Natural number
20 (twenty ; Roman numeral XX) is the
natural number following
19 and preceding
21 .
A group of twenty units may be referred to as a score .
[1]
[2]
Mathematics
Integer properties
Twenty is a
pronic number , as it is the product of consecutive integers, namely 4 and 5.
[3] It is the third
composite number to be the product of a
squared prime and a
prime (and also the second member of the 2 2 × q family in this form). It has an
aliquot sum of
22 ; a
semiprime , within an
aliquot sequence of four
composite numbers (20, 22,
14 ,
10 ,
8 ) that belong to the prime
7 -aliquot tree. It is the smallest
primitive abundant number ,
[4] and the first number to have an
abundance of
2 , followed by
104 .
[5] 20 is the length of a
side of the fifth smallest
right triangle that forms a
primitive Pythagorean triple (20,
21 ,
29 ).
[6]
[a] It is the third
tetrahedral number .
[7]
In
decimal , 20 is the smallest non-trivial neon number equal to the sum of its digits when raised to the thirteenth power (2013 =
8192 × 1013 ).[
citation needed ]
Almost integers
Gelfond's constant and
pi
very nearly have a difference equal to twenty:
e
π
−
π
≈
20
{\displaystyle e^{\pi }-\pi \;\approx \;20}
differing only by about
−
0.000900020811
…
{\displaystyle -0.000900020811\ldots }
from an
integer value.
[8]
[9]
Geometric properties
Tessellations
There are twenty edge-to-edge
2-uniform tilings by convex regular polygons, which are uniform tessellations of the plane containing 2
orbits of
vertices .
[10]
[11] 20 is the number of
parallelogram
polyominoes with 5 cells.
[12]
Bring's curve is a
Riemann surface of
genus four, whose
fundamental polygon is a regular hyperbolic twenty-sided
icosagon , with an area equal to
12
π
{\displaystyle 12\pi }
by the
Gauss-Bonnet theorem .
[13]
Polyhedra
An
icosahedron has twenty triangular
faces .
The largest number of faces a
Platonic solid can have is twenty faces, which make up a regular
icosahedron .
[14] A
dodecahedron , on the other hand, has twenty vertices, likewise the most a regular polyhedron can have.
[15] There are a total of 20
regular and
semiregular polyhedra, aside from the infinite family of semiregular
prisms and
antiprisms that exists in the third dimension: the 5 Platonic solids, and 15
Archimedean solids (including
chiral forms of the
snub cube and
snub dodecahedron ). There are also four
uniform compound polyhedra that contain twenty polyhedra (
UC13 ,
UC14 ,
UC19 ,
UC33 ), which is the most any such solids can have; while another twenty uniform compounds contain five polyhedra (that are not part of classes of infinite families, where there exist three more). The
compound of twenty octahedra can be obtained by orienting two pairs of
compounds of ten octahedra , which can also coincide to yield a regular
compound of five octahedra .
Higher-dimensional polytopes
In total, there are 20
semiregular polytopes that only exist up through the 8th dimension, which include 13 Archimedean solids and 7
Gosset polytopes (without counting
enantiomorphs , or semiregular prisms and antiprisms).
Abstract algebra
The
Happy Family of
sporadic groups is made up of twenty
finite simple groups that are all
subquotients of the
friendly giant , the largest of twenty-six sporadic groups. The largest
supersingular prime factor that divides the order of the friendly giant is
71 , which is the 20th
indexed prime number, where 26 also represents the number of
partitions of 20 into prime parts.
[16] Both 71 and 20 represent
self-convolved Fibonacci numbers, respectively the seventh and fifth members
j
{\displaystyle j}
in this sequence
F
j
2
{\displaystyle F_{j}^{2}}
.
[17]
[18]
Rubik's cube
20 is the number of moves (quarter or half turns) required to optimally solve a
Rubik's Cube in the worst case.
[19]
[20]
Other fields
Science
20 is the third
magic number in physics. In
chemistry , it is the
atomic number of
calcium .
Biology
The number of
proteinogenic
amino acids that are encoded by the standard genetic code
In many disciplines of
developmental psychology , adulthood starts at age 20.
[21]
In some countries, the number 20 is used as an index in measuring
visual acuity . 20/20 indicates normal vision at 20 feet, although it is commonly used to mean "perfect vision" in countries using the
Imperial system. (The metric equivalent is 6/6.) When someone is able to see only after an event how things turned out, that person is often said to have had "20/20 hindsight"
[22]
Sports
A standard
dartboard is laid out as 20
sectors .
Culture
Age 20
Formerly the
age of majority in Japan and in Japanese tradition.
[26]
Number systems
20 is the basis for
vigesimal number systems, used by several different civilizations in the past (and to this day), including the
Maya .
[27]
Board games
In
chess , 20 is the number of legal moves for each player in the starting position.
[28]
Indefinite number
A 'score' is a group of 20 (often used in combination with a
cardinal number , e.g. fourscore to mean 80),
[29] but also often used as an
indefinite number
[30] (e.g. the newspaper headline "Scores of Typhoon Survivors Flown to Manila").
