than those of the Greek era.
The Greeks could hardly count beyond the myriad (10,000). Archimedes shows that gigantic numbers can be named by grouping powers. His calculation is based on the size of the universe according to Aristarchus and, always rounding up, gives at most 10^63 grains.
Source: Ilan Vardi — Archimedes, The Sand Reckoner · Checked on October 24, 2026
European regulations allow a speedometer to show up to 10% + 4 km/h (2.5 mph) more than the real speed, but never less.
At a real 80 km/h (50 mph), the speedometer can therefore show up to 92 km/h (57 mph), but not 79 (49 mph). Speed cameras go by the real speed. GPS generally gives a speed closer to reality than the dashboard speedometer.
Source: Assemblée nationale — Question écrite n° 17072 sur la précision des compteurs · Checked on October 24, 2026
The “honeycomb conjecture,” mentioned since antiquity, was proved by the mathematician Thomas Hales.
Among all ways of dividing the plane into cells of equal area, the regular hexagon has the smallest total perimeter. Bees do not do this calculation: the shape also results from the physics of wax warmed by their bodies.
Source: Quanta Magazine — Mathematicians Complete Quest to Build 'Spherical Cubes' · Checked on October 24, 2026
This is the “37% rule”: after that, you choose the first candidate who is better than all the previous ones.
This strategy gives about a 37% chance of choosing the best candidate, and no strategy does better. It assumes you can’t go back: it’s a simplified model, useful for thinking about hiring or a housing search.
Source: Collège de France — Algorithmes pour flux de données · Checked on October 24, 2026
It is calculated from the other digits.
If the scanner misreads a digit, the calculation no longer adds up and the code is rejected. It is a check digit.
Source: GS1 Standards Organisation — Barcode Check Digits · Checked on October 24, 2026
It takes 2^64 - 1 moves, about 1.8 × 10^19, at one per second. The game was invented by the Frenchman Édouard Lucas in 1883.
According to the legend attached to this puzzle, monks are supposedly moving 64 golden disks: when they finish, the world would vanish. In reality, the number of moves nearly doubles with each added disk: 7 disks require 127, and 10 disks require 1,023.
Source: Scientific American — The Tower of Hanoi · Checked on October 24, 2026
Jacques Perret, professor of Latin philology at the Sorbonne, replied to IBM France on April 16, 1955, suggesting “ordinateur” rather than “calculateur” (calculator).
IBM was looking for a name for its IBM 650 machine, which did far more than calculate. Perret pointed out that the Littré, a French dictionary, already used this word for God, who puts the world in order. IBM first wanted to protect it, then left it in the public domain.
Source: Centenaire IBM France — 1955 : le terme « Ordinateur » est inventé par Jacques Perret, à la demande d'IBM France · Checked on October 24, 2026
Idea of Count Buffon (1733): if the needle is as long as the spacing between the floorboard grooves, it crosses a groove with a probability of 2/π, about 64%.
The more needles you throw, the closer the ratio “needles crossing a groove / throws” gets to 2/π. It is one of the first probability-based calculation methods, an ancestor of Monte Carlo methods. But it converges very slowly.
Source: Scientific American — How to find pi in randomness all around you · Checked on October 24, 2026
It does follow a logarithmic spiral, but that isn’t enough for its growth ratio to be the golden ratio.
There are infinitely many logarithmic spirals: only one matches the golden ratio. Measurements of real shells give growth ratios different from that of the golden spiral. The nautilus has a beautiful spiral, but it is not a symbol of the golden ratio.
Source: Towson University — Nautilus Spirals and the Meta-Golden Ratio Chi · Checked on October 24, 2026
The Republican calendar, used from 1793 to 1806, replaced the week with the décade and Sunday with the décadi.
Workers lost rest days that way, especially since religious holidays were abolished. Each month had 30 days and the year ended with 5 or 6 extra days, the “sans-culottides.”
Source: World History Encyclopedia — Calendrier Républicain · Checked on October 24, 2026
According to the historian Suetonius, Caesar replaced each letter with the one three places further on: A becomes D, B becomes E…
With 25 possible shifts, you just try them all to decrypt the message. A variant, ROT13 (a shift of 13), applied twice returns the original text, since the alphabet has 26 letters.
Source: Fordham University — Suetonius, The Lives of the Caesars: The Deified Julius · Checked on October 24, 2026
Twelve semitones make an octave, and the octave doubles the frequency: 1.0595¹² ≈ 2. The tuning-fork A vibrates at 440 Hz, the next A at 880 Hz.
This “equal temperament” makes it possible to play in every key on the same instrument. In exchange, only the octave is perfectly in tune: the fifth, for example, is very slightly smaller than a pure fifth (1.4983 instead of 1.5).
Source: Simon Fraser University — Handbook for Acoustic Ecology: Equal Temperament · Checked on October 24, 2026
Your right hand stays on the same side in the mirror; only depth is reversed.
The impression of a left-right reversal comes from the fact that you turn around 180° to face the mirror: you compare your reflection to an imaginary double who has been turned around. The mirror itself only changes the axis perpendicular to it.
Source: BBC Science Focus — Why do mirrors reverse left and right, not up and down? · Checked on October 24, 2026
Echinoderms are bilaterians: their five-axis symmetry only appears in adulthood.
The group includes starfish, sea urchins and sea cucumbers. They are distant cousins of vertebrates (the group we belong to): their larvae swim with left-right symmetry before metamorphosis.
Source: Echinoblog — Why five ? Mysteries in Symmetry! · Checked on October 24, 2026
This is Benford's law: 1 opens 30.1% of numbers, 9 only 4.6%. Fraudsters who invent numbers often forget it.
Researcher Mark Nigrini proposed using this law against tax fraud as early as 1992, and the Canada Revenue Agency uses it for an initial risk assessment. A deviation is never proof: it only indicates where to look more closely.
Source: MathWorld, A Wolfram web resource — Benford's Law · Checked on October 26, 2026
The radius grows by 1/(2π) ≈ 0.159 m (6.3 in), no matter how big the circle is.
The same math works for an orange: 1 m of extra rope also lifts it 16 cm off its surface. The distance around the Earth (40,000 km, or about 24,900 mi) changes nothing, because circumference equals 2π × radius.
Source: Omni Calculator — String girdling Earth calculator · Checked on October 24, 2026
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