Special About This Number" Facts
have always been fascinated by NUMBERS...
They are basic elements of mathematics used for counting, measuring, ranking, comparing quantities, and solving equations. Numbers have unique properties, and while some people see them as concise symbols manipulated according to arbitrary rules, others believe they carry occult powers and mystic virtues.
The first known use of numbers dates back to around 30,000 BC when Stone Age people used simple tally
marks, consisting of single strokes, to represent each additional unit.
Each number is unique and has its own beauty. We have collected a vast array of facts pertaining to the magical world of numbers, covering different topics such as mathematics, history, philosophy, psychology, symbolism, etymology, language,
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you got a distinctive fact about any number listed here you think Archimedes'
Lab community might enjoy, why not post it here?
un numero con delle proprietà originali? Contattateci!
un nombre avec des propriétés étonnantes? Contactez-nous!
dei numeri (it), liste des nombres (fr), lista de números (es,
por), Liste besonderer Zahlen (ger), getallen en getalverzamelingen (du), seznam čísel (cz), 數表 (ch), 数の一覧 (jap), список чисел (ru), שמות מספרים (he).
0-6 | 7-12 | 13-23 | 24-69 | 70-200 | 201-∞ | 5H0P
0-6 | 7-12 | 13-23 | 24-69 | 70-200 | 201-∞ | 5H0P
NaN (Not a Number)
is, in computing, a value (or symbol) that is usually produced
as the result of an operation on invalid input operands, especially
calculations. NaNs are close to some undefined or inderterminate expressions
in mathematics. In short, NaN is not really a number but a symbol
that represents a numerical quantity whose magnitude cannot be
determined by the operating system. This mainly occurs when infinity and zero are
misused in expressions.
= log (-n) = ln (-n)
= 0 / 0
= ∞ / ∞ = ∞ / -∞ = -∞ / ∞ =
-∞ / -∞
= 0 x ∞ = 0 x -∞
= (-∞) + ∞ = ∞ + (-∞)
= ln |0| / ln |±∞|
= e±∞ x ln |0|
= (m / ±∞) x (n / 0) if m ±∞ and n 0
all indeterminate forms produce a NaN: for instance,
the division 1/0 makes no sense in pure mathematics, but curiously
enough in IEEE
754 this fraction is, by convention, equal to +∞ (hence
1/∞ = 0). Reality is, there are no answers for expressions
such as n/0 or n/∞ (for n > 0).
For n/0 the problem we are trying to solve is simply:
n = 0 x A
We cannot find any number for A since 0 x A =
0 for any whole number, rational number, real number, and so on.
Regarding the fraction n/∞, if we admit that it
is equal to 0 (when n is small but >0), then:
1 + n/∞ = 1, thus ∞ + n = ∞,
and n = 0...
Which contradicts n > 0. So, don't try to use infinity
as a real number, you will get wrong answers!
cannot be used directly, but we can use a limit: n/∞ is
undefined, we do know however that n/x
(with, say n = 1) approaches 0 as x approaches ∞:
infinite series ∑ = 1 - 1 + 1 - 1 + 1 - 1 + … , called Grandi's
series, also written:
divergent series, meaning that it lacks a sum in the usual sense...
In fact, if you treat this series like a telescoping series and/or
use different bracketing procedures to sum it, you may obtain contradictory
above, it appears to equal 0 and 1, yet in some sense 'sums' to 1/2,
producing a paradox... The error here is that the associative law
cannot be applied freely to an infinite sum unless the sum is absolutely
convergent. We can say that the sum of Grandi's series is NaN.
1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + ...
(1-1) + (1-1) + (1-1) + (1-1) + ...
1 + (-1+1) + (-1+1) + (-1+1) + ...
1 + (1-1+1-1+1-1+ ...) = 1 + ∑ => ∑
is the imaginary
unit of any imaginary number. Discovered by the Italian mathematician Girolamo
number is a number of the form bi where
'b' is a real number, 'i' is the square root of -1, for
Imaginary numbers (and complex numbers in general) are essential
for describing physical reality and have concrete applications
in: electromagnetism, signal processing, control theory, quantum
mechanics, cryptology, and cartography...
result of the folowing equations:
x2 + 1 = 0 (for x -i)
roots of negative numbers other than -1 can be written under
+ i sin (/2)
to the i is a real number
ii = e-/2 ≈ 0.207879576...
(cf. i to
the i is a Real Number)
Euler's formula: eix = cos(x) + i sin(x)
+ i sin(/2)
Raising both sides to i-th power:
e-/2 = ii,
which is approximately 0.207879576...
(Actually, this is one of many possible values for i to
The reciprocal of i is -i:
i-1 = 1/i = i/i2 = i/-1
of i repeat in a definite pattern (i,
-1, -i, 1, ...):
i1 = i
i2 = -1
i3 = i2i = (-1)i =
i4 = i3i = (-i)i =
-(i2) = -(-1) = 1
i5 = i4i = (1)i = i
table with i
first roots of i are:
1i = i
2i = ±(1
4i = ±(i(2
5i = i
(or a math
fallacy?) with i:
d) (1)2 =
e) 1 = -1 and then 2 = 0 ??? Is this possible? Can you discover
what led to this poetic licenced conclusion?
A strange right triangle involving i:
the first and largest negative integer.
is a Heegner
number theory, "Wilson's theorem" states that a natural
number greater than 1 is a prime number if and only if:
(n - 1)! == -1(mod n)
any number by -1 is equivalent to changing the sign on the number.
Curiously enough, one of the values of (−1)2.2 is −1
a separate and special entity called 'Identity
element'. 0 is actually the identity element under addition
for the real numbers, since if a is any real number, a +
0 = 0 + a = a. Mathematicians refers
to 0 as the additive identity (or better said, the reflexive
identity of addition).
to be a purely imaginary number: 0 is the only complex number
which is both real and purely imaginary.
the concept of "almost" impossible in probability.
More generally, the concept of almost nowhere in measure theory.
0 = n / ∞ (according
a0 = 1, only when a doesn't
you cannot divide any number by zero.
In theory, zero multiplied by infinity is undetermined (as is zero
divided by zero).
the only integer (actually, the only real number) that is neither
negative nor positive. The question whether 'zero' is odd or
even seems to be totally subjective. But technically, 0 should
be considered an even number. All even numbers can be
expressed in the algebraic form 2n, where n is any integer,
positive, negative or zero. Thus 0 = 2
x 0, 2 =
2 x 1, 4 = 2 x 2, and so on. All odd numbers can be expressed
in the form 2n+1, thus 1 = (2 x 0) + 1, 3 = (2 x 1)
+ 1, 5 = (2 x 2) + 1, etc. Zero cannot be odd, since there
is no whole
number n such that 2n+1 = 0.
equations with one or more unknown factors are solved by equalizing
them to zero.
number of n x n magic squares for n =
Remarkably, a string of eight zeroes (00000000 !) emerges at position 172,330,850 in the decimal representation of π, counting from the digit immediately following the decimal point.
Below is the string, along with the digits surrounding it:
The difference between 3, 30, and 300 may seem like just a few extra zeros, but those little circles are actually one of the world's greatest inventions. Around 200 B.C., Hindu scholars started using nine oddly shaped symbols and a dot to bring order to the world of math. These symbols and the dot were the earliest predecessors of our modern numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. With only ten symbols and a base of ten, the Hindu numeral system was simple to learn and use. It's unknown who first thought of using a dot (bindu in Sanskrit) as the tenth number. However, it's possible that a Hindu, using an abacus, wanted to keep a written record of his calculations. One day, he used a symbol '.' called shunya to represent a column on his counting board where no beads were moved... Originally, shunya (), the dot, was not the number zero itself, but simply a mark indicating empty space.
