## 60 interesting facts about Mathematics that will surprise, entertain and educate you.

Four is the only number that has the same number of letters as its meaning
F,O,U,R.

A number is divisible by 9 if the sum of the digits is divisible by 9.
9,18,27,36,45...

The number zero does not have its own Roman numeral
IX,XV,CM,VII...

Think to yourself 'How I wish I could calculate pi' and then count the letters in each of the words of that sentence. You now have a way of remembering the first seven digits of pi: 3.141592.
π
There are lots of pi facts on the Pi Day page.

The first number to contain the letter a is 'one thousand'. See A NUMBER for the discussion behind this fact.
1,000

The only number to have its letters in alphabetical order is forty. See Alphanumbetical and try to think of other alphanumbetical mathematical words!
Forty

The numbers on opposite sides of a dice add up to seven.

There are more than 64 squares on a chess board. If you count the squares made up of multiple squares there are 204 altogether. There is one 8x8 square, four 7x7 squares, nine 6x6 squares, 16 5x5 squares, 25 4x4 squares, 36 3x3 squares, 49 2x2 squares and 64 1x1 squares.

A prime number has exactly two factors. Two is the only even prime number and it is also the only prime number not to contain the letter 'e'.
2

It should take no more than 20 moves to solve a Rubiks cube no matter which of the 43 quintillion possible starting positions you begin with.

A dodecahedron has twelve pentagonal sides.
.

A googol is one followed by one hundred zeros. This can be written as:
10100.

Not many people appreciate (or understand) the mind-blowing fact that:
e = -1

Triangles, squares and hexagons are the only regular polygons that tessellate.

Check for yourself at the Tessellations page.

The equals sign was invented in 1557 by Welsh mathematician Robert Recorde. The word 'equal' is from the Latin word aequalis as meaning uniform, identical, or equal.
=

111111111 x 111111111 = 12345678987654321.

These two fractions add up to one and between them they contain all of the digits from nought to nine. It is the only way that this can be done.

[Update: 12th Aug 2019, received a message on Twitter from @ignormatyk saying that this was not the only way and there are others for example: 45/90+138/276 and 38/76+145/290]

Eight comes first if all the numbers are arranged alphabetically. What number would come last?
8

More numbers begin with the digit one than any other digit. This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers and mathematical constants. This fact was famously attributed to physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881.

Alice in Wonderland learns that in a class of 23 pupils the probability that two have the same birthday is more than a half. Alice is a fictional character created by author and mathemetician Lewis Carroll (1832-1898).

42 is the answer to the 'Ultimate Question of Life, the Universe, and Everything' according to 'The Hitchhiker's Guide to the Galaxy' created by Douglas Adams.

18 is the only number that is twice the sum of its digits.

Most clocks which have Roman numerals on their face use IIII for four instead of the more familiar IV.

.

There are currently over 7 billion people in the world and the number is growing very quickly. To see just how quickly have a look at our population counter.

Any number to the power zero is 1, and zero to any power is 0. The only unanswered question here is what is zero to the power zero?
00

The Fibonacci sequence is a sequence of numbers where each term is the sum of the previous two terms. The first two terms are both one. The ratio of the nth term to the next term gets closer to the golden ratio as n increases.

Air France, Iberia, Ryanair, AirTran, Continental Airlines, and Lufthansa don’t have a row 13 on their airlines because they are aware that many of their passengers consider 13 to be an unlucky number. Many office blocks, office buildings and hotels do not have a 13th floor for the same reason.

The following three consecutive numbers are the lowest that are divisible by cubes other than 1:

1375; 1376; 1377
(divisible by the cubes of 5, 2 and 3 respectively).

The digits of the number are the same as the digits of the power of ten in these cases:
1.3712885742 = 100.13712885742
237.5812087593 = 102.375812087593
3550.2601815865 = 103.5502601815865
46692.4683 = 10 4.669246833

The polar diameter of the Earth is quite close to (within 0.1%) half a billion inches.

