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What's Special About This Number?

Fun facts on numbers (and their peculiar properties), both mathematical and cultural, tantalising problems and anecdotes. The number facts in this website are also available as features for print and electronic publishing.

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is a congruent number because it is the area of a 35/12, 24/5, 337/60 triangle (a congruent number is an integer that is the area of a right triangle with three rational number sides).

is the minimum number of distinct integer-sided rectangles needed to tile a rectangle such that no 2 rectangles share a common side-length (see: uncomparable rectangles).

is also the minimum number of distinct rectangles with sides in the ratio 1:2 to perfectly tile a rectangle:

is the maximum number of different types of Frieze patterns. The Frieze patterns consist of a variety of linear transformations like reflection (mirror/lake reflection), rotation, glide reflection and translation:

is a Mersenne prime (2³ - 1).
is the unity digit of the number 3³¹.
is the positive solution to: 3x² = 16x + 35
is the divisor of 999,999 [in fact 999,999 / 7 = 142857, see the characteristic of this cyclic number futher below]

is probably the smallest prime whose 4^th power is of the form a⁴ + b⁴ - c⁴:
7⁴ = 157⁴ + 227⁴ - 239⁴
  - posted by Morten Risager

is the only integer when increased by 1 gives the double of a square, and whose square increased by 1 gives also the double of a square:
7¹ + 1 = 2 x 2²
7² + 1 = 2 x 5² (this property is used in the magic Tangram)

10/√2 = 5√2 ≈ 7

= 3! + 1 (n! + 1 is prime for n = 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, and no other values below 546)

Solution to Brocard's problem n! + 1 = m² :
7! + 1 = 71², the only other pairs are:
4! + 1 = 5² and 5! + 1 = 11²

= 4 + 3 = 4² - 3²
= 1² + 1² + 1² + 2² (sum of 4 squares)
= 2⁵ - 5²

1⁷ + 4⁷ + 4⁷ + 5⁷ + 9⁷ + 9⁷ + 2⁷ + 9⁷ = 14459929

7² = 13 + 17 + 19 (sum of consecutive primes)
7² = 3⁴ - 2⁵
7³ = 2⁹ - 13²
7³ = 18⁰ + 18¹ + 18² (sum of consecutive powers of 18)

Is the only solution to the following equations (see further above):
x = 2a² - 1
and x² = 2b² - 1
(x = 7, a = 2, and b = 5)

Srinivasa Ramanujan conjectured that the exponential Diophantine equation 2ⁿ- x² = 7 has a solution - in which both n and x are integers - only when n = 3, 4, 5, 7, and 15

The factorial 7! = 5040 contains 50% zeroes. It seems that it is the unique factorial with this property.

2x7! is the fastest way to calculate the number of minutes in a week with a calculator.

= 16,758/2,394
= 18,459/2,637
= 31,689/4,527
= 36,918/5,274
= 37,926/5,418
= 41,832/5,976
= 53,298/7,614
(every ratio of the equalities above uses the digits 1 to 9 once)

= 98,532/14,076 (is the unique pandigital ratio that includes 0)

To multiply the number 1,014,492,753,623,188,405,797 by seven, you just have to move the last digit 7 to the beginning of the number: 7,101,449,275,362,318,840,579. Numbers with such properties are called parasitic numbers.

No perfect square ends in a 7 (perfect squares can only end in a 0, 1, 4, 5, 6, or 9).

x⁷ + y⁷ = z⁷ has no solutions in integers. -- Lamé

The only single digit prime number to produce a square when its cube and the cube's proper divisors are added:
7¹ + 7² + 7³ + 1 = 20²

Some multiples of 7 are palindromic, such as:
77, 161, 252, 343,434, 525, 595, 616, 686, 707, 777, 868, 959, 1001, 1771, 2002, 2772, 3003, 3773, 4004, 4774, 5005, ...

The smallest positive integer whose reciprocal (1/7) has a pattern of more than one repeating digit:
1/7 = 0.142857142857142857...
It is also the smallest number for which the periodic sequence of 1/n is of length n-1. The next such numbers are 17, 19, 23, 29, 47, 59, 61, 97, ...

Other notable properties:
by multiplying the cyclic number 142857 by 2, 3, 4, 5, or 6, the answer will be a cyclic permutation of itself...
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142
  - posted by Larry Bickford

Interestingly, if we square the last three digits of 142857 and subtract the square of the first three digits, we also get back a cyclic permutation of the number!
857² - 142² = 714285

Adding 3 to the reciprocal of 7 gives a rough approximation of Pi (3.142857...).

(987'654'321 - (123'456'789 + 9)) / 123'456'789 = 7
- by Gianni A. Sarcone in 'Il Mio Computer', nr. 101 -
(493827161² - 493827160² - 61728395² + 61728394² - 3²) / (61728395² - 61728394²) = 7

Divisibility by Seven: take the digits of the number in reverse order, from right to left, multiplying them successively by the digits 1, 3, 2, 6, 4, 5, ... (repeating with this sequence of 6 multipliers as long as necessary). Add the products.
For example: is 1708 divisible by 7? Well, reverse the number, 8071, multiply and add its digits as explained, 8x1+0x3+7x2+1x6 = 28. The sum is divisible by 7, so 1708 is.