The origin of the word "zero" can be traced back to the Italian mathematician Leonardo Pisano, also known as Fibonacci. He took the Arabic word 'صِفْر' (sifr, from the semitic root s.p.r.), meaning 'empty', and transformed it into the Italian word zefiro, which later evolved into "zero." This term has been adopted by many languages such as English, Catalan, French (zéro), Portuguese, Romanian, Spanish (cero), Wallon (zérô), Albanian, Polish, and Japanese.
Europe is divided into two regions: the 'zero region' (mentioned earlier) and the 'nullus region' (derived from the Latin word for 'zero', nullus). The 'nullus region' includes Germanic, Scandinavian, and some Slavic countries. Below is a table showcasing the word for 0 in a selection of languages from the 'nullus region':
Greek word for zero is μηδεν, read as
'meden', which means, etymologically, not even one (i.e. nothing).
The Oracle of Delphi in ancient Greece had a wise motto, like
this: "meden agan" - nothing too much (or nothing
in excess)... -
posted by George Pantazis
The Chinese character for 0, 零, combines 雨 (yǔ) meaning "rain" and 令 (lìng) meaning "to order." This fusion originally represented a fine mist and symbolized the 'last part.' Picture it as an enveloping mist where nothing (zero) is visible or as the round shape of a raindrop.
a score of 0 in tennis.
English word contains 0 vowels?
Answer: hymn, gypsyfy, myth, rhythm, sylph, syzygy, etc.
Czech phrase: Strc prst skrz krk meaning "thrust
finger through neck", contains 0 vowels
the expression in Null Komma nichts (in
zero point nothing) means 'in a trice'
the expression a chilometri zero (in
zero kilometers from any location) means 'local'. For instance, un
gelato a chilometri zero translates as 'an ice-cream produced
with local products'.
are no letters assigned to the numbers 0 and 1 on
a phone dial. These numbers remain unassigned
because they are so-called 'flag' numbers, kept for special purposes
such as emergency or operator services.
0), in the Mystical Numbers of Taoism, represents the Null, the
Chaos, the Origin and the End.
Chuck Norris can divide by zero. (More Chuck
Star Hotel (Null Stern Hotel)
Stern", or "Zero
Star" Hotel is a cross between a hostel and an art installation
by Swiss concept artists Frank and Patrik Riklin. This hotel is
actually a converted bomb shelter...
= 1/3 + 1/6
A strange factorial:
all digits from 1 to 9 once:
= 6 729 / 13 458
= 9 327 / 18 654 (there are 10 other possibilities
to write similar fractions by using all digits from 1 to 9 once)
= (123 - 45) / (67 + 89)
the same number twice, but just swapping the place of ONE digit:
105263157894736842 / 210526315789473684
= 157894736842105263 / 315789473684210526
= 210526315789473684 / 421052631578947368
= 263157894736842105 / 526315789473684210
= 315789473684210526 / 631578947368421052
= 368421052631578947 / 736842105263157894
= 421052631578947368 / 842105263157894736
= 473684210526315789 / 947368421052631578
Numbers with such properties are called 'parasit
or parasitic numbers'.
magnitude of the Sun, and of the Moon.
group of 23 people, at least two have the same birthday with
the probability greater than 1/2.
fallacy?) involving 1/2:
Since (1/2)2 = 1/4
and (1/2)3 = 1/8
then (1/2)3 < (1/2)2
using the logarithms we obtain:
3 log (1/2) < 2 log (1/2)
and after dividing by log (1/2):
3 < 2
How can that be?
population of the Roman Empire under Augustus was
about one hundred millions, of which more than one half were
is a 1/2 percent probability you are related to Genghis Khan...
group of geneticists studying Y-chromosome data have found
that nearly 8 percent of the men living in the region of the former
Mongol empire carry y-chromosomes that are nearly identical to
those of Genghis Khan, the fearsome Mongolian warrior of the 13th
century, whose adopted name means "Universal Ruler" in
Altaic, his native tongue. That translates to 0.5 percent of the
global population in the world (or roughly 16 million descendants
you know that the Romans too could transcribe unit fractions?
e.g. to write 1/2 they
used the letter S (semis). Knowing that, what represents
the Roman numeral SIX? Obviously
not 6, but 8.5! (10 - 1 - 1/2)
Italy, "fojetta" (small leaf, in Roman
dialect) is a measure corresponding to half a liter of
typical 'fojetta' ->
is an amazing formula concocted by Jeff Tupper that, when graphed
in 2 dimensions, can visually reproduce the formula itself:
If one graphs the set of points (x, y)
with 0 < x < 106 and k < y < (k +
17), such that they satisfy the inequality given above, the resulting
self-referential 'plot' looks like this:
a separate and special entity called 'Unity' or 'Identity
element'. 1 is actually the identity element under multiplication
for the real numbers, since a x 1 = 1 x a = a.
Mathematicians refers to 1 as the multiplicative identity (or
better said, the reflexive identity of multiplication).
is NOT prime!
Primes or prime
numbers can be poetically described as the 'atoms' of mathematics
- the building blocks of the world of numbers. But, mathematically
speaking: "a prime number is a positive integer with
exactly TWO positive divisors: 1 and itself". Modern
textbooks consider 1 neither prime nor composite, whereas older
texts generally asserted the contrary. In 1859, Henri
Lebesgue stated explicitly that 1 is prime in "Exercices
d'analyse numérique". It is also prime in "Primary
Elements of Algebra for Common Schools and Academies" (1866)
by Joseph Ray, and in "Standard Arithmetic" (1892)
by William J. Milne. A list of primes to 10,006,721 published
in 1914 by Derrick N. Lehmer includes 1 ("List of prime
numbers from 1 to 10,006,721", Carnegie Institution of Washington).
solution of the equation: x3 - x = 0 (for x -1,
[Note: x3 - x can be factorized as follows:
x(x + 1)(x - 1)]
only real solution of the equation x3 + 3x -
4 = 0
law states that in a huge assortment of number sequences
- in listings, tables of statistics, random samples from a
day's stock quotations, a tournament's tennis scores, the populations
of towns, electricity bills in the Solomon Islands, and much
more, the digit 1 tends to occur with probability ∼30%,
much greater than the expected 11.1% (i.e., one digit out of
9). Dr. Nigrini gained recognition by applying a system he
devised based on Benford's Law to some fraud cases in Brooklyn.
The idea underlying his system is that if the numbers in a
set of data like a tax return more or less match the frequencies
and ratios predicted by Benford's Law, the data are probably
honest. But if a graph of such numbers is markedly different
from the one predicted by Benford's Law, he said, "I think
I'd call someone in for a detailed audit".
define a 'sphere' as the surface of a sphere, not a solid ball,
so a sphere has 2 sides: the outside and the inside. However,
there are also 1-sided
f(x) = ex at the point x = 0 is exactly
Why 0! = 1? Because 4! = 4x3x2x1 and 3! = 3x2x1. Therefore 4! =
4x3! In the same way 3! = 3x2! and 2! = 2x1! So it follows
that 1! = 1x0! Therefore 0! must be equal to 1 or 1! would
be 0... And so 2! would be zero and then 3! and so on.
x1 = x and 1x =
logaa = logba /
= a0 (for a0)
= a2 - (a + 1)(a - 1)
= 35 - 32 -
= 75 - 72 -
= 1/2 + 1/3 + 1/6
= 1/2 + 1/4 + 1/6 + 1/12
= 1/21 + 1/22 + 1/23 + 1/24 +
1/25 + ...
= (2 + 5)1/3 +
(2 - 5)1/3
= (1 + i)(1 - i)/2
= sin2 (a) + cos2 (a)
= | Fn x Fn+3 - Fn+1 x
Fn+2 | (F = Fibonacci numbers)
+ 1/(2x3) + 1/(3x4) + 1/(4x5) + ... + 1/n(n+1)
= 0.9 =
0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + ...