The first time a digit repeats six times in succession in pi is at the 762nd position where you can find six nines in a row. This is known as the Feynman Point.

The term googol (a 1 followed by 100 zeroes) was first used by a 9- year old boy,Milton Sirotta, in 1938.

Trivia submitted by Paul Christian Sarmiento, Philippines

As weird as it may seem at first glance, f(x) = -1/(x+1) and g(x) = x/(x+1) have the same derivative.

Trivia submitted by Shiraz Dagia, Malawi

A number if multiply by 11 is just you bring down the last digits add the digit to the number on it's left and bring down the first number.
Example:
(15)(11)=---
Bring down 5
(15)(11)=--5
Then, 5+1=6
(15)(11)=-65
Last bring down the first digit which is 1
So,(15)(11)=165.

Trivia submitted by Jericho Fernandez, Laguna, Philippines

There is a number smaller than 'a thousand' or 'a hundred and one' with the letter a - it is any number like 0.001 or 'one thousandth' which is smaller than 101 or 1000. These decimals can get infinitely smaller so the proper term for the trivia should be that the smallest whole number not just the smallest number.

Trivia submitted by QA, Makaben

You can remember the value of Pi (3.1415926) by counting each word's letters in
'May I have a large container of coffee?'.

Trivia submitted by Ms. Prescott,

Trivia improves critical thinking.

Trivia submitted by Wisani, Gauteng, South Africa

A googolplex is a googola googol, or (10100) to the power(10100).

Trivia submitted by Anonymous, Planet Earth

40 when written in words "forty" is the only number with letters in alphabetical order, while one is the only one with letters in reverse order.

Trivia submitted by Dustin Joseph C. Manalo, Bulacan,Philippines

The number 0 is originally called cipher.

Trivia submitted by Paras, Philipines

The billionth digit of Pi (3.1415 ...) is 9.

Trivia submitted by Joy, Manila, Philippines

What is the correct mathematical name of the division bar in a fraction? The answer is VINCULUM.

Trivia submitted by Lovely Tinam-isan, Muntinlupa, Philippines

The term "jiffy" is an actual unit of time which is the 1/100th of a second.

Trivia submitted by Josh Anilov C. Funelas, Manila, Philippines

The value of zero was first used by the ancient Indian mathematician Aryabhata.

Trivia submitted by Wency Orbina, Philippines

2520 is the smallest number that is divisible by 1,2,3,4,5,6,7,8,9 and 10.

Trivia submitted by MathWizard, Phillipines

Moving each letter of the word 'yes' 16 places further up the alphabet produces the word 'oui', the French for 'yes'.

Trivia submitted by Greg Ross, Futility Closet

Forty-two percent of Slovenian two-year-olds know the number two, while only four percent of English two-year-olds do.

Trivia submitted by Francie Diep, Popular Science

The word 'twelve' is worth 12 points in Scrabble. .

Trivia submitted by Greg Ross, Futility Closet

The words 'ace, two, three, four, five, six, seven, eight, nine, ten, jack, queen, king' contain 52 letters. There are 52 cards in a pack (excluding jokers).

Trivia submitted by Greg Ross, Futility Closet

If you square11111111 the answer would be 123456787654321. (count the number of 1s and that's the middle number).

Trivia submitted by Ranz Louie Ricasa, Philippines

The polygon with 1000000 sides is called megagon.

Trivia submitted by Ranz Louie Ricasa, Philippines

99*99=9801
999*999=998001
9999*9999=99980001
99999*99999=9999800001.

Trivia submitted by Ranz Louie Ricasa, Philippines

If you find the difference between the number of edges and the number of faces of the tetrahedron, cube, octahedron and other solid shapes, the results will always be 2.

Trivia submitted by Ranz Louie Ricasa, Olongapo City,Philippines

The second hand on a clock is actually the minute hand.

Trivia submitted by Will, Northampton, England

If you write out pi to two decimal places, backwards it spells “pie”.
Found from buzzfeed.

