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06  712  1323  2469  70200  2012016  5H0P
7
⠼⠛

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 integersided rectangles needed to
tile a rectangle such that no 2 rectangles share a common sidelength
(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 (2^{3}  1).
is the unity digit of the number 3^{31}.
is the positive solution to: 3x^{2} = 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 a^{4 }+ b^{4}  c^{4}:
7^{4} = 157^{4} + 227^{4}  239^{4
}  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:
7^{1} + 1 = 2 x
2^{2}
7^{2} + 1 = 2 x
5^{2} (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)
= 4 + 3 = 4^{2}  3^{2}
= 1^{2} + 1^{2} + 1^{2} + 2^{2} (sum
of 4 squares)
= 2^{5}  5^{2}
1^{7} +
4^{7} +
4^{7} +
5^{7} +
9^{7} +
9^{7} +
2^{7} +
9^{7} =
14459929
7^{2} =
13 + 17 + 19 (sum of consecutive primes)
7^{2} = 3^{4 } 2^{5
}7^{3} = 2^{9 } 13^{2
}7^{3} = 18^{0 }+ 18^{1 }+ 18^{2 } (sum
of consecutive powers of 18)
Is the
only solution to the following equations (see further above):
x = 2a^{2}  1
and x^{2} = 2b^{2}  1
(x = 7, a = 2, and b = 5)
Srinivasa
Ramanujan conjectured that the exponential Diophantine
equation 2^{n} x^{2} = 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.
= 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).
x^{7} + y^{7} = z^{7} 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:
7^{1} + 7^{2} + 7^{3} + 1 = 20^{2}
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 n1. 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!
857^{2}  142^{2} = 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 
(493827161^{2} 
493827160^{2}  61728395^{2} + 61728394^{2} 
3^{2}) / (61728395^{2}  61728394^{2})
= 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 2digit 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 righttruncatable
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 (base7)
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 SachsenAnhalt 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 7branch
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 fiveletter 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. 8197)
Even
the formula of the CocaCola softdrink is related to number 7.
In fact, Merchandise
7X is the "secret ingredient" in CocaCola
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 preeminent 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) 
Indoeuropean
 *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  ShB^{c} 
Ancient Egyptian [sfḫ] sefekh;
Akkadian sebe. 
Arabic سبعة sab'a;
Hebrew שבעה shehvah;
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.

8
⠼⠓

is
the second honest number, because
8 = "two cubed".
is the largest cube (2^{3}) 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 = 2^{2} + 2^{2} = 2^{3}
is the only cube that is 1 less than a square (3^{2} 
1).
is the 3^{rd} number that stays the same when written upside
down.
=
2^{4}  2^{3}
= 312^{2}  46^{3}
= (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 =
8^{3}
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
base8 (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
8Ball is a toy made by Tyco Toys used for fortunetelling.
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 20sided 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) 
Indoeuropean
 *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  ThMNy 
Ancient Egyptian [ḫmn] khemennu;
Akkadian samane. 
Arabic ثمانيه thamâniya;
Hebrew שמונה sh^{e}mônah;
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)aransamnu, name of the eighth month of
the Babylonian calendar). In French: OCTANE. In Italian: OTTOCENTESCO,
OTTONARIO, OTTUPLICARE. 
Buy
your favorite
Number (8) here.

9
⠼⠊

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 2digit 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)
=
3^{2}
= 5 + 4 = 5^{2}  4^{2
}= 0^{4} + 1^{3} +
2^{2} + 3^{1} + 4^{0}
= (1^{2} +
4^{2} + 8^{2}) = ^{3}(1^{3} +
6^{3} + 8^{3})
= 1^{3} + 2^{3}
= 1! + 2! + 3! (sum of consecutive factorials)
= !4 = 4! (11/1!+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
2^{5} x 9^{2} = 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 19 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 base9.
1/9
= 1/10 + 1/10^{2} + 1/10^{3} + 1/10^{4} +
1/10^{5 }+ ... = ∑_{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...
_{9}9^{9}_{=
1.9662705 x 10}77
_{but
9}(9^{9})_{ =
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 9^{0} + 9^{1} + 9^{2} + … +
9^{n} is always a triangular number.
8^{n }– 7^{n} +
6^{n }– 5^{n} + 4^{n }– 3^{n} +
2^{n} – 1^{n }with n =
2k, is a multiple of 9.
[(n 
1)^{3} + n^{3} + (n + 1)^{3}] ≡ 0
(mod 9)
(... any sum of cubes of 3 consecutive integers
is a multiple of 9)
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 base10 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 log_{10} 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 HDDVD processing
key useful to decrypt and play most HDDVD 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
16thcentury 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 9pointed 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 onesyllable word in the English language is 9letter long: "screeched".
NINE in
different languages (© G.
Sarcone)
(Old English nigon) 
Indoeuropean
 *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  TSh' 
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. 