+ 2 + 3 + ... + n)1/n = 1
1)/x = 1
+ x)/x = 1
ap-1 ≡ 1
(mod p) [p = prime number]
35/70 + 148/296 (all digits 0 through 9 were used
= 3(133/36 + 5/8)
- 3(133/36 - 5/8)
multiplications using 1's:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
numbers in the series 1, 11, 111, 1111, 11111,
etc... are all triangular
numbers in base-9.
any police lineup the suspects wear nos. 2 through 9 because
it is considered too suggestive to make anyone display the no. 1!
the essence of all phenomena, which is a single unity, before
being divided. It represents also the contrast between essence
and existence; the enduring and the ephemeral; the unity in diversity
(one/many). According to Hopper, the first advance towards counting
is with the use of words for one and for many,
the differentiation from the self from the group. We still say
'numero uno' to speak of ourselves.
termed as "Dayi" or "Taiyi"), in the Mystical
Numbers of Taoism, represents the ONE, the Ultimate, the Order.
The martial art known as "Taijiquan" based its movement's
philosophies upon the notion of Taiji.
the English language, there is a word with just ONE vowel which
occurs 6 times: indivisibility.
is the longest word in the English language with just ONE vowel.
counting system: 1 + 1 = ?
When it comes to counting, a remote Amazonian tribespeople have
been found to be lost for words. In fact, researchers discovered
that Pirahã tribe
of Brazil, with a population of 200, have no words beyond ONE,
two and many.
The word for "one" can also mean "a few", while "two" can
also be used to refer to "not many"... (But is there
any case where not having words for something doesn't allow you
to think about it?) Source BBC
different languages (© G.
(Old English ān)
proto-language: | *TIK |
Indo-european | *OIN-, *OIW-,
*OIK- |, | *SEM- |
| EKA |
/ ekā (f) / ekam (n)
| *HEMS (< sems) |
Greek, Attic | 'EIΣ, MIA, 'EN HÊS (m), MIA (f), HÉN (n)
Latin | VNVS, -A |
Archaic Latin | *ŒNVS, -A |, | *OINOS,
Spanish uno; Romanian, French,
and Catalan un; Provençal uns;
Portuguese um; Romansh in;
Celtic | OINO |
Welsh un; Irish a
haon (cardinal), amháin (thing), duine (person).
Germanic | AINAZ |
German eins; Danish and Norwegian en, et;
Swedish ett; Icelandic einn.
Slavic | JEDINU, -A, -0 |
|Russian один odin;
Czech and Polish jeden; Slovenian êna.
Indo-Iranian | *AIWAS |
|Persian یک yek;
Hindi एक ek.
script' to modern sinograph 一 :
Old Chinese (pron.) | iêt |
|Chinese 一 yī. 幺 yāo is
used as a replacement for yī in series of digits
such as phone numbers, room numbers, etc... to prevent confusion
between similar sounding words.
| *HAD |; | 'IShT |
Semitic root | WHD | or | ?HD |
(? = glotal stop)
Ancient Egyptian [w'.-] ua-; Akkadian ishte'n;
|Arabic واحِد wa:hid;
Hebrew אחת 'aHat;
Maltese: wiehed; Amharic and.
The roots of the word one (un-, sim-,
prin-, cen-) are hidden in the following words: inch (from
Lat. uncia), onion, ounce, primal, primate, primitive,
primrose, prince, recent, simple, simulate, sincere (from Lat. sincerus meaning "clean,
pure, sound", derived from the Indo-European roots ‘sem’ and ‘ker’,
the underlying meaning of which is: 'of one growth', hence
'pure, clean'), single, unanimous, unicorn, uniform, unify,
union, unique, unit, universe; alone, any, lonely, only, none.
In French: ensemble, oignon, premier, printemps, sanglier,
semblable, sincère. In Spanish: centolla, centollo ('spider-crab',
from Celtic *kintuollos, the largest one < *kĭntu-,
first, and *ollos, big). Gaulish person names: Cintullus,
Cintugnatos, 'first born' (< *kĭntu-, first
one; cognates: Lat. re-cens 'new', Gr. kainos 'young,
also called Pythagoras' constant.
is the ratio of diagonal to side length in a square.
7309504880 1688724209 6980785696 7187537694 8073176679 7379907324
7846210703 8850387534 3276415727 3501384623 0912297024 9248360558
of the earliest numerical approximation of 2 was
found on a Babylonian
clay tablet (from the Yale Babylonian Collection), dated
approximately to between 1800 B.C. and 1600 B.C. The annotations
on this tablet give an impressive numerical approximation in
four sexagesimal figures:
1 + 24/60 + 51/602 + 10/603 = 1.41421296...
≈ (Pn+1 -
Pn)/Pn (P = Pell
2sinus(45°) = 2cosinus(45°)
= 1 + (1 / (2 + (1 / (2 + (1 / (2 + ... ))))))
= (i + ii)
you want to have some fun with 2:
start with the very rough approximation 7/5. Then
(7+5+5)/(7+5) = 17/12
(17+12+12)/(17+12) = 41/29
(41+29+29)/(41+29) = 99/70
(99+70+70)/(99+70) = 239/169
continuing closer approximations of 2
posted by Larry Bickford -
numbers using only square roots of 2:
3 = -log2log2((2))
4 = -log2log2(((2)))
5 = -log2log2((((2))))
6 = -log2log2(((((2)))))
paper sizes are all based on a single aspect ratio of the square
root of two, or approximately 1:1.4142. Basing paper upon this
ratio was conceived by Georg Lichtenberg in 1786, and at the
beginning of the 20th century, Dr Walter Porstmann turned Lichtenberg's
idea into a proper system of different paper sizes.
the Golden Number,
also called Golden Ratio or Phi.
Golden Number property: ( +
1)/ = /1
number sequence is intimately connected with the Golden
fraction 1/998999 contains Fibonacci
at 0° and approximately 222.49° divide a circle in the
Golden Ratio: B/A = /1
≈ Fn+1 / Fn (F = Fibonacci
39887 49894 84820 45868 34365 63811...
you can use Fibonacci
successive terms to convert miles to kilometers:
8 miles ≈ 13 kilometers
13 miles ≈ 21 kilometers
This works because the two units stand in the Golden Ratio (to
within 0.5 percent).
last digit of the numbers in the Fibonacci Sequence are cyclic,
they form a pattern that repeats after every 60th number: 0,
1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6,
1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6,
7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1.
3184th Fibonacci number is an apocalypse number (Apocalpyse
numbers are numbers having exactly 666 digits).
Problem” asks for the exact sum of the reciprocal
1 + 1/22 + 1/32 + 1/42 + 1/52 +
... + 1/(n-1)2 + 1/n2
as well as a proof that this sum is correct. The Swiss mathematician Euler found
the exact sum to be π2/6 and
announced this discovery in 1735. The value is denoted by λ (lambda)
and seems to appear everywhere in mathematics. In fact, the probability
that a randomly chosen integer is not divisible by a square (square-free)
is 1/λ or 6/π2
also known as Theodorus' constant (it is named after Theodorus of
Cyrene, who proved that the square roots of the numbers from
3 to 17, excluding 4, 9, and 16, are irrational).
is the diagonal of a cube having 1-unit sides.
is the height of an equilateral triangle having 2-unit sides.
piscis' (fish bladder) has a major axis/minor axis ratio
equal to the square root of 3, this can be shown by constructing
two equilateral triangles within it.
6887729352 7446341505 8723669428 0525381038 0628055806 9794519330
1690880003 7081146186 7572485756 7562614141 5406703029 9699450949
2sinus(60°) = 2sinus(30°)
= 1 + (1 / (1 + (1 / (2
+ (1 / (1 + (1
/ 2 + ...
the only even prime.
is the first taxicab number
posted by Charles Rathbone
are no integers x, y, and z for which xn +
yn = zn is valid,
when n is greater than 2 (see Fermat's
n2 ± n is
always divisible by 2.