Divisibility by Seven (2): for numbers having 3 digits...
154 > (2)+1+5+4+(2) = 14 is divisible by 7, so 154 is.
245 > (4)+2+4+5+(6) = 21 is divisible by 7, so 245 is.
862 > (2)+8+6+2+(1) = 19 and 862 are not multiple of 7.
366 > (6)+3+6+6+(3) = 24 and 366 are not multiple of 7.
The numbers in brackets are added in order to form with their neighbors a 2-digit number multiple of 7. If the sum of all digits is a multiple of 7, then the related number is divisible by 7.
- posted by Silvio Moura Velho -

is a prime number
7 is a prime number
73 is a prime number
739 is a prime number
7393 is a prime number
73939 is a prime number
739391 is a prime number
7393913 is a prime number
73939133 is a prime number
(73939133 is the largest right-truncatable prime)

7 is the smallest number of colors needed to color the regions on a map on a torus (donut shape).

The opposite sides of a die cube always add up to 7.

A square piece of paper cannot be folded in half more than 7 times... However, Britney Gallivan (of Pomona, California) found a formula that tells us to successfully fold paper 12 times, we would need about 1.2 km of paper... and she proved it! - posted by Chris GIbbons

The Bolans of West Africa used for reckoning a kind of heptal (base-7) positional notation system.

Curiously, 'letters' contains seven times itself (selfreferential word). - G. Sarcone

In Germany, a spiteful or quarrelsome woman is called eine böse Sieben, 'an evil Seven'.
Böse Sieben ('evil Seven') is also a stream located in the Sachsen-Anhalt Area of the Country of Germany.

In Japan, the word shi means 'death'. In some cases nana ('7' in early classical Japanese) replaces the word shichi ('7', in modern Japanese) because it contains shi.

The symbol of the Judaic Faith is the menorah, a 7-branch candlestick (see opposite). According to Kabbalah (Judaic Mysticism), God created the world with 7 divine attributes. They are: Kindness (Chesed), Severity (Gevurah), Harmony (Tiferet), Perseverance (Netzach), Splendor (Hod), Attachment (Yesod) and Royalty (Malchut). Accordingly, the entire creation is a reflection of these seven attributes.

"Qixing" (七顆星), in the Mystical Numbers of Taoism, represents the number 7 and symbolizes the Seven Stars -- The Big Dipper.

"Sju sjösjuka sjömän på det sjunkande skeppet Shanghai" (seven seasick seamen on the sinking ship Shanghai), is a Swedish tongue twister.

Find the 7 five-letter English words that use only letters from the Roman numeral alphabet. [Solution]

The word LUCK requires 7 penstrokes.

7 ± 2 is a cognitive numeric limit (cf. 'The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information' by the cognitive psychologist George A. Miller, The Psychological Review, 1956, vol. 63, pp. 81-97)

Even the formula of the Coca-Cola soft-drink is related to number 7. In fact, Merchandise 7X is the "secret ingredient" in Coca-Cola and has apparently remained a secret since its invention in 1886.

The 'Olf' is a unit used to measure the strength of the smell from a standard person defined as an average adult working in an office (or similar non–industrial workplace), with a hygienic standard equivalent of 0.7 baths per day!

Adolf Hitler was reputed to take his coffee or tea with seven teaspoons of sugar.

MAGIC SEVEN
7 is the Holy number. There are 7 days in creation, 7 days in the week, 7 phases of the moon, every 7th year was sabbatical, and 7 times 7 years was the jubilee. There are 7 ages in the life of man, 7 divisions in the Lord's Prayer, 7 bibles, 7 churches of Asia, 7 Graces, 7 Deadly Sins, 7 Senses, 7 Sorrows of the Virgin, 7 Virtues, 7 joys of the Virgin, 7 Precious Things of the Buddhas, 7 Sleepers of Ephesus, 7 Lamps of Architecture. The apostles chose 7 deacons, Enoch, who was translated, was 7th from Adam; Jesus Christ was the 77th in a direct line. The vision of Daniel was 70 weeks; and the elders of Israel were 70. There were also 7 heavens, 7 planets, 7 stars, 7 wise men, 7 champions of Christendom, 7 notes in music, 7 primary colors, 7 sacraments of the Catholic Church, and 7 wonders of the world (see below). 7 gateways were traversed by Inanna, the most important goddess of the Sumerian pantheon, during her descent into the underworld. The 7th son was considered endowed with pre-eminent wisdom; and the 7th son of a 7th son is still thought to possess the power of healing diseases spontaneously.

The 7 wonders of the ancient world are:
- Great Pyramid of Giza,
- Hanging Gardens of Babylon,
- Temple of Artemis at Ephesus,
- Statue of Zeus at Olympia,
- Mausoleum of Maussollos at Halicarnassus,
- Colossus of Rhodes,
- Lighthouse of Alexandria.

The 'Seven Blunders of the World' according to Mahatma Gandhi are:
- Wealth without work,
- Pleasure without conscience,
- Knowledge without character,
- Commerce without morality,
- Science without humanity,
- Worship without sacrifice,
- Politics without principe

The numeral 7 is sometimes used in Irish and Scottish Gaelic texts as a symbol for “et” (and). Because it resembles the Tironian “⁊”, a shorthand symbol still used in Ireland and Scotland to mean ‘and’.
Tironian notes was a system of shorthand invented by Romans. Some Tironian notes are still used today, particularly in English abbreviations like for instance the ‘z’ of "viz." (for 'et' in videlicet).

