Get Our Extension

72 (number)

From Wikipedia, in a visual modern way
← 71 72 73 →
Cardinalseventy-two
Ordinal72nd
(seventy-second)
Factorization23 × 32
Divisors1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Greek numeralΟΒ´
Roman numeralLXXII
Binary10010002
Ternary22003
Senary2006
Octal1108
Duodecimal6012
Hexadecimal4816

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).

Discover more about 72 (number) related topics

In mathematics

Seventy-two is a pronic number, as it is the product of 8 and 9.

72 is an abundant number,[1] with a total of 12 factors, and a Euler totient of 24.[2] 72 is also a highly totient number, as there are 17 solutions to the equation φ(x) = 72, more than any integer below 72.[3] It is equal to the sum the sum of its preceding smaller highly totient numbers 24 and 48, and contains the first six highly totient numbers 1, 2, 4, 8, 12 and 24 as a subset of its proper divisors. 144, or twice 72, is also highly totient, as is 576, the square of 24.[3] While 17 different integers have a totient value of 72, the sum of Euler's totient function φ(x) over the first 15 integers is 72.[4] 72 is also a Harshad number in decimal, as it is divisible by the sum of its digits.[5]

  • 72 is the smallest Achilles number, as it's a powerful number that is not itself a power.[6]
  • 72 is the sum of four consecutive primes (13 + 17 + 19 + 23), as well as the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19).
  • 72 is the smallest number whose fifth power is the sum of five smaller fifth powers: 195 + 435 + 465 + 475 + 675 = 725.[7]

72 is the number of degrees in the central angle of a regular pentagon, which is constructible with a compass and straight-edge.

Inside Lie algebras:

There are 72 compact and paracompact Coxeter groups of ranks four through ten: 14 of these are compact finite representations in only three-dimensional and four-dimensional spaces, with the remaining 58 paracompact or noncompact infinite representations in dimensions three through nine. These terminate with three paracompact groups in the ninth dimension, of which the most important is : 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 lattice. Furthermore, shares the same fundamental symmetries with the Coxeter-Dynkin over-extended form ++ equivalent to the tenth-dimensional symmetries of Lie algebra .

72 lies between the eighth 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, with all primes greater than or equal to 73 non-supersingular. Sporadic groups are a family of twenty-six finite simple groups, with , , and representing 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.

Discover more about In mathematics related topics

8

8

8 (eight) is the natural number following 7 and preceding 9.

9

9

9 (nine) is the natural number following 8 and preceding 10.

Abundant number

Abundant number

In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.

12 (number)

12 (number)

12 (twelve) is the natural number following 11 and preceding 13. Twelve is a superior highly composite number, divisible by 2, 3, 4, and 6.

Highly totient number

Highly totient number

A highly totient number is an integer that has more solutions to the equation , where is Euler's totient function, than any integer below it. The first few highly totient numbers are

Euler's totient function

Euler's totient function

In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as or , and may also be called Euler's phi function. In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. The integers k of this form are sometimes referred to as totatives of n.

Harshad number

Harshad number

In mathematics, a harshad number in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base n are also known as n-harshad numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977.

Decimal

Decimal

The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.

Achilles number

Achilles number

An Achilles number is a number that is powerful but not a perfect power. A positive integer n is a powerful number if, for every prime factor p of n, p2 is also a divisor. In other words, every prime factor appears at least squared in the factorization. All Achilles numbers are powerful. However, not all powerful numbers are Achilles numbers: only those that cannot be represented as mk, where m and k are positive integers greater than 1.

Economics

Economics

Economics is the social science that studies the production, distribution, and consumption of goods and services.

Compound interest

Compound interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Interest rate

Interest rate

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.

In science

In astronomy

Discover more about In science related topics

Atomic number

Atomic number

The atomic number or nuclear charge number of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (np) or the number of protons found in the nucleus of every atom of that element. The atomic number can be used to uniquely identify ordinary chemical elements. In an ordinary uncharged atom, the atomic number is also equal to the number of electrons.