2 = 2 x 2 = 22
= 33 - 52
= 42 - 32 - 22 - 12
= (32 + 42 + 52 + 62 +
72 + 82 + 92)/
(12 + 22 + 32 + 42 +
52 + 62 + 72)
+ ... )))) ;
Proof: if N = (2+(2+(2+(...
then N2 = 2 + (2+(2+(2
+ ... ))) = 2 + N ,
solving N2 - N - 2 = 0 , we find the
positive solution N = 2
+ 10) - 3(63
= loga a2
+ i)(1 - i)
25·92 = 2592,
the only 4-digit number of the form ABxCD=ABCD.
The only other known number that shares this property is 24547284284866560000000000
Such numbers arec called narcissistic
27 = 712 -
the smallest prime that can grow 7 times by the right:
2 is prime,
29 is prime,
293 is prime,
2939 is prime,
29399 is prime,
293999 is prime,
2939999 is prime.
29399999 is prime.
Tetration: nn =
2, when n is about 1.559610469... (which is a transcendental
you increase the area of a square of 1 unit-square, the side n of
this square - for n > 3 - increases approximately
of 1/2n. For example: (12 +
122) ≈ 12 + 1/(2 x 12) ≈ 12.0416... -
An everyday example when 1 + 1 ≠ 2:
1 liter of water + 1 liter of alcohol = 1.926 liters of liquid
2), in the Mystical Numbers of Taoism, symbolizes the Twin, the
First Division, the Duality of Opposites (Yin/Yang).
Cantonese the number two is fortunate, because it sounds similar
to "easy" in the dialect.
pre-1972 Indonesian and Malay orthography, the digit 2 was
shorthand for the reduplication that forms plurals, for instance: orang "person",
and orang-orang or orang2 "people".
This orthography has resurfaced widely in text messaging and
other forms of electronic communication.
rule is an easy way to make sure you have left enough
following distance between your car and the vehicle in front,
no matter what speed you're travelling at. To check if you
are travelling two seconds behind the vehicle in front:
- watch the vehicle in front of you pass a landmark (such as a
sign, tree, or power pole) at the side of the road,
- as it passes the landmark, start counting 'One thousand and one,
one thousand and two',
- if you pass the landmark before you finish saying those eight
words, you are following too closely. Slow down, pick another landmark
and repeat the words to make sure you have increased your following
distance. -- Source Land
most common two-letter words in order of frequency are: of, to,
in, it, is, be, as, at, so, we, he, by, or, on, do, if, me, my,
up, an, go, no, us, am.
is the only word in the English language with TWO i.
honey bee must tap TWO million flowers to make ONE pound of honey!
man is a person who will pay two dollars for
a one-dollar item he wants. A woman will pay one dollar for a
two-dollar item she doesn't want..." -- William
different languages (© G.
(Old English twā)
proto-language: | *PAL |
Indo-european | *DWI-, *DUWO-
| DVÎ |
/ dvā (f) / dve (n)
| *DWO |, Greek, Attic | ΔYO DUO |
Latin | DVO, -Æ |,
| BI- |, Archaic Latin | *DWO |, | *DWI-
French deux; Spanish and Catalan dos;
Provençal dous (m), dos (f);
Portuguese dois (m), duas (f);
Romanian doi (m), două (f);
Romansh dus (m), duas (f);
Sardinian dúos (m), dúas (f).
Celtic | DO |
|Breton daou (m), div (f);
Welsh dau (m), dwy (f);
Irish a dó (cardinal), dhá (things), beirt (persons).
Germanic | TWAIZ |
German zwei (often zwo is
used to avoid confusion with drei, 3); Danish and
Norwegian to; Swedish två;
Slavic | DUVA, DVE |
|Russian два dva;
Czech dva; Slovenian dvá;
Indo-Iranian | *DVA: |
|Persian دو do;
Hindi दो d̪oː.
script' to modern sinograph 二 :
Old Chinese (pron.) | ñzhi |
|Chinese 二 èr (is
used for numbers and in counting) / 两 liǎng (is
used when counting objects or persons).
| *ThNÂ |; | KIL' |
Semitic root | Th-N |, derived verb 'thny',
Ancient Egyptian [sn.-] sen; Akkadian shénâ;
|Arabic اِثنان ithna:n;
Hebrew שתיים shtayim;
Maltese: tnejn; Amharic hulät.
Zulu (isi / ku)bili.
The roots of the word two are hidden
in the following words: balance, bezel, bicycle, binary, biscuit,
combine, diploma, diptych, double, doubt, duel, duet, duplex,
duplicate, pinochle; between, twist, twice, twill, twin; Mishnah.
In French: bafouiller, berlue, besace, bévue, bigle,
binocle, bisquer, brouette (< bis-rouette).
an irrational number involved in the formula for the Golden
is also used in statistics when dealing with 5-business day weeks.
is the hypothenuse of a right triangle having 1 and 2-unit sides.
is the diagonal a rectangular box having 1, 2
9978969640 9173668731 2762354406 1835961152 5724270897 2454105209
2563780489 9414414408 3787822749 6950817615 0773783504 2532677244
by the Scottish mathematician John
Napier of Merchistoun.
e stands for exponens (in Latin,
= 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! + ...
e ≈ (1001/1000)1000
this mathematical property:
5904523536 0287471352 6624977572 4709369995 9574966967 6277240766
3035354759 4571382178 5251664274 2746639193 2003059921 8174135966
≈ 6(4 + 5) (mathematical
cos a + i sin a
Ln x ≡ loge x
log x =
log e · Ln x
Peirce suggested the innovative notation, that looked like a
paper clip, for e and shown
From J. D. Runkin's Mathematical Monthly, vol. I, No. 5, Feb. 1859
the only prime 1 less than a perfect square. -
is the number of spatial dimensions needed to mathematically describe
are the primary colors.
the geometric constructions you cannot build using just a ruler
and compasses: 1. You cannot trisect - divide into three equal
parts - a given angle; 2. Double a cube; and 3. Square a circle.
is divisible by 3 when the sum of its digits can be divided by
denominator of a rational number is not divisible by 3,
then the repeating part of its decimal
expansion is an integer divisible by 9. Example: 1/7 = 0.142857...
has a repeating part '142857' divisible by 9. Another example
with a larger recurring
decimal: 1/23 = 0.0434782608695652173913... has a repeating
part '0434782608695652173913' divisible by 9.
3 + 2 =
+ 5 (sum
of two square roots)
= 4! / (4 x 4)
= XV/V = CL/L = MD/D
= 4 + 4 – 5 =
43 + 43 – 53
= 17,469 / 5,823 (this division contains all
digits 1 through 9 once)
51249876 = 153749628 (the multiplication uses
all 9 digits once - and so does its product!)
37 = 111
33 x 3367 = 111,111
333 x 333667 = 111,111,111
3333 x 33336667 = 111,111,111,111
33333 x 3333366667 = 111,111,111,111,111
3 x 1.5 =
3 + 1.5
3! + 3
32 = 52 - 42
33 = 63 - 53 - 43
33 = 32 + 32 + 32
425 = 34425 (see
also 312 x
325 = 312325)
is the minimum colors needed to create camouflage patches, usually
used in military compounds and vehicles. -
posted by George Pantazis
product of the 3 numbers in each row, column, or diagonal
of the geometric magic
square opposite - involving powers of 3 - gives the magic
constant 14,348,907. Moreover, the exponents are arranged
the same as in the normal 3x3 magic square!