Trivia submitted by Me, England

The Reuleaux Triangle is a shape of constant width, the simplest and best known such curve other than a circle.

Trivia submitted by Manuel Henryk Fabunan, Philippines

The mathematical name for # (number sign) is octothorpe.

Trivia submitted by Kz Fernandez, Philippines

Can you find two numbers without a final 0 that have a product of 10, 100, 1000, 10000 etc. Here is a method:

5(5)*2(2)=25*4=100
25(5)*4(2)=125*8=1000
125(5)*8(2)=625*16=10000
and so on...

Trivia submitted by Ranz Louie Ricasa, Olongapo City,Philippines

Did you know there are five hundred and twenty-five thousand, six hundred minutes in a year? This special number is the main 'hook' of the song Seasons of Love written for the musical Rent.

In the year 1514 the German artist Albrecht Dürer created an engraving called Melencolia with a magic square in the background. The image below shows an enlargement of the magic square. The date appears in the bottom row of the magic square.

Using consecutive whole numbers and counting rotations and reflections of a given square as being the same there are precisely:

1 magic square of size 3 × 3
880 magic squares of size 4 × 4
275,305,224 magic squares of size 5 × 5.

For the 6×6 case, there are estimated to be approximately 1.77 × 1019 squares.

This trivia is from the excellent book by Professor Ian Stewart called Cabinet Of Mathematical Curiosities.

Zero is the number with the most names or synonyms. It is also known as nought, naught, ow, nil, zilch, zip, diddly-squat, love and scratch.

0

Did you know that if you add 429 and 138 the answer is 567? The calculation contains the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9.

[Transum: There are another 335 ways to construct a similar calculation. Have a go at finding them using the Nine Digit Sum drag-and-drop activity.]

Trivia submitted by April Jean Elumba, University Of Southern Mindanao

J and K are the only letters not in any of the numbers when written as words.

Trivia submitted by Theo,

Using only addition, you can add 8's to get the number 1,000 by:
888+88+8+8+8=1,000.

Trivia submitted by Nightshade, Iligan City

The word Trivia comes from the Latin meaning three ways (tri is the prefix for three). At a three way junction there would be a signpost giving information about each direction. This information could be called trivia!

There are exactly 8! (eight factorial) minutes in four weeks.

This is calculated as follows: 4x7x24x60

= 8x7x6x5x4x3x2x1

= 8!

All ten digit pandigital numbers are divisible by 3 (a pandigital number contains all the digits 0 to 9).

[You can find out more about tests for divisibility here.]

King's Cross station in London has a platform zero! It is the longest platform at the station.

The number 2 is the only prime number that doesn't have the letter e in its name.

Trivia submitted by Origaminess, Naperville

Did you know that rather than (in the UK) having 1p, 2p, 5p etc. coins it would be mathematically more efficient to have 1p, 3p, 11p and 37p coins?

Trivia submitted by No Such Thing As A Fish, Podcast

There are 385072 ways of arranging the numbers 1 - 18 in a circle so that the sum of each pair of adjacent numbers is prime.

Try to find just one of them on the Prime Pairs Game page.

153, 370, 371 and 407 are the only three-digit numbers equal to the sum of the cubes of their digits.

Any four digit number typed by using four calculator keys at the corners of a rectangle is a multiple of eleven.

Here's a useful counterintuitive fact: one 18 inch pizza has more 'pizza' than two 12 inch pizzas.
Area of 18" pizza is π × 92 = 254 square inches.
Area of two 12" pizzas is 2π × 62 = 226 square inches.

Trivia submitted by Fermat's Library via Twitter,

The volume of a deep-pan pizza with radius Z and depth A is
Pi × Z × Z × A

Older people were born longer ago.

142857 is a circular number
142857 × 2 = 285714
142857 × 3 = 428571
142857 × 4 = 571428
142857 × 5 = 714285.