Hafnium

Hafnium

Hafnium is a chemical element with the symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in many zirconium minerals. Its existence was predicted by Dmitri Mendeleev in 1869, though it was not identified until 1923, by Dirk Coster and George de Hevesy, making it the penultimate stable element to be discovered. Hafnium is named after Hafnia, the Latin name for Copenhagen, where it was discovered.

Room temperature

Room temperature

Colloquially, "room temperature" is a range of air temperatures that most people prefer for indoor settings. It feels comfortable to a person when they are wearing typical indoor clothing. Human comfort can extend beyond this range depending on humidity, air circulation and other factors. Food or beverages may be served at room temperature, meaning neither heated nor cooled.

Messier object

Messier object

The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his Catalogue des Nébuleuses et des Amas d'Étoiles. Because Messier was only interested in finding comets, he created a list of those non-comet objects that frustrated his hunt for them. The compilation of this list, in collaboration with his assistant Pierre Méchain, is known as the Messier catalogue. This catalogue of objects is one of the most famous lists of astronomical objects, and many Messier objects are still referenced by their Messier numbers. The catalogue includes most of the astronomical deep-sky objects that can easily be observed from Earth's Northern Hemisphere; many Messier objects are popular targets for amateur astronomers.

Messier 72

Messier 72

Messier 72 is a globular cluster in the south west of the very mildly southern constellation of Aquarius.

Globular cluster

Globular cluster

A globular cluster is a spheroidal conglomeration of stars. Globular clusters are bound together by gravity, with a higher concentration of stars towards their centers. They can contain anywhere from tens of thousands to many millions of member stars. Their name is derived from Latin globulus. Globular clusters are occasionally known simply as "globulars".

Constellation

Constellation

A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object.

Aquarius (constellation)

Aquarius (constellation)

Aquarius is an equatorial constellation of the zodiac, between Capricornus and Pisces. Its name is Latin for "water-carrier" or "cup-carrier", and its old astronomical symbol is (♒︎), a representation of water. Aquarius is one of the oldest of the recognized constellations along the zodiac. It was one of the 48 constellations listed by the 2nd century astronomer Ptolemy, and it remains one of the 88 modern constellations. It is found in a region often called the Sea due to its profusion of constellations with watery associations such as Cetus the whale, Pisces the fish, and Eridanus the river.

New General Catalogue

New General Catalogue

The New General Catalogue of Nebulae and Clusters of Stars is an astronomical catalogue of deep-sky objects compiled by John Louis Emil Dreyer in 1888. The NGC contains 7,840 objects, including galaxies, star clusters and emission nebulae. Dreyer published two supplements to the NGC in 1895 and 1908, known as the Index Catalogues, describing a further 5,386 astronomical objects. Thousands of these objects are best known by their NGC or IC numbers, which remain in widespread use.

NGC 72

NGC 72

NGC 72 is a barred spiral galaxy estimated to be about 320 million light-years away in the constellation of Andromeda. It was discovered by R. J. Mitchell in 1855 and its magnitude is 13.5.

Barred spiral galaxy

Barred spiral galaxy

A barred spiral galaxy is a spiral galaxy with a central bar-shaped structure composed of stars. Bars are found in about two thirds of all spiral galaxies, and generally affect both the motions of stars and interstellar gas within spiral galaxies and can affect spiral arms as well. The Milky Way Galaxy, where the Solar System is located, is classified as a barred spiral galaxy.

Andromeda (constellation)

Andromeda (constellation)

Andromeda is one of the 48 constellations listed by the 2nd-century Greco-Roman astronomer Ptolemy, and one of the 88 modern constellations. Located in the northern celestial hemisphere, it is named for Andromeda, daughter of Cassiopeia, in the Greek myth, who was chained to a rock to be eaten by the sea monster Cetus. Andromeda is most prominent during autumn evenings in the Northern Hemisphere, along with several other constellations named for characters in the Perseus myth. Because of its northern declination, Andromeda is visible only north of 40° south latitude; for observers farther south, it lies below the horizon. It is one of the largest constellations, with an area of 722 square degrees. This is over 1,400 times the size of the full moon, 55% of the size of the largest constellation, Hydra, and over 10 times the size of the smallest constellation, Crux.