3 x 3 alphamagic
square is a magic
square for which the number of letters in the word for each
number generates another magic square, for instance:
A 3 x
6 rectangle has an area equal to its perimeter.
one gram of water the number of molecules is about:
3.3 x 1022 = 33000000000000000000000
ternary base, is a numeral system which uses 3
values or digits: -1, 0, and 1. It works as follows
(in the example, the symbol 1 denotes the digit -1):
or base-3 numbers can
be converted to balanced ternary notation by adding 1111... with
carry, then subtracting 1111... without borrow. For instance:
0213 + 1113 = 2023, 2023 -
1113 = 1113(bal) = 710
non-standard positional numeral system is easily represented as
electronic signals, as potential can either be negative, neutral,
or positive (comparison logic). The balance ternary system is also
useful to solve the classical 2-pan
letters A, F, H, K, N, Y and Z are
made up with 3 lines.
SMS language <3 means
'I love you', and <333,
'I love you so much'.
millions of Indians live with less than 1 dollar per day (2004).
rates: statistically, one in three men who ask
test turn out not to be the biological parent.
has 3 hearts.
number 3 symbolizes the principle of growth. In Guangdong province,
China, three is associated with living or giving birth.
known as "Sanxing" or "Sancai"), in the Mystical
Numbers of Taoism, represents the number 3 and symbolizes the
Three Luminaries: Sun, Moon, Stars. It also defines the concept
of "Heaven, Mankind, Earth" as well as "Upper,
thought: "There are 3 kinds of people: those who can count
and those who can't".
1: Spell 'mousetrap' in 3 letters...
2: Spell 'water' in 3 letters...
Norris once won a game of Connect
Four in 3 moves!
you’re a Simpsons fan, then you problably know about “Blinky”,
fish found near the nuclear plant where Homer Simpson was
working. As it turns out, the Simpsons were right yet again,
as fishermen in Córdoba, Argentina caught a three-eyed
wolf fish in a reservoir fed by a local nuclear power plan! (Fri,
Oct 28, 2011)
the taoist mythology, Erlang Shen (二郎神),
or Erlang is a Chinese God with a third truth-seeing
eye in the middle of his forehead.
French sentence 'un bonhomme haut comme trois pommes' (a 3-apple-tall
fellow) and the German sentence 'ein Kerlchen drei Käse
hoch' (a 3-cheese-tall fellow) mean both a
fourmis, chacune d'elles ressemble au chiffre 3.
Et il y en a! Il y en a 333333333333... jusqu'à l'infini" (Jules
Renard, 'Histoires naturelles').
Translation: "The ants. Each of them resembles a figure
3. That's, it. There are 333333333333 to infinity".
and 'bookkeeping' are the only words in the English language
with three consecutive double letters.
most common three-letter words in order of frequency are: the,
and, for, are, but, not, you, all, any, can, had, her, was, one,
our, out, day, get, has, him, his, how, man, new, now, old, see,
two, way, who, boy, did, its, let, put, say, she, too, use.
name "Mitsubishi" (三菱) consists of two
parts: "mitsu" meaning 'three' and "bishi" meaning
'water caltrop', and hence 'rhombus', which is reflected in the
company's famous logo (it is also translated as 'three diamonds').
Other Japanese family names containing the number 3: Mitsudani,
Mitsugi, Mitsui, Mitsuhashi, Mitsude, Mitsuishi, Mitsumura, Mitsubori,
Mitsumata, Mitsuyama, Mitsuzawa, Mitsuya, Mitsukuchi, Mitsukyou,
Mitsuboshi, Mitsuzima, Mitsue, Mitsuike, Mitsuaichou, Mitsubuchi,
Mitsuse, Mitsuyanagi, Mitsumachi, Mitsukunugi, Mitsuwa, Mitsuzaku,
Mitsumatsu, Mitsuhuzi, Mitsuduka, Mitsuwari.
different languages (© G.
(Old English thrīe)
| *TREYES, *TISORES,
| TRÎ |
/ tisraḥ (f) / trīṇi (f)
Attic | TPEIΣ, TPIA TRÊS, TRIA |
Latin | TRES, TRIA |, Archaic
Latin | *TREIES |
French trois; Spanish and Catalan tres;
Provençal trei, tres;
Portuguese três; Romanian trei;
Romansh trais; Sardinian très.
Celtic | TRI |
|Breton tri (m), teir (f);
Welsh tri (m), tair (f);
Irish trí (m), teoir (f,
old Irish), triúir (people).
Germanic | THRIJIZ |
German drei; Danish, Norwegian,
and Swedish tre; Icelandic þrír.
Slavic | TRIJE, TRI |
|Russian три tri;
Czech tři; Slovenian trí;
Indo-Iranian | *TRAYAS |
|Persian سه se;
Hindi तीन t̪iːn.
script' to modern sinograph 三 :
Old Chinese (pron.) | sâm |
|Chinese 三 sān. The
sinograph 叁 is used as a replacement for sān on
legal and financial documents to prevent fraud.
| *SALATh |
Semitic root | Th-L-Th |
Ancient Egyptian [ḫmt'-] khemet;
|Arabic ثلاثة thalathâ;
Hebrew שלושה shlôshah;
Maltese: tlieta; Amharic sost.
The roots of the word three are hidden
in the following words: contest, detest, obtest, protest, sesterce,
sitar, teapoy, tercet, tertian, tern, terpolymer, test, testament,
testicle, testify, testimony, trammel, travel, trefoil, trench,
trephine, trey, triad, triangle, triathlon, tribe, trio, triple,
triplex, trine, trinity, trimurti, trivial, triumvir, trocar,
troika; third, thrice. In French: travail, treillis, trémail.
In Spanish: terliz, trabajo.
Number (3) here.
Perimeter / Diagonal, of any circle.
to 45 decimal places:
3.14159 26535 89793 23846 26433 83279 50288 41971 69399
to 52 binary places:
11.0010010000111 1110110101010 0010001000010 1101000111001
cannot square a disc using just a ruler and compasses because is
formula for , more formulas here.
- 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... )
= 2(2/1 x 2/3 x 4/3 x 4/5 x 6/5 x 6/7 x 8/7 x 8/9 x ... )
(a real good rational approximation of )
the late 18th century, James Stirling, a Scottish mathematician,
developed an approximation for factorials using the transcendental
numbers 'Pi' and 'e':
n! ≈ (2n)1/2 (n/e)n
most famous formula for calculating Pi is Machin's formula:
= 4 arctan(1/5) – arctan(1/239)
This formula, and similar ones, were used to push
the accuracy of approximations to Pi to over 500 decimal places
by the early 18th century (this was all hand calculation!).
pandigital approximation of by
mathematician E. Pegg:
0 + 3 + [1 - (9 - 8-5)-6]/(7 + 2-4)
number or a formula is said to be "pandigital" if it
contains each of the digits from 0 to 9. You can discuss this here.
there are no occurrences of the sequence 123456 in the first
million digits of Pi. -
posted by George Pantazis
Does Pi equal 3? No? Then have a look on the algebraic equation
x = ( +
2x = +
3) = ( +
- 6x = 2 -
9 - 6x = 2 -
9 - 6x + x2 = 2 -
(3 - x)2 = ( -
3 - x = -
- describe the DNA double helix,
- determining the distribution of primes - the probability that
two randomly selected integers are relatively prime (i.e. have
no common factors) is 6 / p2,
- analyzing the ripples on water,
- checking for accuracy - as there are now millions upon millions
of known decimal places of Pi, by asking a super computer to compute
this many figures its accuracy can be tested,
- in cryptography - the science of coding,
- generate of a random number.
Day (March 14 or 3-14) in 1879, a baby was
born in Ulm, Germany to a German couple whose name meant "one
stone". That baby was Albert Einstein!
naturally in tables of death, in what is known as a Gaussian
distribution of deaths in a population; that is, when a person
dies, the event 'feels' Pi.
symbol for Pi was introduced by the English mathematician William
Jones in 1706.
