147 (number): Difference between revisions
Content deleted Content added
→In mathematics: ref Tag: Reverted |
Undid revision 1260618986 by 107.220.56.248 (talk) |
||
| (5 intermediate revisions by 5 users not shown) | |||
| Line 7: | Line 7: | ||
==In mathematics== |
==In mathematics== |
||
147 is the fourth [[centered icosahedral number]]. |
147 is the fourth [[centered icosahedral number]]. These are a class of [[figurate number]]s that represent points in the shape of a [[regular icosahedron]] or alternatively points in the shape of a [[cuboctahedron]], and are [[Magic number (chemistry)|magic numbers]] for the [[face-centered cubic lattice]].<ref>{{cite OEIS|A005902|Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice}}</ref> Separately, it is also a magic number for the [[diamond cubic]].<ref>{{cite OEIS|A007904|Crystal ball sequence for diamond}}</ref> |
||
It is also the fourth Apéry number <math>a_3</math> following [[19 (number)|19]], where<ref>{{cite OEIS|A005258|Apéry numbers}}</ref> <math display=block>a_n=\sum_{k=0}^n\binom{n}{k}^2\binom{n+k}{k},</math> |
It is also the fourth Apéry number <math>a_3</math> following [[19 (number)|19]], where<ref>{{cite OEIS|A005258|Apéry numbers}}</ref> <math display=block>a_n=\sum_{k=0}^n\binom{n}{k}^2\binom{n+k}{k},</math> |
||
| Line 16: | Line 16: | ||
==In other fields== |
==In other fields== |
||
147 is the [[Maximum break|highest possible break]] in [[snooker]], in the absence of fouls and refereeing errors.<ref>{{cite encyclopedia | last1 = Hill | first1 = Andrew P. | last2 = Mallinson-Howard | first2 = Sarah H. | last3 = Madigan | first3 = Daniel J. | last4 = Jowett | first4 = Gareth E. | editor1-last = Tenenbaum | editor1-first = Gershon | editor2-last = Eklund | editor2-first = Robert C. | contribution = Perfectionism in Sport, Dance, and Exercise | doi = 10.1002/9781119568124.ch7 | edition = 4th | pages = 121–157 | publisher = Wiley | title = Handbook of Sport Psychology | year = 2020| s2cid = 150348844 | url = http://ray.yorksj.ac.uk/id/eprint/1758/1/Routledge%20BC%2011%20-%20Hill%20-%20Accepted%20Version%20%28J%20Stoeber%2014%20Oct%2016%29.pdf }}</ref> |
147 is the [[Maximum break|highest possible break]] in [[snooker]], in the absence of fouls and refereeing errors.<ref>{{cite encyclopedia | last1 = Hill | first1 = Andrew P. | last2 = Mallinson-Howard | first2 = Sarah H. | last3 = Madigan | first3 = Daniel J. | last4 = Jowett | first4 = Gareth E. | editor1-last = Tenenbaum | editor1-first = Gershon | editor2-last = Eklund | editor2-first = Robert C. | contribution = Perfectionism in Sport, Dance, and Exercise | doi = 10.1002/9781119568124.ch7 | edition = 4th | pages = 121–157 | publisher = Wiley | title = Handbook of Sport Psychology | year = 2020| isbn = 978-1-119-56807-0 | s2cid = 150348844 | url = http://ray.yorksj.ac.uk/id/eprint/1758/1/Routledge%20BC%2011%20-%20Hill%20-%20Accepted%20Version%20%28J%20Stoeber%2014%20Oct%2016%29.pdf }}</ref> |
||
In some traditions, there are 147 [[psalms]]. However, current Christian and Jewish traditions list a larger number, leading to the suggestion that some of the psalms in the earlier numbering were split into multiple pieces.<ref>{{cite journal | last = Rabinowitz | first = L. | date = April 1936 | doi = 10.2307/1452095 | issue = 4 | journal = The Jewish Quarterly Review | jstor = 1452095 | pages = 349–368 | title = Does Midrash Tillim Reflect the Triennial Cycle of Psalms? | volume = 26}}</ref><ref>{{cite journal | last = Yarchin | first = William | date = July 2015 | issue = 3 | journal = Revue Biblique | jstor = 44092352 | pages = 355–370 | title = Is There an Authoritative Shape for the Hebrew Book Of Psalms? Profiling the Manuscripts of the Hebrew Psalter | volume = 122}}</ref> |