10
⠼⠁⠚
X

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: 1^{2} + 3^{2 }= 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
= 13^{3 }– 3^{7}
= 4^{2 }– 3^{2} + 2^{2 }– 1^{2}
= 2 + 3 + 5 (sum of the first 3 primes)
= 1 / (1  (3 / (3 + 1/3)))
= ^{googol}googolplex
_{≈ π}3^{2}_{/ e}2^{3}
≈ π^{2} + 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:
10^{0 } = 
2^{0} x
5^{0 } = 
1
x 1 
10^{1 } = 
2^{1} x
5^{1 }= 
2
x 5 
10^{2} = 
2^{2} x
5^{2 }= 
4
x 25 
10^{3} = 
2^{3} x
5^{3 }= 
8
x 125 
10^{4} = 
2^{4} x
5^{4 }= 
16
x 625 
10^{5} = 
2^{5} x
5^{5 }= 
32
x 3125 
10^{6} = 
2^{6} x
5^{6 }= 
64
x 15625 
10^{7} = 
2^{7} x
5^{7 }= 
128
x 78125 
10^{9} = 
2^{9} x
5^{9 }= 
512
x 1953125 
10^{18} = 
2^{18} x
5^{18 }= 
262144
x 3814697265625 
10^{33} = 
2^{33} x
5^{33 }= 
8589934592
x 116415321826934814453125 
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 TopTen 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 IChing: 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) 
Indoeuropean
 *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  'SR 
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). 

11 
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.
= 6
+ 5 = 6^{2}  5^{2
}= (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
11^{11} 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)
11^{2} x 9182736455463728191
= 1111111111111111111111

posted by Yosuke Ikeda, Yasuji Kondo, Yasuhiko Sakaitani, Ken Hirotomi,
Hiroyuki Ozaki, Atushi Tanaka, Ryohei Miyadera (Kwansei Gakuin
High School)
11^{2} =
65 + 56, and 65^{2} – 56^{2} = (3 x 11)^{2},
11^{2} = 3^{0} + 3^{1 }+ 3^{2} +
3^{3 }+ 3^{4} (sum of consecutive
powers of 3)
11^{3} = 3^{2} + 19^{2 }+ 31^{2}
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 (base11) 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 (17621773), 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 "ÖufiBier" (elevenale)
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 11sided goldcoloured 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 11:11phenomenon
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 hardwired 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 fourdimensional 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,
thirtynine, eighty, eightynine, ninety, and ninetyeight.
Modulus
11 is used to check the 8digit
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) 
Indoeuropean
 *OINDEKM(T) 
Sanskrit  ekādaśa 
Greek, Attic  'ENΔEKA héndéka 
Latin  VNDECIM  
Italian undici;
French, Portuguese, Catalan, and Provençal onze;
Spanish once; Romanian unsprezese;
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 asraand. 
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.

12 
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!)
= (3i^{5})(4i)
= DC/L
=
2^{4}  2^{2}
= 3^{1} + 3^{2}
= 4^{2}  4^{1}
12^{2} 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
= 7^{3} + 10^{3}  11^{3}
12^{2} = 10^{3}  8^{3}  7^{3} 
1^{3}
12^{3} = 9^{3} + 10^{3}  1^{3
}12^{5} = 4^{5} + 5^{5} + 6^{5} +
7^{5} + 9^{5} + 11^{5}
1/12^{2} =
1/15^{2} + 1/20^{2 }(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
3^{2} + 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 1800DOGHELP" might
be the advertising slogan for a dog rescue center. This is much
easier to remember than "Call 18003644357".
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) 
Indoeuropean
 *DWÔDEKM(T) 
Sanskrit  dvādaśa 
Greek, Attic  ΔΩΔEKA dódéka 
Latin  DVODECIM  
Italian dodici;
French douze; Spanish doce;
Portuguese doze; Catalan and Provençal dotze;
Romanian doisprezese; 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 שניםעשר shteim'esrei;
Maltese: tnax; Amharic asrahulet. 
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. 

06  712  1323  2469  70200  201684  5H0P
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Encyclopedia
of Numbers © G. Sarcone, Archimedes Lab,
Genoa, Italy