SEVEN in different languages (© G. Sarcone) (Old English seofon)

Indo-european | *SEPTM | Sanskrit | SAPTA | Greek, Attic | 'EΠTA HEPTA | Latin | SEPTEM |

Italian sette; French sept; Spanish siete; Catalan and Provençal set; Portuguese setes; Romanian şapte (sometimes pronounced as 'şepte', when communicating telephone numbers in order to avoid a possible confusion between 6 and 7); Rumansh siat; Sardinian sète.

Old Germanic | SIBUM |

Dutch zeven; German sieben; Danish syv; Norwegian sju; Swedish sju; Icelandic sjö.

Old Slavic | SEDMI |

Russian семь syem'; Czech sedm; Slovenian sedem; Polish siedem.

Evolution from 'seal script' to modern sinograph 七 : Old Chinese (pron.) | ts'yet |

Chinese 七 qī. The sinograph 柒 is used as a replacement for qī on legal and financial documents.

Semitic root | Sh-B-c | Ancient Egyptian [sfḫ-] sefekh; Akkadian sebe.

Arabic سبعة sab'a; Hebrew שבעה sheh-vah; Maltese: sebgha; Amharic sebat.

HIDDEN ROOTS The roots of the word seven are hidden in the following words: hebdomadal, heptagon, heptahedron, september, septennial, septentrion, septuple; Bathsheba, Elizabeth. In French: semaine, septuor.

Buy your favorite Number (7) here.

is the second honest number, because 8 = "two cubed".
is the largest cube (2³) in the Fibonacci sequence.
is the smallest sum of two factorials of distinct primes: 2! + 3!
is also the lowest number which is both a sum of prime squares and a prime cube: 8 = 2² + 2² = 2³
is the only cube that is 1 less than a square (3² - 1).
is the 3^rd number that stays the same when written upside down.

= 2⁴ - 2³
= 312² - 46³
= (7 + 7/7)! / 7!
= (3 - 1)(3 + 1)
= (1 x 2 x 3 x 4 x 5) / (1 + 2 + 3 + 4 + 5)

= CD/L

8 = 5 + 1 + 2 and 512 = 8³
8 + 8 + 8 + 88 + 888 = 1000

If you divide any square integer by 8 you get a remainder of 0, 1 or 4.

(2n - 1)² ≡ 1 (mod 8)
(... any squared odd number is a multiple of 8 plus 1)

Digital sums of prime pair products:
5 x 7 = 35 and 3+5 = 8
11 x 13 = 143 and 1+4+3 = 8
17 x 19 = 323 and 3+2+3 = 8
29 x 31 = 899 and 8+9+9 = 26 and 2+6 = 8
41 x 43 = 1763 and 1+7+6+3 = 17 and 1+7 = 8
59 x 61 = 3599 and 3+5+9+9 = 26 and 2+6 = 8 ... etc.

987654321 / 123456789 = 8.0000000729000006633900060368490... which is very nearly 8, except for the isolated 729, 66339, 6036849... Are those 3 numbers a coincidence?

A base-8 (octal) numeral system was devised by the Yuki of Northern California, who used the spaces between the fingers to count.

Zenzizenzizenzic was a term coined by earlier mathematicians to indicate the 8 power of a number. The root word is the German zenzic from the medieval Italian word censo. The Italians used censo to translate the Arabic word mál (literally "possessions, property") meaning 'squared' in the context of mathematics.

You can split a pie into 8 pieces with three straight cuts.
You can also chop a big lump of cheese into a maximum of 93 bits with just 8 straight cuts!

There are 8 furlongs in a mile and 8 pints in a gallon.

1 human being out of 8 is a Chinese farmer.
Inhabitants of the world (2004): 6.2 billions.
Inhabitants of China (2004): 1.3 billions, 60% of them living in a rural area.
The proportion is then: (1.3 · 60%)/6.2 = approx. 1 Chinese farmer / 8 human beings.
--- Is this article still topical? Please send us your comments!

Magic 8-Ball is a toy made by Tyco Toys used for fortune-telling. It was invented by Abe Bookman of the Alabe Crafts Company in Cincinnati in 1946. Mattel holds the rights after purchasing Tyco in 1997. A 20-sided icosahedron floats inside a murky blue liquid inside the ball, and when you turn the ball upside down, one of the 20 'oracles' appears.

In numerology, 8 is the number of building, and in some theories, also the number of destruction.

Eight are the main directions shown on any compass: north, northeast, east, southeast, south, southwest, west, and northwest.

"Bagua", in the Mystical Numbers of Taoism, represents the number 8 and symbolizes the Eight Signs of Change and Combinations.

Eight is considered a lucky number in Chinese culture because it sounds like the word "prosper". In Northern China, people often say: "If you want to be rich you must stick to the number eight". Dates and times with either a 6 or an 8 have been predominantly chosen as auspicious for important events. So, it's no coincidence that the Beijing Olympic Games started at 08:08:08 pm! When Chinese businessmen stay in a hotel, they would rather choose rooms with numbers such as: 6, 8, 58, 168, 518, 588, 868, and so on.

The Eight Immortals of the Chinese Mythology are:
Li TieGuai 李鐵拐 , Zhongli Quan 鐘離權, Lan CaiHe 藍采和 , Zhang GuoLao 張果老 , He XianGu 何仙姑 , Lu DongBin 呂洞賓 , Han XiangZi 韓湘子 , Cao GuoJiu 曹國舅 .