Trivia submitted by Philip Robinson, New Zealand

The Babylonians were using Pythagoras' Theorem over 1,000 years before Pythagoras was born.

Trivia submitted by QI,

Octothorpe is the another term for the hashtag sign or the no. sign (#).
#octothorpe.

Trivia submitted by Andrew Stevenizer, Philippines

29 is the number of short straight lines needed to make the number 29 when it is written as words:

TWENTY NINE

Here is the formula for solving the equation $$ax^2 + bx + c = 0$$.

$$x = \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a}$$

Did you know that there is another formula for finding the roots of quadratic equations? It is called the 'citardauq' (the word quadratic backwards) formula and you can read more about it here but you will never need it for school Maths.

206 is the smallest number that when written in words contains all five vowels exactly once:

TWO HUNDRED AND SIX

Did you know that the area of the regular pentagon on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the regular pentagons on the other two sides?

Can you prove that it is true?

A seventh is eleven sevenths of an eleventh.

Trivia submitted by Olberjb, Reddit

You’ve met the first six primes:
2,3,5,7,13,11

They form a nice calculation:

23 × 57 = 1311

Trivia submitted by Chris Smith @aap03102 Twitter,

12 + 3 - 4 + 5 + 67 + 8 + 9 equals 100.

Trivia submitted by Jimmy Horton, England

The division slash (/) is called the virgule
For example 30/5 = 6.

Trivia submitted by Jimmy Horton, England

All odd numbers have a letter e in them.

Maths teachers are very good correcting their pupils when they use the letter O name when they really mean nought or zero. It is important to distinguish between letters (as used in algebra) and numbers. There are however exceptions to this rule that have come about by common usage:

1. James Bond's number is double 'O' seven
2. The first Scout camp took place in 1907 (nineteen 'O' seven)
3. My telephone number is 'O' two four nine seven one one one
4. A famous TV series was called Hawaii 5 'O'
5. It's my father's birthday. He's celebrating his big five 'O'.

8,549,017,632
contains all of the digits in alphabetical order.

The division symbol is called obelus.

Trivia submitted by Genius Of Sampaguita 2019-2020, TNHS - Main

TWELVE PLUS ONE = ELEVEN PLUS TWO

The left side of this equation is an anagram of the right side!

142,857 × 1 = 142,857
142,857 × 2 = 285,714
142,857 × 3 = 428,571
142,857 × 4 = 571,428
142,857 × 5 = 714,285
142,857 × 6 = 857,142

But how far will this strange sequence of calculations continue?

Here are the only temperatures that are prime integers in both Celsius and Fahrenheit:

-5oC is equal to 23oF
5oC is equal to 41oF.

Trivia submitted by Fermat's Library On Twitter,

FORTY FIVE is an anagram of OVER FIFTY!

Any six digit number where the first three digits are repeated as the second three digits is always divisible by 7, 11 and 13
eg 136136.

Trivia submitted by Kris Tobin, NSW

41 is prime
41+2 is prime
41+2+4 is prime
41+2+4+6 is prime
41+2+4+6+8 is prime
41+2+4+6+8+10 is prime
41+2+4+6+8+10+12 is prime
41+2+4+6+8+10+12+14 is prime
41+2+4+6+8+10+12+14+16 is prime
41+2+4+6+8+10+12+14+16+18 is prime
41+2+4+6+8+10+12+14+16+18+20 is prime
However, this pattern eventually fails. Do you know when?

Trivia submitted by Math Nerd 1729, Philippines

"A decimal point" is an anagram of "I'm a dot in place".

The ratio of the longer to the shorter side of any A-size paper (A3, A4 etc) is equal to the square root of 2.

The number of milliseconds in a day is:

55 × 44 × 33 × 22 × 11

Only digits 1,2 and 3 are possible in the look and say sequence.
1
11
21
1211
111221
312211
13112221
etc.

Trivia submitted by Mr Phil, TSS

That's 103 interesting and surprising facts but there could be more! Do you know any mathematical trivia that could be added to this page?

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