17 (number)
(Redirected from XVII)
| ||||
|---|---|---|---|---|
| Cardinal | seventeen | |||
| Ordinal | 17th (seventeenth) | |||
| Numeral system | septendecimal | |||
| Factorization | prime | |||
| Prime | 7th | |||
| Divisors | 1, 17 | |||
| Greek numeral | ΙΖ´ | |||
| Roman numeral | XVII | |||
| Binary | 100012 | |||
| Ternary | 1223 | |||
| Senary | 256 | |||
| Octal | 218 | |||
| Duodecimal | 1512 | |||
| Hexadecimal | 1116 | |||
| Hebrew numeral | י"ז | |||
| Babylonian numeral | 𒌋𒐛 | |||
17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. 17 was described at MIT as "the least random number", according to the Jargon File.[1][a]
Mathematics
[edit]- 17 forms a twin prime with 19,[3] a cousin prime with 13,[4] and a sexy prime with both 11 and 23.[5]
- 17 is one of six lucky numbers of Euler, the positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k2 − k + n produces a prime number.[6]
- The number of integer partitions of 17 into prime parts is 17. It is the only natural number with this property.[7]
- As seventeen is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler. A proof by Carl Friedrich Gauss ultimately led him to choose mathematics over philology for his studies.[8][9]
- There are seventeen crystallographic space groups in two dimensions.[10] These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.
- Seventeen is the number of combinations of regular polygons that completely fill a plane vertex.[11] Eleven of these belong to regular and semiregular tilings, while 6 of these (3.7.42,[12] 3.8.24,[13] 3.9.18,[14] 3.10.15,[15] 4.5.20,[16] and 5.5.10)[17] exclusively surround a point in the plane and fill it only when irregular polygons are included.[18]
- 17 is the smallest for the Theodorus Spiral to complete one revolution.[19]
- 17 is the longest sequence for which a solution exists in the irregularity of distributions problem.[20]
- The minimum possible number of givens for a sudoku puzzle with a unique solution is 17.[21][22]
In science
[edit]
Physics
[edit]Seventeen is the number of elementary particles with unique names in the Standard Model of physics.[23]
Chemistry
[edit]Group 17 of the periodic table is called the halogens. The atomic number of chlorine is 17.
Biology
[edit]Some species of cicadas have a life cycle of 17 years (i.e. they are buried in the ground for 17 years between every mating season).
In religion
[edit]- In the Yasna of Zoroastrianism, seventeen chapters were written by Zoroaster himself. These are the five Gathas.
- The number of surat al-Isra in the Qur'an is seventeen, at times included as one of seven Al-Musabbihat. 17 is the total number of Rak'as that Muslims perform during Salat on a daily basis.
Other fields
[edit]Seventeen is:
- The total number of syllables in a haiku (5 + 7 + 5).
- The maximum number of strokes of a Chinese radical.
Music
[edit]Where Pythagoreans saw 17 in between 16 from its Epogdoon of 18 in distaste,[24] the ratio 18:17 was a popular approximation for the equal tempered semitone (12-tone) during the Renaissance.
Notes
[edit]References
[edit]- ^ "random numbers". catb.org/.
- ^ "The Power of 17". Cosmic Variance. Archived from the original on 2008-12-04. Retrieved 2010-06-14.
- ^ Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
- ^ Sloane, N. J. A. (ed.). "Sequence A046132 (Larger member p+4 of cousin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
- ^ Sloane, N. J. A. (ed.). "Sequence A023201 (Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
- ^ Sloane, N. J. A. (ed.). "Sequence A014556 (Euler's "Lucky" numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
- ^ 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 2024-02-12.
- ^ John H. Conway and Richard K. Guy, The Book of Numbers. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygons) could be constructed with ruler and compasses."
- ^ Pappas, Theoni, Mathematical Snippets, 2008, p. 42.
- ^ Sloane, N. J. A. (ed.). "Sequence A006227 (Number of n-dimensional space groups (including enantiomorphs))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
- ^ Dallas, Elmslie William (1855), The Elements of Plane Practical Geometry, Etc, John W. Parker & Son, p. 134.
- ^ "Shield - a 3.7.42 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
- ^ "Dancer - a 3.8.24 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
- ^ "Art - a 3.9.18 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
- ^ "Fighters - a 3.10.15 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
- ^ "Compass - a 4.5.20 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
- ^ "Broken roses - three 5.5.10 tilings". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
- ^ "Pentagon-Decagon Packing". American Mathematical Society. AMS. Retrieved 2022-03-07.
- ^ Sloane, N. J. A. (ed.). "Sequence A072895 (Least k for the Theodorus spiral to complete n revolutions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-19.
- ^ Berlekamp, E. R.; Graham, R. L. (1970). "Irregularities in the distributions of finite sequences". Journal of Number Theory. 2 (2): 152–161. Bibcode:1970JNT.....2..152B. doi:10.1016/0022-314X(70)90015-6. MR 0269605.
- ^ McGuire, Gary (2012). "There is no 16-clue sudoku: solving the sudoku minimum number of clues problem". arXiv:1201.0749 [cs.DS].
- ^ McGuire, Gary; Tugemann, Bastian; Civario, Gilles (2014). "There is no 16-clue sudoku: Solving the sudoku minimum number of clues problem via hitting set enumeration". Experimental Mathematics. 23 (2): 190–217. doi:10.1080/10586458.2013.870056. S2CID 8973439.
- ^ Glenn Elert (2021). "The Standard Model". The Physics Hypertextbook.
- ^ Plutarch, Moralia (1936). Isis and Osiris (Part 3 of 5). Loeb Classical Library edition.
- Berlekamp, E. R.; Graham, R. L. (1970). "Irregularities in the distributions of finite sequences". Journal of Number Theory. 2 (2): 152–161. Bibcode:1970JNT.....2..152B. doi:10.1016/0022-314X(70)90015-6. MR 0269605.
External links
[edit]
Wikimedia Commons has media related to 17 (number).
Look up seventeen in Wiktionary, the free dictionary.