The Buddha's Eightfold Path to Enlightenment (Ārya 'ṣṭāṅga mārgaḥ) is declared to be the way that leads to the cessation of suffering:
Right View, Right Intention, Right Speech, Right Action, Right Livelihood, Right Effort, Right Concentration, Right Mindfulness.

Hanukkah is an eight day Jewish holiday that starts on the 25th day of December.

Joke. What did 0 say to 8? Answer: "Nice belt!".

The word 'buffalo' repeated 8 times: "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo" forms a grammatically correct English sentence meaning bison from Buffalo, New York, who are intimidated by other bison in their community also happen to intimidate other bison in their community.

"Cats are smarter than dogs. You cannot get eight cats to pull a sled through snow" -- Jeff Valdez

EIGHT in different languages (© G. Sarcone) (Old English eahta)

Indo-european | *OKTÔ(U) | [oktô(u) is grammatically a dual and meant originally '2 groups of 4 fingers'] Sanskrit | ASHTA | Greek, Attic | OKTΩ OKTÔ| Latin | OCTO |

Italian otto; French huit; Spanish ocho; Portuguese oito; Catalan vuit; Provençal oit; Romanian opt; Rumansh otg; Sardinian òto.

Old Germanic | AHTÔ |

Dutch and German acht; Danish otte; Norwegian åtte; Swedish åtta; Icelandic átta.

Old Slavic | OS(T)MI |

Russian восемь vósyem'; Czech osm; Slovenian ósem; Polish osiem.

Evolution from 'seal script' to modern sinograph 八 : Old Chinese (pron.) | pwat |

Chinese 八 bā. The sinograph 捌 is used as a replacement for bā on legal and financial documents.

Semitic root | Th-M-Ny | Ancient Egyptian [ḫmn-] khemennu; Akkadian samane.

Arabic ثمانيه thamâniya; Hebrew שמונה shemônah; Maltese: tmienja; Amharic semmint (pron. səmənətə).

HIDDEN ROOTS The roots of the word eight are hidden in the following words: OCTANS, OCTANT, OCTAVE, OCTAVO, OCTET, OCTOBER, OCTONARY; OCTODECIMO, OCTOGENARIAN; OCTAD, OCTAGON, OCTAHEDRON, OCTANDRY, OCTOPUS; SHEMINI ATZERETH, HESHVAN (from Akkadian (w)aran-samnu, name of the eighth month of the Babylonian calendar). In French: OCTANE. In Italian: OTTOCENTESCO, OTTONARIO, OTTUPLICARE.

Buy your favorite Number (8) here.

is the largest number of cubes needed to sum to positive integers (in 1939, the mathematician L.E. Dickson proved that the only integers requiring exactly 9 positive cubes are 23 and 239).

Each and every 2-digit number that ends with a 9 is the sum of the multiple of the two digits plus the sum of the two
digits. Thus, for instance: 39= (3 x 9) + (3 + 9)

= 3²
= 5 + 4 = 5² - 4²
= 0⁴ + 1³ + 2² + 3¹ + 4⁰
= (1² + 4² + 8²) = ³(1³ + 6³ + 8³)
= 1³ + 2³
= 1! + 2! + 3! (sum of consecutive factorials)
= !4 = 4! (1-1/1!+1/2!-1/3!+1/4!)
= 4 + 4 + 4/4 = (4/.4)(4 - 4)! - G. Sarcone (four 4's diversion)
= MC/C = (MD - DC)/C = CV/V - DC/L - G. Sarcone

2⁵ x 9² = 2592

0 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 0 is a mnemonic trick to remember your 9x table.

(9 x 123,456,789) - 123,456,789 = 987,654,321 - 9

= 97524/10836
= 95823/10647
= 95742/10638
= 75249/08361
= 58239/06471
= 57429/06381
(in each fraction above all digits from 0 to 9 were used once)

In the multiplications below, digits 1-9 were used once giving pandigital products:
9 x 57,624,831 = 1,037,246,958
9 x 58,132,764 = 1,046,389,752
9 x 71,465,328 = 1,286,375,904
9 x 72,645,831 = 1,307,624,958
9 x 76,125,483 = 1,370,258,694
9 x 81,274,365 = 1,462,938,570

Curious arrangements with 9's:
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1 111
1234 x 9 + 5 = 11 111
12345 x 9 + 6 = 111 111
123456 x 9 + 7 = 1 111 111
1234567 x 9 + 8 = 11 111 111
12345678 x 9 + 9 = 111 111 111
The results above are all triangular numbers in base-9.

1/9 = 1/10 + 1/10² + 1/10³ + 1/10⁴ + 1/10⁵ + ... = ∑_i=1 10^-i

Notably, the recurrent number 0.999999... denotes a real number which is equal to 1:
9 x 1/9 = 9 x 0.111111...
Thus, 1 = 0.999999...

₉9⁹_{= 1.9662705 x 10}77

_{but 9}(9⁹) _{= a number containing 369,000,000 of digits!}

To multiply 10,112,359,550,561,797,752,808,988,764,044,943,820,224,719 by 9 you just have to move the 9 at the very end up to the front. Apparently, it is the only number that does this!

1/1089 = 0,00091827364554637281... (the decimal expansion is a sequence of numbers of the 9 times table: 9, 18, 27, 36, ...)

