Difference between revisions of "Ten"
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==Etymology== | ==Etymology== | ||
[https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [https://nordan.daynal.org/wiki/index.php?title=English#ca._600-1100.09THE_OLD_ENGLISH.2C_OR_ANGLO-SAXON_PERIOD Old English] tīene, from tīen, adjective, ten; akin to Old High German zehan ten, [[Latin]] decem, [[Greek]] deka | [https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English], from [https://nordan.daynal.org/wiki/index.php?title=English#ca._600-1100.09THE_OLD_ENGLISH.2C_OR_ANGLO-SAXON_PERIOD Old English] tīene, from tīen, adjective, ten; akin to Old High German zehan ten, [[Latin]] decem, [[Greek]] deka | ||
| − | *Date: before [ | + | *Date: before [https://www.wikipedia.org/wiki/12th_Century 12th century] |
==Definitions== | ==Definitions== | ||
*1 : the 10th in a set or [[series]] <wears a ten> | *1 : the 10th in a set or [[series]] <wears a ten> | ||
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*4 : one deserving the highest rating; specifically : an exceptionally [[attractive]] [[person]] | *4 : one deserving the highest rating; specifically : an exceptionally [[attractive]] [[person]] | ||
==Description== | ==Description== | ||
| − | 10 (ten) is an even [ | + | 10 (ten) is an even [https://en.wikipedia.org/wiki/Natural_number natural number] following 9 and preceding 11. |
==In mathematics== | ==In mathematics== | ||
| − | '''Ten''' is a [ | + | '''Ten''' is a [https://en.wikipedia.org/wiki/Composite_number composite number], its proper divisors being 1, 2 and 5. Ten is the smallest [https://en.wikipedia.org/wiki/Noncototient noncototient], a [[number]] that cannot be [[expressed]] as the [[difference]] between any integer and the total number of [https://en.wikipedia.org/wiki/Coprime coprimes] below it. |
| − | Ten is the second discrete [ | + | Ten is the second discrete [https://en.wikipedia.org/wiki/Semiprime semiprime] (2.5) and the second member of the (2.q) discrete semiprime family. Ten has an [https://en.wikipedia.org/wiki/Aliquot_sum aliquot sum] σ(n) of 8 and is accordingly the first discrete semiprime to be in deficit. All subsequent discrete semiprimes are in deficit. The [https://en.wikipedia.org/wiki/Aliquot_sequence aliquot sequence] for 10 comprises five members (10,8,7,1,0) with this [[number]] being the second composite member of the 7-aliquot tree. |
| − | It is the [ | + | It is the [https://en.wikipedia.org/wiki/Aliquot_sequence aliquot sum] of only one [[number]] the discrete semiprime 14. |
| − | Ten is a [ | + | Ten is a [https://en.wikipedia.org/wiki/Semi-meandric_number semi-meandric number]. |
| − | Ten is the sum of the first [[three]] [ | + | Ten is the sum of the first [[three]] [https://en.wikipedia.org/wiki/Prime_number prime numbers], of the four first numbers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four [https://en.wikipedia.org/wiki/Factorial factorials] (0! + 1! + 2! + 3!). Ten is the eighth [https://en.wikipedia.org/wiki/Perrin_number Perrin number], preceded in the sequence by 5, 5, 7. |
| − | A polygon with ten sides is a [ | + | A polygon with ten sides is a [https://en.wikipedia.org/wiki/Decagon decagon], and 10 is a decagonal number. But it is also a [https://en.wikipedia.org/wiki/Triangular_number triangular number] and a [https://en.wikipedia.org/wiki/Centered_triangular_number centered triangular number]. |
| − | Ten is the number of [ | + | Ten is the number of [https://en.wikipedia.org/wiki/Eight_queens_puzzle n-Queens Problem] solutions for n = 5. |
==In numeral systems== | ==In numeral systems== | ||
| − | Ten is the base of the [[decimal]] [ | + | Ten is the base of the [[decimal]] [https://en.wikipedia.org/wiki/Numeral_system numeral system], by far the most common [[system]] of denoting [[numbers]] in both [[spoken]] and [[written]] [[language]]. Ten is the first two-digit [[number]] in [[decimal]] and thus the lowest number where the position of a numeral affects its [[value]]. Any integer written in the decimal system can be multiplied by ten by adding a zero to the end (e.g. 855 * 10 = 8550). The [[reason]] for the [[choice]] of ten is [[assumed]] to be that humans have ten fingers (digits). |
The digit '1' followed by '0' is how the value of p is written in base p. (E.g. 16 in hexadecimal is 10.) | The digit '1' followed by '0' is how the value of p is written in base p. (E.g. 16 in hexadecimal is 10.) | ||
| − | The [ | + | The [https://en.wikipedia.org/wiki/Roman_numeral Roman numeral] for ten is X (which looks like two V's [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed). The [https://en.wikipedia.org/wiki/Chinese_numeral Chinese word numeral] for ten is 十, which resembles a cross. |
==See also== | ==See also== | ||
| − | *[ | + | *[https://powersof10.com/index.php?mod=register_film Powers of Ten film] |
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Latest revision as of 02:32, 13 December 2020
Etymology
Middle English, from Old English tīene, from tīen, adjective, ten; akin to Old High German zehan ten, Latin decem, Greek deka
- Date: before 12th century
Definitions
- 1 : the 10th in a set or series <wears a ten>
- 2 : something having 10 units or members
- 3 : a 10-dollar bill
- 4 : one deserving the highest rating; specifically : an exceptionally attractive person
Description
10 (ten) is an even natural number following 9 and preceding 11.
In mathematics
Ten is a composite number, its proper divisors being 1, 2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.
Ten is the second discrete semiprime (2.5) and the second member of the (2.q) discrete semiprime family. Ten has an aliquot sum σ(n) of 8 and is accordingly the first discrete semiprime to be in deficit. All subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members (10,8,7,1,0) with this number being the second composite member of the 7-aliquot tree.
It is the aliquot sum of only one number the discrete semiprime 14.
Ten is a semi-meandric number.
Ten is the sum of the first three prime numbers, of the four first numbers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four factorials (0! + 1! + 2! + 3!). Ten is the eighth Perrin number, preceded in the sequence by 5, 5, 7.
A polygon with ten sides is a decagon, and 10 is a decagonal number. But it is also a triangular number and a centered triangular number.
Ten is the number of n-Queens Problem solutions for n = 5.
In numeral systems
Ten is the base of the decimal numeral system, by far the most common system of denoting numbers in both spoken and written language. Ten is the first two-digit number in decimal and thus the lowest number where the position of a numeral affects its value. Any integer written in the decimal system can be multiplied by ten by adding a zero to the end (e.g. 855 * 10 = 8550). The reason for the choice of ten is assumed to be that humans have ten fingers (digits).
The digit '1' followed by '0' is how the value of p is written in base p. (E.g. 16 in hexadecimal is 10.)
The Roman numeral for ten is X (which looks like two V's [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed). The Chinese word numeral for ten is 十, which resembles a cross.
