40 (number)

← 39 40 41 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty
Ordinal	40th (fortieth)
Numeral system	quadragesimal
Factorization	23× 5
Divisors	1, 2, 4, 5, 8, 10, 20, 40
Roman numeral	XL
Latin prefix	quadrage-
Binary	1010002
Ternary	11113
Quaternary	2204
Quinary	1305
Senary	1046
Octal	508
Duodecimal	3412
Hexadecimal	2816
Vigesimal	2020
Base 36	1436

40 (forty) is the natural number following 39 and preceding 41.

Despite being related to the word "four" (4), the modern spelling of 40 is "forty". The archaic form "fourty" is now considered a misspelling. The modern spelling possibly reflects a pronunciation change due to the horse–hoarse merger.

In mathematics

Forty is a composite number, an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10 and 20) gives 40, hence 40 is a semiperfect number.

Given 40, the Mertens function returns 0. 40 is the smallest number n with exactly 9 solutions to the equation φ(x) = n.

Forty is the number of n-queens problem solutions for n = 7.

Since 40² + 1 = 1601 is prime, 40 is a Størmer number.

40 is a repdigit in base 3 (1111, i.e. 3⁰ + 3¹ + 3² + 3³) and a Harshad number in base 10.

In science

• The atomic number of zirconium.
• Negative forty is the unique temperature at which the Fahrenheit and Celsius scales correspond; that is, −40 °F = −40 °C. It is referred to as either "minus forty" or "forty below".

Astronomy

• The planet Venus forms a pentagram in the night sky every eight years with it returning to its original point every 40 years with a 40-day regression (some scholars believe that this ancient information was the basis for the number 40 becoming sacred to Jews, Christians, and Muslims).
• Messier object M40, a magnitude 9.0 double star in the constellation Ursa Major
• The New General Catalogue object NGC 40, a magnitude 12.4 planetary nebula in the constellation Cepheus
• The Saros number of the
  • solar eclipse series which began on -1653 May 28 and ended on -373 July 4. The duration of Saros series 40 was 1280.1 years, and it contained 72 solar eclipses.
  • lunar eclipse series which began on -1387 February 12 and ended on -71 April 12. The duration of Saros series 40 was 1316.2 years, and it contained 74 lunar eclipses.

In religion

The number 40 is used in Jewish, Christian, Islamic, and other Middle Eastern traditions to represent a large, approximate number, similar to "umpteen".

Judaism

In the Hebrew Bible, forty is often used for time periods, forty days or forty years, which separate "two distinct epochs".

• Rain fell for "forty days and forty nights" during the Flood. (Genesis 7:4)
• Spies explored the land of Israel for "forty days." (Numbers 13:25)
• The Hebrew people lived in the Sinai desert for "forty years". This period of years represents the time it takes for a new generation to arise. (Numbers 32:13)
• Moses' life is divided into three 40-year segments, separated by his growing to adulthood, fleeing from Egypt, and his return to lead his people out. (Acts 7:23,30,36)
• Several Jewish leaders and kings are said to have ruled for "forty years", that is, a generation. Examples include Eli (1 Samuel 4:18), Saul (Acts 13:21), David (2 Samuel 5:4), and Solomon (1 Kings 11:42).
• Goliath challenged the Israelites twice a day for forty days before David defeated him. (1 Samuel 17:16)
• Moses spent three consecutive periods of "forty days and forty nights" on Mount Sinai:

1. He went up on the seventh day of Sivan, after God gave the Torah to the Jewish people, in order to learn the Torah from God, and came down on the seventeenth day of Tammuz, when he saw the Jews worshiping the Golden Calf and broke the tablets. (Deuteronomy 9:11)
2. He went up on the eighteenth day of Tammuz to beg forgiveness for the people's sin and came down without God's atonement on the twenty-ninth day of Av. (Deuteronomy 9:25)
3. He went up on the first day of Elul and came down on the tenth day of Tishrei, the first Yom Kippur, with God's atonement. (Deuteronomy 10:10)

• A mikvah consists of 40 se'ah (approximately 200 gallons) of water
• 40 lashes is one of the punishments meted out by the Sanhedrin, though in actual practice only 39 lashes were administered.
• One of the prerequisites for a man to study Kabbalah is that he is forty years old.

Christianity

Christianity similarly uses forty to designate important time periods.