The sum 9⁰ + 9¹ + 9² + … + 9ⁿ is always a triangular number.

8ⁿ – 7ⁿ + 6ⁿ – 5ⁿ + 4ⁿ – 3ⁿ + 2ⁿ – 1ⁿ with n = 2k, is a multiple of 9.

[(n - 1)³ + n³ + (n + 1)³] ≡ 0 (mod 9)
(... any sum of cubes of 3 consecutive integers is a multiple of 9)

Strangely enough, this number
999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999
999999999999899999999999999999999999999999999999
999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999
99999999999999999999999999 is prime!

Intriguing sums:
9 = nine + zero = eight + one = seven + two = six + three = five + four
(the sums above contain all precisely 9 alphanumeric symbols)

Water expands by about 9% as it freezes.

9.81 meters per second squared is g, the gravity constant on earth.

In probability, the 'nine' is a logarithmic measure of reliability or probability of an event, defined as the negative of the base-10 logarithm of the probability of the event's complement. For instance, an event that is 99% likely to occur has an unlikelihood of 1% or 0.01, which amounts to -log₁₀ 0.01 = 2 nines of probability.

09:F9:11:02:9D:74:E3:5B:D8:41:56:C5:63:56:88:C0... This string of hexadecimal numbers appears to be the HD-DVD processing key useful to decrypt and play most HD-DVD movies in Linux.

NUNDINAE ("9th day", the Roman market day): from earliest times, a market day occurred every eight days - every 9th day, according to the Roman method of inclusive reckoning. It was a day of rest from agricultural labor and a time to take produce to market.

Being the number of fingers or toes, 10 became the base of the decimal number system. It is the number of completeness or finality. With ten as complete, 9 comes into prominence as almost complete. Troy was besieged for 9 days and fell on the tenth. Odysseus (Lat. Ulysses) wandered for 9 years and arrived home on the tenth.

The 16th-century Catholic theologian Peter Bungus pointed out that the 9th Psalm predicts the coming of the Antichrist. In Islamic cosmology the universe is made from 9 spheres - the traditional 8 of Ptolemy, plus a ninth added by the Arab astronomer Thābit ibn Qurra to explain the precession of the equinoxes.

In Guangdong province, China, nine is associated with eternity or power.

"Jiugong" (also known as "Jiuxuan"), in the Mystical Numbers of Taoism, represents the number 9 and symbolizes the Nine Chambers. It is the last number of order before returning back to chaos. After that, the cycle repeats...

Bart Simpson has 9 spikes of hair (at least, since season 2).

The symbol of the Bahai Faith is a 9-pointed star (see opposite).

A full moon is nine times brighter than a half moon.

The standard dimensions of a play card are: 6.35 x 9 cm.

The first nine letters of the Maldivian alphabet (h, sh, n, r, b, lh, k, ', and v) are graphically derived from the Arabic numerals from 1 to 9: ١, ٢, ٣, ٤, ٥, ٦, ٧, ٨, ٩.

The longest one-syllable word in the English language is 9-letter long: "screeched".

NINE in different languages (© G. Sarcone) (Old English nigon)

Indo-european | *NEWN | Sanskrit | NAVA | Greek, Attic | ENNEA hennea | Latin | NOVEM |, Archaic Latin | NEVEN |

Italian and Portuguese nove; French neuf; Spanish nueve; Catalan nou; Provençal nòu; Romanian nouă; Rumansh nov; Sardinian nòbe.

Old Germanic | NIWUN |

Dutch negen; German neun; Danish and Norwegian ni; Swedish nio; Icelandic níu.

Old Slavic | DEVETI (< neveti) |

Russian девять devyat'; Czech devět; Slovenian devét; Polish dziewięć.

Evolution from 'seal script' to modern sinograph 九 : Old Chinese (pron.) | kyeu |

Chinese 九 jiǔ. The sinograph 玖 is used as a replacement for 九 to prevent forgery on legal and financial documents.

Semitic root | T-Sh-' | Ancient Egyptian [psḏ-] pest.; Akkadian tishe.

Arabic تِسْعة tisha; Hebrew תשע tésha; Maltese: disgħa; Amharic zethain (pron. zäṭäñ).

HIDDEN ROOTS The roots of the word nine are hidden in the following words: NOVEMBER, NOVENA; NONAGENARIAN; NONES, NOON; NONAGON, NONANOIC ACID; ENNEAD, ENNEAGON.

is the base of our numerical system.
is a triangular number: 1 + 2 + 3 + 4 = 10
is the only triangular number which is also the sum of 2 consecutive square odd numbers: 1² + 3² = 10
cannot be the difference of 2 squares, because 10 is of the form 4n + 2

= (5 + -15) + (5 - -15) = (5 + -15)(5 - -15)/4
= 13³ – 3⁷
= 4² – 3² + 2² – 1²
= 2 + 3 + 5 (sum of the first 3 primes)
= 1 / (1 - (3 / (3 + 1/3)))
= ^googolgoogolplex

_{≈ π}3²_{/ e}2³

≈ π² + π/24
≈ (e^π - π)/2

10! = 6! x 7! = 3! x 5! x 7! (Unique solution to the factorial equation n! = a! x b! x c! with consecutive prime factors)

(10!)² + 1 is prime...

