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	th
Numeral system	quadragesimal
Factorization	$2^{3}\cdot 5$
Divisors	1, 2, 4, 5, 8, 10, 20, 40
Greek numeral	Μ´
Roman numeral	XL
Binary	1010002
Ternary	11113
Senary	1046
Octal	508
Duodecimal	3412
Hexadecimal	2816

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

Notwithstanding being related to the word "four" (4), 40 is spelled "forty", and not "fourty". The reason is that etymologically (also in accents without the horse-hoarse merger), the words have different vowels, "forty" containing a contraction in the same way that "fifty" contains a contraction of "five". The letters of the word "forty" are in alphabetical order; this is the only number that has this linguistic property in English.

In mathematics

Forty is 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) 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 significant in Jewish, Christian, Islamic, and other Middle Eastern traditions. It can represent an estimate, or many of something.

Judaism

• Rain fell for "forty days and forty nights" during the flood
• Spies explored the land of Israel for "forty days." (Numbers 13)
• 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.
• Moses' life is divided into three 40-year segments, separated by his fleeing from Egypt, and his return to lead his people out.
• Several Jewish leaders and kings are said to have ruled for "forty years", that is, a generation. (Examples: Eli, Saul, David, Solomon.)
• Goliath challenged the Israelites twice a day for forty days before David defeated him.
• 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
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
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

• 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

• Before the temptation of Christ, Jesus fasted "Forty days and forty nights" in the Judean desert.
• Forty days was the period from the resurrection of Jesus to the ascension of Jesus.
• 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.

Islam

• 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.
• Muhammad was forty years old when he first received the revelation delivered by the archangel Gabriel.
• The Quran says that a person is only fully grown when they reach the age of 40.
• The Significance of the Number 40 in Islam
• MV: The number 40 is repeated in Islam a lot of times. Only Allah knows the answer, so gathering a lot of information I have found lots of things that took place with the number 40.
• Musa Alahi salam traveled 40 years in the desert.
• Musa spent 40 days on Mount Sinai where he received the 10 commandments.
• Prophet Ibrahim spent 40 days in a fire and lived because Allah made the fire like flowers.
• Prophet Yunus was in a whales mouth for 40 days.
• On the 40th ayat of surah baqarah Allah changes the topic.
• Forty was the number of days that Prophet Ilyas spent in the wilderness before God appeared to him in a cave on Mount Horeb.
• Forty was the number of days that Prophet Isa was tempted in the desert by Satan.
• Muhammad was praying and fasting in the cave for 40 days.
• Muhammad then had 40 followers to spread the religion of Islam.
• Prophets Dauud 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.
• Prophet Isa walked the desert and fasted in the wilderness for forty days.
• 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 Allah 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.

Russian folklore

• Some Russians believe that ghosts of the dead linger at the site of their death for forty days.

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 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.
• 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.
• 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 Atlanta Hawks, for Jason Collier.
    • 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

Forty is also:

• 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
• 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 band Crush 40
• 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.

Historical years

40 A.D., 40 B.C., 1940, 2040, etc.

See also

• 40 acres and a mule