John Conway pointed out that if you break down the digits of
Pi into blocks of ten, the probability that one of those blocks
will contain ten distinct digits is about one in 40,000. Curiously,
this first happens in the 7th block of ten digits.
is the little rhyme to help the memorisation of twenty-one digits
Now, I wish I could recollect pi.
"Eureka," cried the great inventor.
Christmas Pudding; Christmas Pie
Is the problem's very center.
A round pizza with radius 'z' and thickness 'a' has the volume Pi·z·z·a.
is the Silver
Number or silver constant given by:
x3 - 5x2 + 6x - 1 = 0
S = 37
+ (7 · 37
+ (7 · 37
+ ... ))
the smallest number of colors sufficient to color all planar
maps with no adjoining countries sharing the same color.
are the number of coordinates needed to describe an event in 'spacetime':
t, x, y, z.
any whole number... If the number is even, divide it by 2; if
it is odd, multiply it by 3, then add 1. By repeating this procedure,
sooner or later you'll arrive at the number 4,
which will give you 2, which in turn gives you 1, and then get
a 4 again! No matter what number you choose, you'll always arrive
at the 4-2-1 cycle.
word 'four' has 4 letters and is the smallest honest
number. Honest numbers are numbers n that can be
described using exactly n letters in standard mathematical
x 4 square has an area equal to its perimeter.
only solution of xy = xy involving integers is:
x = y = 2, and xy = xy = 4
24, is the solution to the equation ab = ba,
for a b.
to Brocard's problem n! + 1
= m2 :
4! + 1 = 52 , the only other pairs
5! + 1 = 112 and 7! + 1 = 712
y2 is divisible by 4 only when (x
- y) is even.
integer of the form n4 + 4 is
not a prime, except for n=1, because it can be factorized
n4 + 4 = (n2 -
2n + 2)(n2 + 2n + 2) (Aurifeuillean factorization)
ends with digits 0, 1, 5 or 6.
prime of the form 4k + 1 is the sum
of two square numbers:
13 = 4 x 3 + 1 = 22 + 32 ;
73 = 4 x 18 + 1 = 32 + 82 ;
137 = 4 x 34 + 1 = 42 + 112
32 - 22 - 12
- ... ))))
= 1(1/2)0 + 2(1/2)1 + 3(1/2)2 +
4(1/2)3 + 5(1/2)4 + 6(1/2)5 +
multiply the number 21978 by 4, it turns backwards!
/ 3,942 (contains all digits 1 through 9 once)
two equalities 4 x 1738 = 6952 and 4 x 1963 = 7852, use the digits
1-9 exactly once!
intriguing 4 x 4 magic
square (fig. 1) that works just as well upside-down (fig.
the smallest digit that never occurs in any term of the "look-and-say" sequence.
The Shadok's numbers
are a kind of quaternary or base-4 numeration system:
digit 4 on an LCD calculator is made up of 4 bars.
famous riddle: Show how one-half of five is four!
Answer: Take off the first and last letters and you have the roman
numeral for 4. The Roman numeral for four is IV (whose
letters are one-half of the four letters in the spelled-out word "five").
is the Roman numeral IIII used instead of IV on
clocks and watches?
- using IIII brings more symmetry and balance to the dial. The
IIII offsets the heavy VIII that is found on the other side.
- the strict use of IV instead of IIII wasn't common until after
the middle ages (the practice of placing smaller digits before
large ones to indicate subtraction came into popularity in Europe
after the invention of the printing press), the Romans generally
used IIII. Clocks and watches are patterned after sundials, which
were in use long before the middle ages.
his book "Bauwerk und Plastik des Parthenon, in Antike Kunst" (Basel,
1980). E. Berger presents a study that investigates the way that
the Pythagorean ideas of ratios of small numbers were used in the
construction of the Temple
of Athena Parthenos. In his opinion the ratio 4 : 9 were fundamental
to the construction. A basic rectangle of sides 4 and 9 was constructed
from three rectangles of sides 3 and 4 with diagonal 5 (see drawing).
This form of construction also meant that the 3-4-5 Pythagorean
triangle could be used to good effect to ensure that right angles
in the building were accurately determined.
The length of the Temple of Athena Parthenos is 69.5 m, its width
is 30.88 m and the height at the cornice is 13.72 m. To a fairly
high degree of accuracy this means that the ratio width : length
= 4 : 9 while also the ratio height : width = 4 : 9.
- Source: Article by
J.J. O'Connor and E.F. Robertson.
rule is the amount of time that internet user will
wait for a page to load before leaving and going to another
The phrase "four-letter word" is used
to describe most swear words in the English language.
oath, as quoted by the Renaissance magician Cornelius Agrippa,
is as follows:
"I with pure mind by the number four do swear;
That's holy, and the fountain of nature
Eternal, parent of the mind..."
and in most Asiatic cultures, the number 4 (sinograph: 四)
is considered unlucky because it is prounounced shi which
sounds like the word 'death'. Due to that, many numbered product
lines skip the number 4. However, in some cases the word yon ('4'
in early classical Japanese) is used instead of shi:
when counting floors in a building, or when you are asked "which
floor?" in an elevator... The aversion or fear of the number
4 is called "Tetraphobia".
Four equals three!
Suppose: a + b = c .
This can also be written as:
4a - 3a + 4b - 3b = 4c - 3c .
4a + 4b - 4c = 3a + 3b - 3c .
Take the constants out of the brackets:
4(a + b - c) = 3(a + b - c) .
Remove the same term left and right, then:
4 = 3
Where is the error?
using four 4's and any operations, try to write
equations that have the integers from 1 to 100 as the answer
(see example below):
1 = 44/44
2 = 4/4 + 4/4
3 = (4 + 4 + 4)/4
4 = 4(4 - 4) + 4, etc...
(click here to
Think of any number and write it out in WORDS. Count the number
of letters it contains and write that down in WORDS. And so
• TWENTY-EIGHT (11 letters) ->
• ELEVEN (6 letters) ->
• SIX (3 letters) ->
• THREE (5 letters) ->
• FIVE (4 letters) ->
• FOUR (4 letters) -> etc.
You will always arrive at FOUR!
bill can be double folded (forward and backwards) 4x103 times
before it will tear.
= For instance!
the expression in quattro e quattr'otto (in
four and four eight) means 'in a trice'.
Finnish word that contains 4 y: Yötyöhyöty (advantage
gained from working night shifts with the correspondingly higher
salary). - posted by Juhani Sirkiä
rivers are mentioned in the Old Testament, Gen 2, 10:
"And a river went out of Eden ... and parted ... into four heads. The ...
first [is] Pison ... which compasses the whole land of Havilah ... the
second [is] Gihon ... that compasses the whole land of Ethiopia ...
the third [is] Hiddekel ... that goes toward the east of Assyria ...
and the fourth [is] Euphrates that goes eastward to Assyria".
number 4 symbolizes the principle of putting ideas into form.
It signifies work and productivity.
in 4 people worldwide is Muslim, and 2 out of
3 of the world's Muslims are in Asia (data: 2009).
4), in the Mystical Numbers of Taoism, represents the Four Essences:
Earth, Water, Air, Fire.
most common four-letter words in order of frequency are: that,
with, have, this, will, your, from, they, know, want, been, good,
much, some, time, very, when, come, here, just, like, long, make,
many, more, only, over, such, take, than, them, well, were.
are only 4 words in the English language which
end in 'dous': hazardous, horrendous, stupendous and tremendous.
different languages (© G.