In religion

  • The number of languages spoken at the Tower of Babylon, according to later tradition.
  • The conventional number of scholars translating the Septuagint, according to the legendary account in the "Letter of Aristeas".
  • 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 Bible 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 martyred along with Imam Hussain at the Battle of Karbala.
  • The number of houri each Muslim martyr (or every Muslim male, according to some ahadith) shall receive as companions in Paradise.
  • 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.[9]
  • The good god Osiris was enclosed in a coffin by 72 evil disciples and accomplices of Set.[10]
  • 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 prophet Muhammad).[11][12]
  • The number of demons sealed away by King Solomon with The Lesser Key of Solomon.

Discover more about In religion related topics

Septuagint

Septuagint

The Greek Old Testament, or Septuagint, is the earliest extant Greek translation of books from the Hebrew Bible. It includes several books beyond those contained in the Masoretic text of the Hebrew Bible as canonically used in the tradition of mainstream Rabbinical Judaism. The additional books were composed in Greek, Hebrew, or Aramaic, but in most cases, only the Greek version has survived to the present. It is the oldest and most important complete translation of the Hebrew Bible made by the Jews. Some targums translating or paraphrasing the Bible into Aramaic were also made around the same time.

Kabbalah

Kabbalah

Kabbalah is an esoteric method, discipline and school of thought in Jewish mysticism. A traditional Kabbalist in Judaism is called a Mekubbal. The definition of Kabbalah varies according to the tradition and aims of those following it, from its origin in medieval Judaism to its later adaptations in Western esotericism. Jewish Kabbalah is a set of esoteric teachings meant to explain the relationship between the unchanging, eternal God—the mysterious Ein Sof —and the mortal, finite universe. It forms the foundation of mystical religious interpretations within Judaism.

Names of God in Judaism

Names of God in Judaism

Judaism considers some names of God so holy that, once written, they should not be erased: YHWH, Adonai, El ("God"), Elohim, Shaddai ("Almighty"), and Tzevaot ; some also include Ehyeh. Early authorities considered other Hebrew names mere epithets or descriptions of God and wrote that they and names in other languages may be written and erased freely. However, some moderns advise special care even in these cases, and many Orthodox Jews have adopted the chumras of writing "G-d" instead of "God" in English or saying Ṭēt-Vav instead of Yōd-Hē for the number fifteen or Ṭēt-Zayin instead of Yōd-Vav for the number sixteen in Hebrew.

Bible

Bible

The Bible is a collection of religious texts or scriptures that are held to be sacred in Christianity, Judaism, Samaritanism, and many other religions. The Bible is an anthology – a compilation of texts of a variety of forms – originally written in Hebrew, Aramaic, and Koine Greek. These texts include instructions, stories, poetry, and prophecies, among other genres. The collection of materials that are accepted as part of the Bible by a particular religious tradition or community is called a biblical canon. Believers in the Bible generally consider it to be a product of divine inspiration, but the way they understand what that means and interpret the text can vary.

Book of Revelation

Book of Revelation

The Book of Revelation is the final book of the New Testament. Its title is derived from the first word of the Koine Greek text: apokalypsis, meaning "unveiling" or "revelation". The Book of Revelation is the only apocalyptic book in the New Testament canon. It occupies a central place in Christian eschatology.

Battle of Karbala

Battle of Karbala

The Battle of Karbala was fought on 10 October 680 between the army of the second Umayyad Caliph Yazid I and a small army led by Husayn ibn Ali, the grandson of the Islamic prophet Muhammad, at Karbala, Sawad.

Houri

Houri

In Islamic religious belief, houris, are women with beautiful eyes described as a reward for the faithful Muslim believers in Paradise. The term is used four times in the Quran, where they are mentioned indirectly several other times,, and Hadith provide a "great deal of later elaboration". They have been said to have "captured the imagination of Muslims and non-Muslims alike". Muslim scholars differ as to whether they refer to the believing women of this world or a separate creation, with the majority opting for the latter.

Jacob's Ladder

Jacob's Ladder

Jacob's Ladder is a ladder leading to heaven that was featured in a dream the biblical Patriarch Jacob had during his flight from his brother Esau in the Book of Genesis.