• Before his temptation, Jesus fasted "forty days and forty nights" in the Judean desert. (Matthew 4:2, Mark 1:13, Luke 4:2)
• Forty days was the period from the resurrection of Jesus to the ascension of Jesus. (Acts 1:3)
• Biblical verse Numbers 14:33-34 alludes to the same with ties to the prophecy in The Book of Daniel. "For forty years--one year for each of the forty days you explored the land--you will suffer for your sins and know what it is like to have me against you.'"
• In modern Christian practice, Lent consists of the 40 days preceding Easter. In much of Western Christianity, Sundays are excluded from the count; in Eastern Christianity, Sundays are included.
• The Forty Martyrs of Sebaste
• Kirk Kilisse, "Forty Churches" (Σαράντα Εκκλησιές) in Eastern Thrace

Islam

• Muhammad was forty years old when he first received the revelation delivered by the archangel Gabriel.
• Masih ad-Dajjal roams around the Earth in forty days, a period of time that can be as many as forty months, forty years, and so on.
• God forbade the Fasiqun (the non-believers) from entering the Holy Land for 40 years to separate them from Musa (Moses) and his brother.
• Musa (Moses) spent 40 days on Mount Sinai where he received the 10 commandments.
• Prophet Ibrahim spent 40 days in a fire and lived because God made the fire like flowers.
• On the 40th verse (ayat) of the 2nd chapter of the Quran (Al-Baqarah) God changes the topic.
• Forty was the number of days that Prophet Ilyas (Elijah) spent in the wilderness before the angel appeared to him with God's message on Mount Horeb.
• Forty was the number of days that Prophet Isa (Jesus) was tempted in the desert by Satan.
• Muhammad praying and fasting in the cave for 40 days.
• Muhammad then had 40 followers to spread the religion of Islam.
• Prophets Dawuud and Suleiman each ruled for forty years.
• Regarding the flood that Noah encountered, it is said that for forty days water continued to pour from the heavens and to stream out over the earth.
• There is also a hadith from Mohammad that the prayers of a person who gossips would not be accepted for forty days and nights. (Al-Kafi, Vol. 6, p. 400)
• Imam Ali has narrated from Mohammad that one who memorizes and preserves forty hadith relating to their religious needs shall be raised by God as a learned scholar on the Day of Resurrection.
• It is said that a person’s intellect attains maturity in forty years, everyone according to his own capacity.
• It is believed that one who assists a blind man for forty steps becomes worthy of entering heaven.
• Imam Baghir has said: “The prayers of someone who drinks wine are not accepted for forty days.”
• Believers have also been encouraged to devote themselves to God Almighty for forty days to see the springs of wisdom break forth from their hearts and flow from their tongues.
• Mourning period officially last for 40 days.

Yazidism

• In the Yazidi faith, The Chermera Temple (meaning “40 Men” in the Yazidi dialect) is so old that no one remembers how it came to have that name but it is believed to derive from the burial of 40 men on the mountaintop site.

Funerary customs

• Some Russians believe that ghosts of the dead linger at the site of their death for forty days.
• Many Christian Filipinos mark the end of the initial mourning period on the fortieth day after death, and have a Mass said. They believe that the soul remains on the earthly plane for forty days before entering the afterlife, recalling how Christ ascended to heaven forty days after his Resurrection.

Hinduism

• In Hinduism, some popular religious prayers consist of forty shlokas or dohas (couplets, stanzas). The most common being the Hanuman Chalisa (chaalis is the Hindi term for 40).

In Hindu system some of the popular fasting period consist 40 days and is called the period One 'Mandl kal' Kal means a period and Mandal kal means a period of 40 days. For example, the devotees of 'Swami Ayyappa', the name of a Hindu God very popular in Kerala, India ( Sabarimala Swami Ayyappan ) strictly observed forty days fasting and visit ( Only male devotees are permitted to enter into the God's Temple) with their holy submittance or offerings on 41st or a convenient day after a minimum 40 days practice of fasting. The offering is called 'Kanikka'.

Sumerian

• Enki ( /ˈɛŋki/) or Enkil (Sumerian: dEN.KI(G)𒂗𒆠) is a god in Sumerian mythology, later known as Ea in Akkadian and Babylonian mythology. He was originally patron god of the city of Eridu, but later the influence of his cult spread throughout Mesopotamia and to the Canaanites, Hittites and Hurrians. He was the deity of crafts (gašam); mischief; water, seawater, lakewater (a, aba, ab), intelligence (gestú, literally "ear") and creation (Nudimmud: nu, likeness, dim mud, make bear). He was associated with the southern band of constellations called stars of Ea, but also with the constellation AŠ-IKU, the Field (Square of Pegasus). Beginning around the second millennium BCE, he was sometimes referred to in writing by the numeric ideogram for "40," occasionally referred to as his "sacred number."

A large number of myths about Enki have been collected from many sites, stretching from Southern Iraq to the Levantine coast. He figures in the earliest extant cuneiform inscriptions throughout the region and was prominent from the third millennium down to Hellenistic times.