(from Old English feower)
| CATÙR |
catvāraḥ / catasraḥ / catvāri
| *QWET(O)RO- |
Greek, Attic | τέτταρες, τέτταρα TETTARES, TETTARA |
Latin | QUATTUOR |, Archaic Latin | *QUATBORO |
French, Provençal and Catalan quatre;
Spanish cuatro; Portuguese quatro;
Romanian patru; Romansh quatter;
Celtic | PETOR |
|Breton pevar (m), peder (f);
Welsh pedwar (m), pedair (f);
Irish a ceathair (cardinal), ceathre (things), ceathrar (people).
Germanic | FITHWOR |
and German vier; Danish, Norwegian,
and Swedish fire; Icelandic fjórir.
Slavic | CETYRIJE, CETYRI |
|Russian четыре chetyrye;
Czech čtyři; Slovenian štíri;
Indo-Iranian | *K'ATWA:RAS |
|Persian چهار chahar;
Hindi चार chaːr.
script' to modern sinograph 四 :
Old Chinese (pron.) | si |
|Chinese 四 sí.
| *RABA' |
Semitic root | RB' |
Ancient Egyptian [ỉfd'-] aft'u;
Akkadian or erbe;
|Arabic أربعة arba'â;
Hebrew ארבעה ârba'ah;
Maltese: erbgħa; Amharic arat.
The roots of the word four are hidden
in the following words: cadre, cahier, carillon, carnet, carrefour,
casern, czardas, escadrille, petorritum, quadrant, quadriga,
quadroon, quarantine, quarrel, quarry, quarter, quartan, quaternay,
quatrain, quire, squad, square, tetrad, trapezium, trocar;
farthing, filler, firking; rabi, arroba (from Arabic الربع ar-rub', "quarter").
In French: carreau, écarquiller, écarter, Périgord
(< *petru-corii, 'four troops'), Périgueux,
arrobase. In Italian: quadrivio, squadra, squartare, tessera.
In Spanish: ejedrez, from Sanskrit चतुरङ्ग;
caturaṅga, "having four limbs or parts". Gaulish person names:
Petrullus, Petrogenos, Petrusonia ‘fourth
born’ (< *petuares / petru-, 'four').
Number (4) here.
the only prime number that ends in 5.
is the number of Platonic
is the only prime number that ends in 5.
is a congruent
number because it is the area of a 20/3, 3/2, 41/6 triangle
(a congruent number is an integer that is the area of a right triangle
with three rational number sides).
Roman numeral for 5 is V, which comes from a
representation of an outstretched hand.
power of 5 ends in a 5 (except 50).
= 32 -
22 = 12 +
= 25 -
52 = 32 + 42 = 132 -
x 11 - 11)/(11 + 11)
1)! + 1 = 0 (mod 52)
number having a abc5abc5 pattern
is divisible by: 5, 73, 137, and 10001
you count in 'ding-bong'?
inhabitants of 'Fongaponga' use a series of sounds made from this
strange device to represent numbers: 'ding'
with the handbell, 'eek' when squeezing the rubber
bulb of the horn, and 'bong'
when beating the tambourine with the small ball. These very special base-5
numerals are then strings made from 3 sounds each
corresponding to an additive numerical value. Looking at the number
list below, we can guess with the help of some logic that 'eek'
is actually a 'function' that indicates subtraction and that every
'ding' equals 5, and every 'bong', 7.
From number 24 on, all numbers are only
combinations of dings and/or bongs.
- Sarcone's "ding-bong numbers" are
sequence A102701 in
the 'Encyclopedia of integer sequences'.
- "Fongaponga", Focus
BrainTrainer nr. 7, page 51.
polygon (pentagon) has 5 diagonals. This is the only shape for
which the number of sides and diagonals is the same (which may
explain why pentagrams, pentacles, and pentangles are
so common and appear so often as iconographic symbols). -
by Patrick Vennebush -
Pentagram, Pentangle and Pentacle are
all names for a 5-pointed star. This mystical symbol is supposed
to keep away devils and witches.
5 is geometrically represented in the Quincunx pattern.
This design is arranged by marking four corners of an imaginary quadrilateral
and a central axis through a series of dots or objects - as noticed
on dice, playing cards, or dominoes. The significance of the quincunx
pattern originates in Pythagorean mathematical mysticism.
Greek coin marked with Quincunx Pattern
famous riddle involving 5s: How can you make the following
equation true by drawing only one straight line:
famous riddle: From a word of 5 letters,
take 2 letters and have 1.
Answer: ALONE - AL = ONE.
English word contains all 5 vowels ONCE?
Answer: auctioned, authorize, dialogue, discourage, education,
housemaid, mensuration, obnubilate, pneumonia, precarious, precaution,
regulation, sequoia, tambourine, ultraviolet, uncopyrightable...
The words ABSTEMIOUS, ANEMIOUS, ARSENIOUS, CAESIOUS and FACETIOUS
contain all 5 vowels appearing in alphabetical order, while in
the words SUBCONTINENTAL and UNORIENTAL they appear in reverse
alphabetical order! -- G.
Italian/French/Spanish word uses all 5 vowels
Answer: aiuole (flowerbeds) / oiseau (bird) / murciélago
A list of words that contain all 5 vowels once BOTH in Italian
and in Spanish: ADULTERIO, AURIFERO, CAULIFORME, COMUNICANTE, DEPURATIVO,
DELUSORIA, EDUCATIVO, EQUIVOCA, ESTUARIO, EUFORIA, FERRUGINOSA,
INCESTUOSA, LUTERANISMO, PAUPERISMO, PERUVIANO, SURREALISMO, VITUPEROSA,
VOLUMETRIA... -- G.
French, some verbs like 'vouaient' (were dedicating, dedicated),
'jouaient' (were playing, played)... contain 5 different consecutive
this exclamation, there are five i's!" (autoreferential sentence)
+ 5 = 1005 (one thousand five) is the smallest
natural number whose name contains the five vowels a, e, i, o,
u (in any order).
French "je te dis un mot de cinq lettres!" (I tell
you a word of five letters) is an exclamation of anger against
the person for whom the insult is intended.
At 1:02 AM and 3 seconds on Wednesday, April 5, 2006, it was the
1st hour of the day, the 2nd minute of the hour, the 3rd second
of that minute in the 4th month and the 5th day of '06... or just: 01:02:03 04-05-06 for
For many other places, this coincidental chronological oddity happens
at 1:02 AM May 4.
five rivers of Hades are:
• Acheron (the river of woe. Etymologically,
the name probably means 'marsh-like': cf. Greek word akherousai, 'marshlike
• Cocytus (the river of lamentation; from Greek kokutos,
• Phlegethon (the river of fire; from Greek present
participle of phlegethein, 'to blaze'),
• Lethe (the river of forgetfulness; from Greek lethe,
• Styx (the river of hate; cognate with Greek
words stygos 'hatred' and stygnos 'gloomy').
is a very popular number in Chinese culture since it occupies
the central position (one through nine) and also reflects the
'Five Elements Philosophy' (Wuxing) - Wood, Fire, Earth, Metal
(or Gold), and Water (in Chinese: 木, mù; 火,
huǒ; 土, tǔ; 金, jīn; 水, shǔi).
the banking sector employs about 5% of the workforce
to a research by Commtouch, quoted by NYT, only 5 countries:
China, South Korea, Russia, USA and Brazil generate 99% of spams.
name Pontius (Pilatus), in early Italic language means
'the 5th'. We can find the Indo-european root penkwro,
the '5th', in the word finger (finger, from
Germanic fingwraz, "one of five").
- by Gianni A. Sarcone -
the god and patron of art, games, beauty, dance, flowers, and
song in Aztec mythology. His name contains the Nahuatl words xochitl ("flower")
and macuil (five), and hence means "Five-flower" (but
he could also be referred to as Chicomexochitl, "Seven-flower").
number 5 (๕) is
pronounced as 'Ha' in Thai language.
555 is also used by some as slang for 'HaHaHa'!
