72 (number)

← 71 72 73 →
→
Cardinal	seventy-two
Ordinal	72nd (seventy-second)
Factorization	23 × 32
Divisors	1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Greek numeral	ΟΒ´
Roman numeral	LXXII
Binary	10010002
Ternary	22003
Senary	2006
Octal	1108
Duodecimal	6012
Hexadecimal	4816

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen (i.e., 60 in duodecimal).

In mathematics

Seventy-two is a pronic number, as it is the product of 8 and 9.^[1] It is the smallest Achilles number, as it's a powerful number that is not itself a power.^[2]

72 is an

72 plays a role in the Rule of 72 in economics when approximating annual compounding of interest rates of a round 6% to 10%, due in part to its high number of divisors.

Inside ${\displaystyle \mathrm {E} _{n}}$ Lie algebras:

• 72 is the number of
  root vectors of the simple Lie group
  ${\displaystyle \mathrm {E} _{6}}$, which as a honeycomb under 2₂₂ forms the ${\displaystyle \mathrm {E} _{6}}$ lattice. 1₂₂ is part of a family of
  symmetry order 72 and made of six triangular prisms. On the other hand, 3₂₁ ∈ k₂₁ is the only semiregular polytope in the seventh dimension, also featuring a total of 702 6-faces of which 576 are 6-simplexes and 126 are 6-orthoplexes that contain 60 edges and 12 vertices, or collectively 72 one-dimensional and two-dimensional elements; with 126
  the number of root vectors in ${\displaystyle \mathrm {E} _{7}}$, which are contained in the vertices of
  cells
  .
• The complex Hessian polyhedron in ${\displaystyle \mathbb {C} ^{3}}$ contains 72 regular complex triangular edges, as well as 27 polygonal Möbius–Kantor faces and 27 vertices. It is notable for being the vertex figure of the complex Witting polytope, which shares 240 vertices with the eight-dimensional semiregular 4₂₁ polytope whose vertices in turn represent the root vectors of the simple Lie group ${\displaystyle \mathrm {E} _{8}}$.

There are 72

, of which the most important is ${\displaystyle {\tilde {T}}_{9}}$: it contains the final semiregular hyperbolic honeycomb 6₂₁ made of only regular facets and the 5₂₁ Euclidean honeycomb as its vertex figure, which is the geometric representation of the ${\displaystyle \mathrm {E} _{8}}$ lattice. Furthermore, ${\displaystyle {\tilde {T}}_{9}}$ shares the same fundamental symmetries with the Coxeter-Dynkin over-extended form ${\displaystyle \mathrm {E} _{8}}$⁺⁺ equivalent to the tenth-dimensional symmetries of Lie algebra ${\displaystyle \mathrm {E} _{10}}$.

72 lies between the 8th pair of twin primes (71, 73), where 71 is the largest supersingular prime that is a factor of the largest sporadic group (the friendly giant ${\displaystyle \mathbb {F_{1}} }$), and 73 the largest

of ${\displaystyle \mathbb {F_{1}} }$.

finite simple groups

, where ${\displaystyle \mathrm {E} _{6}}$, ${\displaystyle \mathrm {E} _{7}}$, and ${\displaystyle \mathrm {E} _{8}}$ are associated exceptional groups that are part of sixteen finite Lie groups that are also simple, or non-trivial groups whose only normal subgroups are the trivial group and the groups themselves.^[b]

In science

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• The atomic number of hafnium
• In degrees Fahrenheit considered to be room temperature.^{[citation needed]}

In astronomy

• magnitude 10.0 globular cluster in the constellation Aquarius
  .
• The New General Catalogue object NGC 72, a magnitude 13.5 barred spiral galaxy in the constellation Andromeda.
• The
  precession of equinoxes
  traces out a pair of cones joined at their apices in a cycle of approximately 26,000 years, that is 1 degree every 72 years (approximation to the nearmost integer).

In religion

• The number of languages spoken at the
  Tower of Babylon
  , according to later tradition.
• The conventional number of scholars translating the
  Letter of Aristeas
  ".
• The number of companions of Zoroaster who were killed^[24]
• The conventional number of
  disciples sent forth
  by Jesus in Luke 10 in some manuscripts (seventy in others).
• The number of names of God, according to Kabbalah (see names of God in Judaism).
• The
  Shemhamphorasch
  related to the number of the names of God.
• The total number of books in the
  Catholic
  version if the Book of Lamentations is considered part of the Book of Jeremiah.
• The current distribution of the Book of Revelation is 22 chapters, adopted since the 13th century, but the oldest known division of the text is that of the Greek commentator Andrew of Cesary (6th century) in 72 chapters.
• The number of people killed along with
  Imam Hussain at the Battle of Karbala
  .
• The degrees of the Jacob's Ladder were to the number of 72, according to the Zohar.
• The 72 disciples of Confucius who mastered his teachings (also given as 77).
• Mahavira, the twenty-fourth and last tirthankara of Jainism, is said to have attained nirvana after his physical death at the age of 72.
• Thoth, in an Egyptian creation myth, wins a 72nd of each day of the year from the Moon in a game of draughts, as a favour to Nut, the Sky Goddess. He uses these portions to make the five intercalary days on which the remaining Gods and Goddesses are born.^[25][26][27]
• The god
  Set.^[28]
• At the age of the puberty, the young Parsee received the investiture of the sacred cord Kucti made of 72 linens in symbol of the community.
• In
  Cao Đài
  , the number of planets between hell and heaven.
• There are 72
  stupas which comprise Borobudur
  , the world's largest Buddhist temple.
• 72 major temples have been found at Angkor, seat of the ancient Khmer Empire.
• In Islam, 72 is the number of sects or denominations that are doomed to Hell, according to Hadith (sayings of Muhammad).^[29][30]
• The number of demons sealed away by King Solomon with The Lesser Key of Solomon.
• In Islam 72 is the number of beautiful wives that are promised to martyrs in paradise, according to Hadith (sayings of Muhammad).^[31][32]