In some traditions, there are 147 [[psalms]]. However, current Christian and Jewish traditions list a larger number, leading to the suggestion that some of the psalms in the earlier numbering were split into multiple pieces.<ref>{{cite journal | last = Rabinowitz | first = L. | date = April 1936 | doi = 10.2307/1452095 | issue = 4 | journal = The Jewish Quarterly Review | jstor = 1452095 | pages = 349–368 | title = Does Midrash Tillim Reflect the Triennial Cycle of Psalms? | volume = 26}}</ref><ref>{{cite journal | last = Yarchin | first = William | date = July 2015 | issue = 3 | journal = Revue Biblique | jstor = 44092352 | pages = 355–370 | title = Is There an Authoritative Shape for the Hebrew Book Of Psalms? Profiling the Manuscripts of the Hebrew Psalter | volume = 122}}</ref> |
||
Latest revision as of 20:02, 1 December 2024
| ||||
|---|---|---|---|---|
| Cardinal | one hundred forty-seven | |||
| Ordinal | 147th (one hundred forty-seventh) | |||
| Factorization | 3 × 72 | |||
| Divisors | 1, 3, 7, 21, 49, 147 | |||
| Greek numeral | ΡΜΖ´ | |||
| Roman numeral | CXLVII | |||
| Binary | 100100112 | |||
| Ternary | 121103 | |||
| Senary | 4036 | |||
| Octal | 2238 | |||
| Duodecimal | 10312 | |||
| Hexadecimal | 9316 | |||
147 (one hundred [and] forty-seven) is the natural number following 146 and preceding 148.
In mathematics
[edit]147 is the fourth centered icosahedral number. These are a class of figurate numbers that represent points in the shape of a regular icosahedron or alternatively points in the shape of a cuboctahedron, and are magic numbers for the face-centered cubic lattice.[1] Separately, it is also a magic number for the diamond cubic.[2]
It is also the fourth Apéry number following 19, where[3]
with 147 the composite index of the nineteenth triangle number, 190.[4][5]
There are 147 different ways of representing one as a sum of unit fractions with five terms, allowing repeated fractions,[6] and 147 different self-avoiding polygonal chains of length six using horizontal and vertical segments of the integer lattice.[7]
In other fields
[edit]147 is the highest possible break in snooker, in the absence of fouls and refereeing errors.[8]
In some traditions, there are 147 psalms. However, current Christian and Jewish traditions list a larger number, leading to the suggestion that some of the psalms in the earlier numbering were split into multiple pieces.[9][10]
147 is the telephonic number of the 27 Brazilian Civil Police forces.
See also
[edit]References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A005902 (Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007904 (Crystal ball sequence for diamond)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005258 (Apéry numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-29.
- ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular number: a(n) is the binomial(n+1,2) equivalent to n*(n+1)/2 that is 0 + 1 + 2 + ... + n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-29.
- ^ Sloane, N. J. A. (ed.). "Sequence A002966 (Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n where 0 < x_1 ≤ ... ≤ x_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A037245 (Number of unrooted self-avoiding walks of n steps on square lattice)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Hill, Andrew P.; Mallinson-Howard, Sarah H.; Madigan, Daniel J.; Jowett, Gareth E. (2020). "Perfectionism in Sport, Dance, and Exercise". In Tenenbaum, Gershon; Eklund, Robert C. (eds.). Handbook of Sport Psychology (PDF) (4th ed.). Wiley. pp. 121–157. doi:10.1002/9781119568124.ch7. ISBN 978-1-119-56807-0. S2CID 150348844.
- ^ Rabinowitz, L. (April 1936). "Does Midrash Tillim Reflect the Triennial Cycle of Psalms?". The Jewish Quarterly Review. 26 (4): 349–368. doi:10.2307/1452095. JSTOR 1452095.
- ^ Yarchin, William (July 2015). "Is There an Authoritative Shape for the Hebrew Book Of Psalms? Profiling the Manuscripts of the Hebrew Psalter". Revue Biblique. 122 (3): 355–370. JSTOR 44092352.