There seems to be only 11 powers of ten that are products of two integers without any zero digits:

Marion's theorem states that the area of the central hexagonal region determined by trisection of each side of any triangle ABC and connecting the corresponding points with the opposite vertex is exactly one tenth (1/10) the area of the whole triangle ABC.

Some people argue that we only use 10% of our brains... No, this is wrong: while the majority of the brain may not be active at any one moment, all of it is essential for normal function. See mythical numbers.

In most advertisements, including newspapers, the time displayed on a watch is approximately 10:10. Neuroscientists suggest that obliquely oriented lines are more attention getters than orthogonal oriented ones (and could be a benefit to clock sellers!).
Another reason for this is to "frame" the logo of the watch maker. The hands at that number cause the eyes to look right at the logo! - posted by Shaun Hussey, Graphic Designer
The hands on the dial indicating 10:10 also represent a smiling face, sells better than watches indicating e.g. 08:20. - posted by Pander

"One father is better at caring for ten children than ten children are for one father".

Top ten lists are very recurrent. The first top ten to do and to not do list was perhaps the "Ten Commandments of God" given to Moses. The Top-Ten lists usually are: Top Ten To Do, Top Ten Jokes, Top Ten Reasons, Top Ten Links/Websites, Top Ten Music/Songs, Top Ten Movies, Top Ten Headlines, Top Ten Mistakes, Late Show Top Ten, Top Ten Reviews/Lists, Tot Ten Inventions of the Century, and... Top Ten Numbers!

10/10/10 represents Sunday, October 10, 2010. This occurrence is special because the first two numbers added together equal the first two digits of the year: 10/10/2010 > 10 + 10 = 20. Such dates occur every 201 years, the previous one was 09/09/1809 and the next one will be 11/11/2211. In China, the number ten has a special place as it symbolises 'perfection' in almost everything. Hence 10/10/10 becomes a special day for the Chinese. In fact, many people in China are planning their wedding on this auspicious day...

The 10th hexagram of the I-Ching: Lü (履)/ Treading (Conduct)
THE IMAGE
Heaven above, the lake below:
The image of TREADING.
Thus the superior man discriminates
between high and low,
And thereby fortifies the thinking of the people.

TEN in different languages (© G. Sarcone) (Old English tēn, tīen)

Indo-european | *DEKM(T) | Sanskrit | DASA | Greek, Attic | ΔEKA deka | Latin | DECEM |

Italian dieci; French dix; Spanish diez; Portuguese dez; Catalan déu; Provençal dètz; Romanian zese; Rumansh diesch; Sardinian dèche.

Old Germanic | TEHUN |

Dutch tien; German zehn; Danish and Norwegian ti; Swedish tio; Icelandic tíu.

Old Slavic | DESETI |

Russian десять desyat'; Czech and Slovenian deset; Polish dziesięć.

Evolution from 'seal script' to modern sinograph 十 : Old Chinese (pron.) | zhyep |

Chinese 十 shí. The sinograph 拾 is used as a replacement for 十 to prevent forgery on legal and financial documents.

Semitic root | '-S-R | Ancient Egyptian [mḏ-] met; Akkadian esher.

Arabic عَشَرة 'ashra; Hebrew עשר éser; Maltese: għaxra; Amharic asir (pron. asər).

HIDDEN ROOTS The roots of the word ten are hidden in the following words: DECI-, DECIMAL, DECIMATE, DECUPLE, DECURION, DICKER, DIME; DECEMBER, DECEMVIR, DECENNARY, DECENNIUM, DECUSSATE; DENARIUS, DENARY, DENIER; DEAN, DECA-, DECADE, DOYEN; DECAGON, DECALOGUE, DECAMERON, DECAPOD; TENTH, TITHE. German: DECHANT, DEKAN, -ZIG. French: DENIER, DENRÉE, DÎME. Italian: DANAIO. DERRATA (< denarata).

is the third honest number, because 11 = "two plus nine".
is the only palindromic prime with an even number of digits.
is the smallest prime with multiplicative and additive persistence of 1.

11 can be partioned into two or more distinct digits:
9 + 2 = 8 + 3 = 7 + 5 = 6 + 3 + 2 = 5 + 4 + 2 = 5 + 3 + 2 + 1

= 6 + 5 = 6² - 5²
= (5! + 1)
= LV/V = CX/X = DL/L = MC/C   -- G. Sarcone

Any power of 11 ends in a 1.

1x9+2 = 11
12x9+3 = 111
123x9+4 = 1,111
1234x9+5 = 11,111
12,345x9+6 = 111,111
123,456x9+7 = 1,111,111
1,234,567x9+8 = 11,111,111
12,345,678x9+9 = 111,111,111
123,456,789x9+10 = 1,111,111,111

11¹¹ contains two embedded elevens.

Displayed on a calculator, the number 11 reads the same whether the calculator is turned upside down or reflected on a mirror, or both.

Divisibility
Any large number is divisible by 11 if the difference between the sum of its odd position digits (units, hundreds, etc.) and the sum of its even position digits (tens, thousands, etc.) is 0 or a number divisible by 11.
Another neat method to test for divisibility by 11 works by repeatedly subtracting the last digit from the remaining digits:
5915 - 8 = 5907; 590 - 7 = 583; 58 - 3 = 55; 5 - 5 = 0
If this process results in 0, the original number is divisible by 11, and the sequence of last digits gives the quotient. In this case, the last digits are 8, 7, 3 and 5, so 59158/11 = 5378.