In other fields

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Seventy-two is also:

• In
  Apple Macintosh
  screen.
• In typography, a point is 1/72 inch.
• The number of the French department Sarthe.
• The registry of the U.S. Navy's nuclear aircraft carrier USS Abraham Lincoln (CVN-72), named after U.S. President Abraham Lincoln.
• The designation of the Soviet T-72 tank.
• The Rule of 72 in finance.
• Book: 72 Hour Hold by Bebe Moore Campbell
• CD: Seventy Two & Sunny by Uncle Kracker
• Jill Clayburgh and LeVar Burton starred in Firestorm: 72 Hours in Oakland (1993)
• Alternative music band The Delta 72
• The Persian classical
  santur
  , a hammered dulcimer, has 72 strings in 24 triple-stringed courses.
• The Turin Brakes song, also known as Emergency 72
• The number of members in National
  Senate of Argentina
  .
• A Civil Air Patrol unit in Laramie, WY, RMR-WY-072.
• There are 72 demons and other spirits in the
  goetia The Lesser Key of Solomon
  .
• A common limit for characters per line in computing
• 72 equal temperament is a tuning used in Byzantine music and by some modern composers.
• The number of microseasons in the traditional Japanese calendar^[33]

In sports and games

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• The usual par for an 18-hole golf course, especially those in tournament play.
• The number of spaces in a game of Parcheesi, from start space to "home".

Notes

References

1. ^ Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
2. ^ Sloane, N. J. A. (ed.). "Sequence A052486 (Achilles numbers - powerful but imperfect.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
3. ^ Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
4. ^ Sloane, N. J. A. (ed.). "Sequence A081357 (Sublime numbers, numbers for which the number of divisors and the sum of the divisors are both perfect.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
5. ^ Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.

   The sequence of refactorable numbers goes: 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96, ...

6. ^ Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
7. ^ ^{a b} Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
8. ^ Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
9. ^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
10. ^ Sloane, N. J. A. (ed.). "Sequence A034963 (Sums of four consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-02.
11. ^ Sloane, N. J. A. (ed.). "Sequence A127333 (Numbers that are the sum of 6 consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-02.
12. ^ Sloane, N. J. A. (ed.). "Sequence A090788 (Numbers that can be expressed as the difference of the squares of primes in just two distinct ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-03.
13. ^ Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-13.
14. ^ Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-13.
15. ^ Sloane, N. J. A. (ed.). "Sequence A033880 (Abundance of n, or (sum of divisors of n) - 2n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-13.
16. S2CID 235037714
    .
17. ^ Sloane, N. J. A. (ed.). "Sequence A007450 (Decimal expansion of 1/17.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-24.
18. ^ Sloane, N. J. A. (ed.). "Sequence A005179 (Smallest number with exactly n divisors.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-11.
19. ^ Sloane, N. J. A. (ed.). "Sequence A200720 (Number of distinct normal magic stars of type {n/2}.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-09.
20. ^ Sloane, N. J. A. (ed.). "Sequence A005418 (...row sums of Losanitsch's triangle.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
21. ^ David Wells: The Penguin Dictionary of Curious and Interesting Numbers
22. ^ Sloane, N. J. A. (ed.). "Sequence A154363 (Numbers from Bhargava's prime-universality criterion theorem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

    {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 67, 73}

23. arXiv:1505.06742 [math.AG
    ].
24. ^ "صدویک نام خداوند چیست؟" (in Persian). Amordad. 22 May 2018. Retrieved 8 January 2023.
25. ISBN 0-292-72076-9
    .
26. ISBN 9780292720763
    .
27. ^ Plutarch. Isis and Osiris. Loeb Classics. pp. LCL 306: 30–31.
28. ^ "Egyptian Myths", George Hart, p41, University of Texas Press, 1990
29. ^ "Sects In Islam - 73 Groups in Islam, Division - Denominations". Archived from the original on 6 May 2013. Retrieved 24 March 2013.
30. ^ Sunan Ibn Maajah, no. 3982 "My Ummah will be divided into seventy-three sects, one of which will be in Paradise and seventy-two will be in the Fire"
31. ^ Jami`at-Tirmidhi. "The Book on Virtues of Jihad, Vol. 3, Book 20, Hadith 1663". Sunnah.com - Sayings and Teachings of Prophet Muhammad (صلى الله عليه و سلم). Retrieved 2024-04-02.
32. ISSN 0162-895X
    .
33. ^ "Japan's 72 Microseasons". 16 October 2015.

External links

• Go Figure: What can 72 tell us about life, BBC News, 20 July 2011