5, variously spelled 'Soup Number Five' or 'Soup #5',
is a soup made from bull's testicles or penis.The dish originates
from Filipino cuisine. It is believed to have strong aphrodisiac
For those who know German:
- Mr. Freud, what is between fear and sex?
different languages (© G.
(from Old English fîf)
| *PENKWE |
Sanskrit | PAÑCA |
Greek, Attic | ΠENTE PENTE |
Latin | QVINQVE |, Archaic Latin | *PENQVE |
Vulgar Latin | *CINQUE |
French cinq; Spanish and Portuguese cinco;
Provençal and Catalan cinc;
Romanian cinci; Romansh tschintg;
Celtic | PEMPE |
Welsh pump; Irish cúig (things), ciúigear (persons).
Germanic | FIMFI |
German fünf; Danish, Norwegian,
and Swedish fem; Icelandic fimm.
Slavic | PEnTI |
|Russian пять p'jat';
Czech pět; Slovenian pét;
Indo-Iranian | *PANK'A |
|Persian پنج panj;
Hindi पाँच panch.
script' to modern sinograph 五 :
Old Chinese (pron.) | nguo |
|Chinese 五 wǔ.
| *KhAMSh |
Semitic root | Kh-M-Sh |
Ancient Egyptian [dỉ'-] t'uau;
|Arabic خمسة khamsâ;
Hebrew חמשה khamishah;
Maltese: hamsa; Amharic amist (pron.
The roots of the word five are hidden
in the following words: cinquain, Cinquecento, cinquefoil,
keno, pachisi, Pentecost, pentesmon, pentagon, pentameter,
pentathlon, pinkster flower, Pontius, punch, Quentin, quincunx,
quinial, quintain, quintessence, quintet, quintuple; femto-,
fin, finger, fist, foist; khamsin. In French: esquinter, quinquagénaire.
In Spanish: quintar. In German: Pfinztag, Quentchen.
number because it is the area of a 3, 4, 5 triangle (a congruent
number is an integer that is the area of a right triangle with
three rational number sides).
is the smallest perfect
number, that is a number whose divisors add up to itself, e.g.:
1 x 2 x 3 = 1 + 2 + 3 = 6
probability that a number picked at random from the set of integers
will have no repeated prime divisors is 6/2.
n3 - n is
divisible by 6. That is, any product of 3 consecutive integers
is divisible by 6.
The equation xn - ym = ±6 with n, m > 1
has NO solution. In other words, 6 cannot be a
difference of two powers!
3(1/1 + 1/2 + 1/3 + 1/6) = 62(1/1 - 1/2 - 1/3)
= 1/20 + 3/21 + 5/22 + 7/23 +
9/24 + 11/25 + 13/26 + ... (sum
of consecutive odd numbers with reciprocal powers
= 4! / 22 = 4! / 2!2
= (Log(10 x 10 x 10))!
= 102 + 102 + 102 = 1102
62 = 13 + 23 + 33
63 = 33 + 43 + 53
Simple Mnemonic Math Trick
When you multiply 6 by an even number, they both end in the same
Example: 6x2=12, 6x4=24,
the smallest number of colors needed to color the regions on
a map on a Möbius
strip. A Möbius strip is a continuous closed surface
with only one side; formed from a rectangular strip by rotating
one end 180 degrees and joining it with the other end.
circles of the same size (try this with 6 coins of the same denomination)
will always perfectly surround, all touching, without gaps, 1
circle of that same size. - Posted by Aaron
probability to get one 6 with 6 dice is 0.665...
The probability to get two 6's with 2 x 6 = 12
dice is 0.619...
The probability to get three 6's with 3 x 6 =
18 dice is 0.597...
nut with 6: "From six take nine; from nine
take ten; from forty take fifty, and have six left" (see
(senary or heximal) numeral system is used by the Ndom people
of the Frederik Hendrik Island, near New Guinea. For example,
in Ndom language the number 7 is mer abo sas (6 + 1),
and the number 17, mer an thef abo meregh (6 x 2 + 5).
exclamation has unexpectedly six 's',
six 'i' and six 'x'!" (autoreferential
sentence) - G. Sarcone.
one of us is only about 6 acquaintances away from anyone else
in the world.
have two different names for six: seis or meia (short
for meia duzia, 'half dozen').
old French, the word 'hasart' meant 6 at the
game of dice. The earliest meaning of HAZARD (<hasart) was,
however, 'stroke of luck (or bad luck)'. In the past, the dice
featured on one face a flower pattern. Thus the Arabs called
gaming dice "flowers", in Arabic 'az-zahr'.
sick sheik's sixth sheep's sick" is said to be
the hardest tongue twister in English.
can you transform the Roman number IX into 6 by
drawing only one line?
Answer: SIX (yes, the line is curvilinear...).
Solving the equation by one dumbo:
people like the number 6. One possible reason is because it is
the largest number on a dice, and when gambling, one wins if
the number six is thrown. When playing mah-jong, the host is
the most likely to be the one who throws the number six, and
who therefore has a better chance of winning. Reflecting this,
the Chinese have a saying, "double six makes you the happiest".
For Chinese businessmen the number six means "a smooth business".
in the Mystical Numbers of Taoism, represents the number 6 and
symbolizes the Six Harmonies:
體 合 於 心 (Body in harmony with Heart),
心 合 於 意 (Heart in harmony with Intent),
意 合 於 氣 (Intent in harmony with Qi),
氣 合 於 神 (Qi in
harmony with Spirit),
神 合 於 動 (Spirit in harmony with Motion),
動 合 於 空 (Motion in harmony with Nothing).
man in Nigeria get really attracted to a woman, he sends six shells
to her. In fact, the Yoruban word efa means both 'six'
and 'attracted'. If this chat up line works, the girl replies
with eight shells - ejo meaning both 'eight' and 'I
Whenever two people meet, there are really six people
present. There is each man as he sees himself, each man as the
other person sees him, and each man as he really is.
-- William James.
9 , 111 111 = 6 un-o dop-o un 9 (this
Italian sentence means "6 ones after
a 9" and can be read the same upside down).
Photo Snuff is an Indian tobacco brand.
words which contain strings of 6 consonants: "bergschrund", "borschts", "eschscholtzia", "latchstring", "weltschmerz".
105 is the number of engineers China produced in 2005.
In comparison, India produces nearly 5 x 105 technical
graduates annually! (data 2008)
different languages (© G.
(Old English siex)
| *SEKS | | *SWEKS |
Sanskrit | S'AS' |
Greek, Attic | 'EΞ HEX |
Latin | SEX |
French six; Spanish and Portuguese seis;
Catalan and Romansh sis; Romanian şase;
Celtic | SUEK(O)S |, | SVEK(O)S |
Welsh chwech; Irish sé (things), seisear (persons).
Germanic | SEKS |
German sechs; Danish and Norwegian seks;
Swedish and Icelandic sex.
Slavic | ShESTI |
|Russian шесть shest';
Czech šest; Slovenian šést;
Indo-Iranian | *(K)SWACSH |
|Persian شش shesh;
Hindi छः ch'eh.
script' to modern sinograph 六 :
Old Chinese (pron.) | lyuk |
|Chinese 六 liù.
| *ShIDTh |
Semitic root | Sh-Sh |, | Sh-T |
Ancient Egyptian [sỉs'- or ỉs'- (?)] sas;
|Arabic ستة sittâ;
Hebrew ששה shishah;
Maltese: sitta; Amharic sidist (pron.
The roots of the word six are hidden
in the following words: bisextil, hexad, hexagon, Seicento,
semester, senary, sestet, sestina, sext, sextant, sextile,
sextuple, siesta, Sistine. In French: setier, sexagénaire,
sextuor, sizain. In Italian: sciamito [< Greek (he)xámiton],
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