AB + BA, ABBA and ABCABC are all multiple of 11 (A, B and C are digits, zero included).

11 x 11 = 65 + 56 (palindromic equality)
11² x 9182736455463728191 = 1111111111111111111111
- posted by Yosuke Ikeda, Yasuji Kondo, Yasuhiko Sakaitani, Ken Hirotomi, Hiroyuki Ozaki, Atushi Tanaka, Ryohei Miyadera (Kwansei Gakuin High School)
11² = 65 + 56, and 65² – 56² = (3 x 11)²,
11² = 3⁰ + 3¹ + 3² + 3³ + 3⁴ (sum of consecutive powers of 3)
11³ = 3² + 19² + 31²

1 / 11 = 0.09 09 …
2 / 11 = 0.18 18 …
3 / 11 = 0.27 27 …
4 / 11 = 0.36 36 …
5 / 11 = 0.45 45 …
6 / 11 = 0.54 54 …
etc.

11 + 1.1 = 11 x 1.1

Magic triangle with a constant of 11;
2 + 3 + 6 = 2 + 5 + 4 = 6 + 1 + 4 = 11

'Eleven plus two' is the anagram of 'twelve plus one'.

The Maoris, the initial inhabitants of New Zealand, used for reckoning or accounting purposes the undecimal (base-11) positional notation system.

The Swiss town of Solothurn has a special affinity with the number 11. This number is everywhere in the city: there are 11 museums, chapels and churches, as well as eleven historical fountains and eleven towers, and a clock with a dial that only shows 11 hours. There are also some interesting facts about the presence of the number 11 on the city’s landmark, the Cathedral of St. Ursus. It took 11 years to build it (1762-1773), the facade is 3 x 11 meters high, the tower measures 6 x 11 meters up to the weathercock; the stairs in front of the cathedral have levels between every eleven steps. The inhabitants of Solothurn even call their local beer "Öufi-Bier" (eleven-ale) in German. The Canton of Solothurn was the eleventh to become part of the Swiss Confederation.

The Canadian one dollar coin (commonly called "Loonie") is a 11-sided gold-coloured coin.

11:11 Phenomenon
If your attention has been drawn to clocks and watches at exactly 11:11, 12:12, 10:10, 22:22, 12:34, 2:22, 3:33, 4:44 or 5:55, then you are a 11:11-phenomenon addict... In fact, some people believe that when they notice the number pattern 1111 or the digits 11:11 on digital time pieces, time/temperature signs, and so on, that there is an underlying reason besides mere chance or coincidence. A belief of this nature is related to the idea of synchronicity.

November 11
The date ‘November 11th, 2011’ has three 11’s aligned for the first time in a century.

11.11.11, the perfect palindromic day, is being considered lucky by many, as couples all over the world are planning to get into wedlock on this date.

On November 11th, 2011, at 48 minutes and 47 8/9 seconds before Noon the time will be:
11/11/11 11:11:11.1111111111111... -- Bob Morris

Numbers which are already significant to us, such as calendar dates that also coincidentally fall into an obvious pattern, become doubly significant. It is known that the human brain is hard-wired to look for meaningful patterns in the sensory data it collects from the world. The fact that the date 11/11/11 appears important to some people, teaches us that human nature is cognitively prone to find ‘significance’ in coincidences.

Air is heavy...
An average room holds 11 x 100 pounds of air!

11 Dimensions
According to Dr Michio Kaku our universe is a four-dimensional ball floating in eleven dimensions.

According to a survey of Graham Waters, Tuesday morning at 11:45 AM is the most stressful time of the working week.

Statistically, the most boring day of the 20th century was 11 April 1954. The date was discovered after 300 million facts were fed into a new computer search engine in Cambridge called "True Knowledge".

Interchangeability is the word in the English language that contains the letters to form the most numbers. With its letters it is possible to spell 11 numbers: three, eight, nine, ten, thirteen, thirty, thirty-nine, eighty, eighty-nine, ninety, and ninety-eight.

Modulus 11 is used to check the 8-digit ISSN (International Standard Serial Number for periodicals and magazines).

The number 11 is a favorite of gamblers - particularly blackjack and Keno players.

Stuck between the divine numbers 10 and 12, the number 11 was, according to Medieval numerologists, pure evil, and represented sinners.

A million seconds is 11 days and a half.

The French numeral onze (= eleven) was also an old French slang term meaning 'a pair of legs' (1833).

Aibohphobia is a fictional term for the fear of palindromes, which is a palindrome itself and contains 11 letters. The term is a piece of computer humor entered into the 1981 "The Devil's DP Dictionary".

ELEVEN in different languages (© G. Sarcone) (Old English endleofon)

Indo-european | *OINDEKM(T) | Sanskrit | ekādaśa | Greek, Attic | 'ENΔEKA héndéka | Latin | VNDECIM |

Italian undici; French, Portuguese, Catalan, and Provençal onze; Spanish once; Romanian un-spre-zese; Rumansh endisch; Sardinian úndagi.

Old Germanic | AINLIF (means 'one left over') |

Dutch and German elf; Danish and Norwegian elleve; Swedish elva; Icelandic ellefu.

Old Slavic | JEDINU NA DESETJE |

Russian оди́ннадцать odinnadtsat'; Czech jedenáct; Slovenian enajst; Polish jedenaście.

Chinese 十一 shíyī.