Confucius

Confucius

Confucius was a Chinese philosopher and politician of the Spring and Autumn period who is traditionally considered the paragon of Chinese sages. Confucius's teachings and philosophy underpin East Asian culture and society, remaining influential across China and East Asia to this day.

Mahavira

Mahavira

Mahavira also known as Vardhamana, was the 24th tirthankara of Jainism. He was the spiritual successor of the 23rd tirthankara Parshvanatha. Mahavira was born in the early part of the 6th century BCE into a royal Kshatriya Jain family in ancient India. His mother's name was Trishala and his father's name was Siddhartha. They were lay devotees of Parshvanatha. Mahavira abandoned all worldly possessions at the age of about 30 and left home in pursuit of spiritual awakening, becoming an ascetic. Mahavira practiced intense meditation and severe austerities for twelve and a half years, after which he attained Kevala Jnana (omniscience). He preached for 30 years and attained Moksha (liberation) in the 6th century BCE, although the year varies by sect.

Tirthankara

Tirthankara

In Jainism, a Tirthankara is a saviour and spiritual teacher of the dharma. The word tirthankara signifies the founder of a tirtha, which is a fordable passage across the sea of interminable births and deaths, the saṃsāra. According to Jains, a Tirthankara is an individual who has conquered the saṃsāra, the cycle of death and rebirth, on their own, and made a path for others to follow. After understanding the true nature of the self or soul, the Tīrthaṅkara attains Kevala Jnana (omniscience). Tirthankara provides a bridge for others to follow the new teacher from saṃsāra to moksha (liberation).

Jainism

Jainism

Jainism, also known as Jain Dharma, is an Indian religion. Jainism traces its spiritual ideas and history through the succession of twenty-four Tirthankaras, with the first in the current time cycle being Rishabhadeva, whom the tradition holds to have lived millions of years ago, the twenty-third tirthankara Parshvanatha, whom historians date to the 9th century BCE, and the twenty-fourth tirthankara Mahavira, around 600 BCE. Jainism is considered to be an eternal dharma with the tirthankaras guiding every time cycle of the cosmology. The three main pillars of Jainism are ahiṃsā (non-violence), anekāntavāda (non-absolutism), and aparigraha (asceticism).

In other fields

Seventy-two is also:

Discover more about In other fields related topics

List of highways numbered 72

List of highways numbered 72

The following highways are numbered 72:

Dots per inch

Dots per inch

Dots per inch is a measure of spatial printing, video or image scanner dot density, in particular the number of individual dots that can be placed in a line within the span of 1 inch (2.54 cm). Similarly, dots per centimetre refers to the number of individual dots that can be placed within a line of 1 centimetre (0.394 in).

Point (typography)

Point (typography)

In typography, the point is the smallest unit of measure. It is used for measuring font size, leading, and other items on a printed page. The size of the point has varied throughout printing's history. Since the 18th century, the size of a point has been between 0.18 and 0.4 millimeters. Following the advent of desktop publishing in the 1980s and 1990s, digital printing has largely supplanted the letterpress printing and has established the DTP point as the de facto standard. The DTP point is defined as 1⁄72 of an international inch and, as with earlier American point sizes, is considered to be 1⁄12 of a pica.

Sarthe

Sarthe

Sarthe is a department of the French region of Pays de la Loire, and the province of Maine, situated in the Grand-Ouest of the country. It is named after the river Sarthe, which flows from east of Le Mans to just north of Angers. It had a population of 566,412 in 2019.

Aircraft carrier

Aircraft carrier

An aircraft carrier is a warship that serves as a seagoing airbase, equipped with a full-length flight deck and facilities for carrying, arming, deploying, and recovering aircraft. Typically, it is the capital ship of a fleet, as it allows a naval force to project air power worldwide without depending on local bases for staging aircraft operations. Carriers have evolved since their inception in the early twentieth century from wooden vessels used to deploy balloons to nuclear-powered warships that carry numerous fighters, strike aircraft, helicopters, and other types of aircraft. While heavier aircraft such as fixed-wing gunships and bombers have been launched from aircraft carriers, these aircraft have not successfully landed on a carrier. By its diplomatic and tactical power, its mobility, its autonomy and the variety of its means, the aircraft carrier is often the centerpiece of modern combat fleets. Tactically or even strategically, it replaced the battleship in the role of flagship of a fleet. One of its great advantages is that, by sailing in international waters, it does not interfere with any territorial sovereignty and thus obviates the need for overflight authorizations from third-party countries, reduces the times and transit distances of aircraft and therefore significantly increase the time of availability on the combat zone.