[31]
References
^ This is the second Pythagorean triple
(
a
,
b
,
c
)
{\displaystyle (a,b,c)}
that can be formed using
Pell numbers where
a
{\displaystyle a}
and
b
{\displaystyle b}
are
one unit apart. The first such triple is the smallest Pythagorean triple, (4,3,5). These can be formed using Pell numbers that yield a Pythagorean triple of the form
(
2
P
n
P
n
+
1
,
P
n
+
1
2
−
P
n
2
,
P
n
+
1
2
+
P
n
2
=
P
2
n
+
1
)
{\displaystyle \left(2P_{n}P_{n+1},P_{n+1}^{2}-P_{n}^{2},P_{n+1}^{2}+P_{n}^{2}=P_{2n+1}\right)}
.
^ John H. Conway and Richard K. Guy, The Book of Numbers . New York: Copernicus (1996): 11. ""Score" is related to "share" and comes from the Old Norse "skor" meaning a "notch" or "tally" on a stick used for counting. ... Often people counted in 20s; every 20th notch was larger,
so "score" also came to mean 20."
^
"score | Origin and meaning of score by Online Etymology Dictionary" . www.etymonline.com . Retrieved 2020-08-16 .
^
"Sloane's A002378: Pronic numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2020-11-30 .
^
"Sloane's A071395 : Primitive abundant numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-31 .
^
Sloane, N. J. A. (ed.).
"Sequence A088831 (Numbers k whose abundance is 2: sigma(k) - 2k is 2.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-23 .
^
Sloane, N. J. A. (ed.).
"Sequence A103606 (Primitive Pythagorean triples in nondecreasing order of perimeter, with each triple in increasing order, and if perimeters coincide then increasing order of the even members.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-07-06 .
^
"Sloane's A000292 : Tetrahedral numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-31 .
^ Maze, Gérard; Minder, Lorenz (2007).
"A new family of almost identities" .
Elemente der Mathematik . 62 (3). Hensinki:
European Mathematical Society : 90.
arXiv :
math/0409014 .
doi :
10.4171/EM/61 .
MR
2350250 .
S2CID
56024534 .
Zbl
1213.40002 .
^
Sloane, N. J. A. (ed.).
"Sequence A018938 (Decimal expansion of e^Pi - Pi.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-12-09 .
^ Grünbaum, Branko; Shephard, Geoffrey C. (1977).
"Tilings by regular polygons" (PDF) .
Mathematics Magazine . 50 (5): 235.
doi :
10.2307/2689529 .
JSTOR
2689529 .
S2CID
123776612 .
Zbl
0385.51006 .
^
Sloane, N. J. A. (ed.).
"Sequence A068599 (Number of n-uniform tilings.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-01-07 .
^
Sloane, N. J. A. (ed.).
"Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Weber, Matthias (2005).
"Kepler's small stellated dodecahedron as a Riemann surface" (PDF) .
Pacific Journal of Mathematics . 220 (1): 172.
doi :
10.2140/pjm.2005.220.167 .
MR
2195068 .
S2CID
54518859 .
Zbl
1100.30036 .
^ Weisstein, Eric W.
"Icosahedron" . mathworld.wolfram.com . Retrieved 2020-08-16 .
^ Weisstein, Eric W.
"Dodecahedron" . mathworld.wolfram.com . Retrieved 2020-08-16 .
^
Sloane, N. J. A. (ed.).
"Sequence A000607 (Number of partitions of n into prime parts.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-24 .
^
Sloane, N. J. A. (ed.).
"Sequence A001629 (Self-convolution of Fibonacci numbers.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-07-16 .
^ Moree, Pieter (2004).
"Convoluted Convolved Fibonacci Numbers" (PDF) .
Journal of Integer Sequences . 7 (2). Waterloo, Ont., CA:
University of Waterloo
David R. Cheriton School of Computer Science : 13 (Article 04.2.2).
arXiv :
math.CO/0311205 .
Bibcode :
2004JIntS...7...22M .
MR
2084694 .
S2CID
14126332 .
Zbl
1069.11004 .
^
"God's Number is 20" . Cube20.org
^ Jonathan Fildes (August 11, 2010).
"Rubik's Cube quest for speedy solution comes to an end" .
BBC News .
^
"Adulthood | Introduction to Psychology" . lumenlearning.com .
^
"Definition of 20/20" . www.merriam-webster.com . Retrieved 2020-08-16 .
^ Draper, Nick (2014-12-05).
Exercise Physiology: For Health and Sports Performance . Routledge. p. 404.
ISBN
978-1-317-90260-7 . played over four 20 min quarters
^
"International Ice Hockey Federation - Olympic Sport" . International Olympic Committee . 9 November 2020. Retrieved 22 January 2021 .
^ Ziemba, William T. (2017-08-23).
The Adventures Of A Modern Renaissance Academic In Investing And Gambling . World Scientific. p. 352.
ISBN
978-981-314-853-6 . It has always been for a long time a maximum of 20 horses ...
^
"Japan's Age of Majority Changed to 18 - Living the Japon.com" . www.japan-experience.com . Retrieved 19 March 2018 .
^ Weisstein, Eric W.
"Vigesimal" . mathworld.wolfram.com . Retrieved 2020-08-16 .
^ Jordan, Bill.
Opening Moves Made Easy: A new way to learn how to play Chess openings . Bill Jordan. there are 20 legal moves for White and 20 legal replies for Black
^
"Definition of SCORE" . www.merriam-webster.com . Retrieved 2020-08-16 .
^ "Biblical Criticism", The Classical Journal 36 :71:83ff (March 1827)
full text
^ "CBS News",
Scores of Typhoon Survivors Flown to Manila (November 2013)
External links
Look up
twenty in Wiktionary, the free dictionary.
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