Ancient Egyptian metwie; Akkadian ishteshsheret.

Arabic إحدى عشر ahada‘ashar; Hebrew אחד עשר ahat'esrei; Maltese: ħdax; Amharic asra-and.

HIDDEN ROOTS The roots of the word eleven are hidden in the following words: UNDECUMANI, Roman soldiers from the eleventh Legion; UNDECIREMIS, an ancient Greek or Roman war galley with eleven banks of oars; UNDECAGON, UNDECILLION. Italian: UNDICENNE.

Buy your favorite Number (11) here.

is a pentagonal number.
is the smallest number with exactly six divisors, and the smallest abundant number.
is the largest known even number expressible as the sum of two primes in one way (5 + 7).

= 22 / (1 + (1 / (1 + 1/5)))
= (0! + 0! + 0!)! x (0! + 0!)
= (-3i⁵)(4i)
= DC/L

= 2⁴ - 2²
= 3¹ + 3²
= 4² - 4¹

12² x 1122334455667789 = 161616161616161616 (periodic number) - posted by Yosuke Ikeda, Yasuji Kondo, Yasuhiko Sakaitani, Ken Hirotomi, Hiroyuki Ozaki, Atushi Tanaka, Ryohei Miyadera (Kwansei Gakuin High School) -

12 = 7³ + 10³ - 11³
12² = 10³ - 8³ - 7³ - 1³
12³ = 9³ + 10³ - 1³
12⁵ = 4⁵ + 5⁵ + 6⁵ + 7⁵ + 9⁵ + 11⁵

1/12² = 1/15² + 1/20² (smallest integers of the reciprocal pythagorean equation)

12 x 12 = 144 is palindromic to 441 = 21 x 21
12 x 12 + 21 x 21 = 585 is also palindromic
other curious palindromic equalities involving 12:
12 x 42 = 24 x 21
12 x 63 = 36 x 21
12 x 84 = 48 x 21

12 + 21 = 3 + 4 + 5 + 6 + 7 + 8

12! + 34567 is prime.

12 x 3² + 3 = 111
400/33 = 12.1212121212...

There are 12 primary ways of arranging 8 queens on a chessboard so that no queen can capture any other queen.

Two + eleven = twoeleven, twOelEveN - ONE = twelve.

are the symbols of the phone dial.
Telephone Number Mnemonics
American visitors are familiar with an ingenious method of making telephone numbers more memorable. In the US many companies advertise their telephone numbers with words. For example "Call 1800-DOG-HELP" might be the advertising slogan for a dog rescue center. This is much easier to remember than "Call 1800-364-4357".
To aid this system, the buttons on telephones are marked with letters, as shown on the right. This method has been used in Britain too, although it is now far less popular.

Which is correct: 12 Midnight A.M. or 12 Midnight P.M.? Neither!
12 midnight A.M. and 12 midnight P.M., or 00:00 A.M. and 00:00 P.M., mean nothing at all. They are simply the midpoints that divide the day into two equal halves.
Each and every day begins exactly at midnight, and each A.M. begins precisely thereafter. Similarly, each P.M. begins immediately after noon. No meaning can be assigned to 12:00 A.M. (00:00 A.M.), or to 12:00 P.M. (00:00 P.M.). They are merely reference points meant to simplify timetables for us.

A dozen is a group or set of 12: a dozen bottles of sherry.

A shock is a group of 12 sheaves of grain stacked upright in a field for drying. The word shock means also a lot consisting of 60 pieces; -- a term applied in some Baltic ports to loose goods.

A jury consists of twelve persons chosen to decide who has the better lawyer. -- Robert Frost

Doomsday? 21 | 12 | 2012
2012 is claimed by some to be a great year of spiritual transformation (or apocalypse). Many esoteric sources interpret the completion of the 13th B'ak'tun cycle in the 'Long Count' of the Maya calendar (which occurs on December 21 by the most widely held correlation) to mean there will be a major change in world order.

TWELVE in different languages (© G. Sarcone) (Old English twelfe)

Indo-european | *DWÔDEKM(T) | Sanskrit | dvādaśa | Greek, Attic | ΔΩΔEKA dódéka | Latin | DVODECIM |

Italian dodici; French douze; Spanish doce; Portuguese doze; Catalan and Provençal dotze; Romanian doi-spre-zese; Rumansh dudisch; Sardinian dóghi.

Old Germanic | TWALIF (means 'two left over') |

Dutch twaalf; German zwölf; Danish, Norwegian, and Swedish tolv; Icelandic tólf.

Old Slavic | DVANADESETJE |

Russian дванадцать dvënadtsat'; Czech dvanáct; Slovenian dvanajst; Polish dwanaście.

Chinese 十二 shí'èr.

Ancient Egyptian metsn'wse; Akkadian shinsher(et).

Arabic إثنا عشر ithna'ashar; Hebrew שנים-עשר shteim'esrei; Maltese: tnax; Amharic asra-hulet.

HIDDEN ROOTS The roots of the word twelve are hidden in the following words: DUODECILLION, DUODECIMAL, DUODENAL, DUODENARY, DUODENUM; DODECAGON, DODECAHEDRON, DODECANESE, DODECAPHONIC; DOZEN; TWELVEMO. French: DOUZAINE. Italian: DODICENNE, DOZZINA.

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Encyclopedia of Numbers © G. Sarcone, Archimedes Lab, Genoa, Italy