The exact meaning of his name is uncertain: the common translation is "Lord of the Earth": the Sumerian en is translated as a title equivalent to "lord"; it was originally a title given to the High Priest; ki means "earth"; but there are theories that ki in this name has another origin, possibly kig of unknown meaning, or kur meaning "mound". The name Ea is allegedly Hurrian in origin while others claim that it is possibly of Semitic origin and may be a derivation from the West-Semitic root *hyy meaning "life" in this case used for "spring", "running water." In Sumerian E-A means "the house of water", and it has been suggested that this was originally the name for the shrine to the God at Eridu.

In sports

• In football (soccer), generally considered the number of points that a Premier League team (or, by extension, a team in any 20-team league with a standard home-and-away season) needs to avoid relegation.
• In baseball, each team in Major League Baseball is allowed to have 40 players under major-league contracts at any given time (not including players on the 60-day disabled list). From September 1 to the end of the regular season, teams are allowed to expand their game-day rosters to include the entire 40-man roster.
• In horse racing, the maximum permitted number of runners in the grand national is 40.
• The distance run in the 40 yard dash, an important metric in American football scouting.
• In tennis, the number 40 represents the third point gained in a game. A score of 40-40 (three points each) is called "deuce", at which time a player must score two consecutive points to win the game.
• Beginning with the 2013 season, the number of cars that will run each race in NASCAR's second-level Nationwide Series.
• The jersey number 40 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The Houston Astros, for Don Wilson.
    • The Pittsburgh Pirates, for Danny Murtaugh, most noted as the team's longtime manager.
  • In the NBA:
    • The Denver Nuggets, for Byron Beck.
    • The Detroit Pistons, for Bill Laimbeer.
  • In the NFL:
    • The Arizona Cardinals, for Pat Tillman.
    • The Chicago Bears, for Hall of Famer Gale Sayers.
    • The New England Patriots, for Hall of Famer Mike Haynes.
    • The New York Giants, for Joe Morrison.
    • The Philadelphia Eagles, for Tom Brookshier.

In other fields

The number on the logo for the American-Japanese hard rock band Crush 40.

Forty is also:

• Literally in other fields, after the Civil War, there were plans to offer the freed slaves 40 acres and a mule
• To understand a people, you must live among them for 40 days. ~Arabic proverb
• the caliber of the bullet in a number of firearms cartridges, most notably the .40 S&W. (The 10mm Auto, although designated as metric caliber, uses the same caliber, and often uses the same bullets.)
• in the Saying "Life begins at forty"
• in the expression "forty winks", meaning a short sleep
• The highest number ever counted to on Sesame Street
• A song by Dave Matthews Band
• the number of years of marriage as the ruby wedding anniversary
• the code for direct dial international phone calls to Romania
• the number in the designation of:
  • Interstate 40, a freeway that runs from California to North Carolina
  • U.S. Route 40, the 2,285-mile (3,677 km) highway that runs from Baltimore, Maryland, to Park City, Utah, a portion of which follows the National Road
  • European route E40 from Calais to Ridder
  • the A40 and M40, important highways in the UK. The A40 is a trunk road in England and Wales, connecting London to Fishguard. The M40 motorway is the second motorway in the British transport network to connect London to Birmingham
• "40", a 1983 song by U2 from their album War
• "40'" is the title of a song by Franz Ferdinand
• The number of spaces in a standard Monopoly game board
• The American-Japanese hard rock band Crush 40 featured in Sega's Sonic the Hedgehog franchise with guitarist Jun Senoue and vocalist Johnny Gioeli
• The radio program American Top 40
• The radio program Rick Dees' Weekly Top 40
• the number of thieves in Ali Baba and the Forty Thieves and in Ali Shar and Zumurrud, from Thousand and One Nights (both the numbers 40 and 1001 are more likely to mean "many" than to indicate a specific number)
• the customary number of hours in a regular workweek in some Western countries.
• the number of positions on a number of radio countdown programs, most notably American Top 40 and American Country Countdown.
• for The Early Show segment "Chef on a Shoestring", chefs are given a $40 budget.
• The number of weeks for an average term of pregnancy, counting from the woman’s last menstrual period.
• A 40-ounce bottle of malt liquor, referenced in the song "40oz. to Freedom" by Sublime.
• Canadian hip-hop producer Noah Shebib is known as "40".
• Forty Shades of Green is a visual term for rural Ireland, Johnny Cash popularized it with his 1961 song of the name.
• The Tessarakonteres, or 40, the largest ship of antiquity, constructed by Ptolemy IV
• Forty is the only integer whose English name has its letters in alphabetical order.
• Forty Foot, a promontory on the southern tip of Dublin Bay, Ireland, from which people have been swimming in the Irish Sea all year round for some 250 years

References

• Stanley Brandes, Forty:The Age and the Symbol. (Knoxville, Univ of Tennessee Press, 1985)

External links

Wikimedia Commons has media related to 40 (number).