Abraham Lincoln

Abraham Lincoln

Abraham Lincoln, sometimes known as The Great Emancipator or Honest Abe, was an American lawyer and statesman who served as the 16th president of the United States from 1861 until his assassination in 1865. Lincoln led the nation through the American Civil War and succeeded in preserving the Union, abolishing slavery, bolstering the federal government, and modernizing the U.S. economy.

Rule of 72

Rule of 72

In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number is divided by the interest percentage per period to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.

Finance

Finance

Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services . Finance activities take place in financial systems at various scopes, thus the field can be roughly divided into personal, corporate, and public finance.

Bebe Moore Campbell

Bebe Moore Campbell

Bebe Moore Campbell was an American author, journalist and teacher. Campbell was the author of three New York Times bestsellers: Brothers and Sisters, Singing in the Comeback Choir, and What You Owe Me, which was also a Los Angeles Times "Best Book of 2001". Her other works include the novel Your Blues Ain't Like Mine, which was a New York Times Notable Book of the Year and the winner of the NAACP Image Award for Literature; her memoir, Sweet Summer: Growing Up With and Without My Dad; and her first nonfiction book, Successful Women, Angry Men: Backlash in the Two-Career Marriage. Her essays, articles, and excerpts appear in many anthologies.

Jill Clayburgh

Jill Clayburgh

Jill Clayburgh was an American actress known for her work in theater, television, and cinema. She received the Cannes Film Festival Award for Best Actress and was nominated for the Academy Award for Best Actress for her breakthrough role in Paul Mazursky's comedy drama An Unmarried Woman (1978). She also received a second consecutive Academy Award nomination for Starting Over (1979) as well as four Golden Globe nominations for her film performances.

LeVar Burton

LeVar Burton

Levar Burton Jr. is an American actor, director, and television host, best known for playing Geordi La Forge in Star Trek: The Next Generation (1987–1994). He also played Kunta Kinte in the ABC miniseries Roots (1977), and was host of the PBS Kids educational television series Reading Rainbow for more than 23 years (1983–2006). He received 12 Daytime Emmy Awards and a Peabody Award as host and executive producer of Reading Rainbow.

Civil Air Patrol

Civil Air Patrol

Civil Air Patrol (CAP) is a congressionally chartered, federally supported non-profit corporation that serves as the official civilian auxiliary of the United States Air Force (USAF). CAP is a volunteer organization with an aviation-minded membership that includes people from all backgrounds, lifestyles, and occupations. The program is established as an organization by Title 10 of the United States Code and its purposes defined by Title 36.

Source: "72 (number)", Wikipedia, Wikimedia Foundation, (2022, November 25th), https://en.wikipedia.org/wiki/72_(number).

Enjoying Wikiz?

Enjoying Wikiz?

Get our FREE extension now!

Footnotes
  1. ^ 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.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
  3. ^ 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.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-22.
  5. ^ 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.
  6. ^ 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.
  7. ^ David Wells: The Penguin Dictionary of Curious and Interesting Numbers
  8. ^ 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.
  9. ^ ISBN 0-292-72076-9
  10. ^ "Egyptian Myths", George Hart, p41, University of Texas Press, 1990
  11. ^ "Sects In Islam - 73 Groups in Islam, Division - Denominations". Archived from the original on 6 May 2013. Retrieved 24 March 2013.
  12. ^ 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"
External links

The content of this page is based on the Wikipedia article written by contributors..
The text is available under the Creative Commons Attribution-ShareAlike Licence & the media files are available under their respective licenses; additional terms may apply.
By using this site, you agree to the Terms of Use & Privacy Policy.
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization & is not affiliated to WikiZ.com.