40 (number)

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

Despite being related to the word "four" (4), 40 is spelled as "forty", not "fourty". This is because etymologically (and still 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.

← 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	40 forty
Ordinal	40th fortieth
Numeral system	quadragesimal
Factorization	$2^3 \cdot 5$
Divisors	1, 2, 4, 5, 8, 10, 20, 40
Roman numeral	XL
Roman numeral (Unicode)	XL, xl
Binary	101000
Octal	50
Duodecimal	34
Hexadecimal	28

Look up forty in
Wiktionary, the free dictionary.

1 In mathematics
2 In science
- 2.1 Astronomy
3 In religion
4 In other fields
5 Historical years
6 See also
7 References

[edit] 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 the greatest prime factor of 40² + 1 = 1601 is prime and obviously more than 40 twice, 40 is a Størmer number.

40 is a repdigit in base 3 (1111) and a Harshad number in base 10.

[edit] In science

The atomic number of zirconium.
Negative forty is the 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".

[edit] 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 #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.

[edit] In religion

The number 40 is significant in Jewish, Christian, Islamic, and other Middle Eastern traditions; it can also represent a rough calculation, a huge sum of units, or simply put, a lot of something.

"Forty days and forty nights" describes the period for which rain fell during Noah's flood
"Forty days" was the length of the period that the twelve spies explored the Promised Land (Numbers 13)
"Forty years" was the length of Israel's wandering in the wilderness. This period of years represents a generation, that is, 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 the people out.
Several Israelite leaders and kings are said to have ruled for "forty years", that is, a generation. (Examples: Eli, Saul, David, Solomon.)
According to the Midrash, Moses spent three consecutive periods of "forty days and forty nights" on Mount Sinai:

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
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
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

Rabbi Akiva, the greatest expositor of the Oral Torah, only began learning how to read Hebrew when he was 40 years old
A mikvah consists of 40 se'ah (approximately 200 gallons) of water
40 lashes is one of the punishments meted out by the Sanhedrin (in actual practice, only 39 lashes were administered)
"Forty days and forty nights" was the period Jesus spent fasting in the wilderness, after which he was tempted by Satan.
Forty days was the period from Jesus' resurrection till his ascension into heaven.
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 dead are usually mourned for forty days in Muslim cultures
Ad-Dajjal roams around the Earth in forty days, forty days that can be as many as forty months, forty years, and so on.
Khadijah is said to be forty years old when she married Muhammad
Muhammad is said to be forty years old when he first received the revelation delivered by an angel
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.
Some Russians believe that ghosts of the dead linger at the site of their death for forty days
In Eternalism, 40 is believed to be the number of the Corrupter, the Anti-Christ in Christianity, and is formed from the numbers 18+1+6+6+9. This also spells Raffi with correct numero-alphabetic translation.
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) .

[edit] In other fields

Forty is also:

To understand a people, you must live among them for 40 days. ~Arabic proverb ^[1]^[2]
the caliber of the bullet in the .40 S&W handgun cartridge
in the Saying "Life begins at forty"
in the expression "forty winks", meaning a short sleep
the distance run in the 40 yard dash in American football scouting
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 2285-mile 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
in the title of the Food Network show $40 a Day
in the name of WD-40, a spray lubricant
in the name of the food additive FD & C Red Dye #40, commonly known as "Red 40"
the 40 ounce size used for liquor, typically fairly cheap malt beer; a person sometimes "pours a forty on the curb", i.e., pours out said bottle onto the street, in memory of a person who has died
the number of questions asked in the theory road test in the Republic of Ireland
the number of thieves in Ali Baba and the Forty Thieves, 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 song, "40 Hour Week (For a Livin')" by Alabama (as well as their album, 40-Hour Week), takes its name from the standard workweek length.
the classic Russian vodka is alcohol content 40 percent by volume
the jersey number of Pat Tillman, which was retired by the Arizona Cardinals
the number of wires in a Parallel ATA-cable
Form 1040 (referred to as a "ten-forty") is a standard Internal Revenue Service form used to file for federal taxes in the United Sates
UB40 is a form for those claiming unemployment benefits in the United Kingdom. The band UB40 was named after this form
The Rolling Stones CD "Forty Licks"
David Stremme's Nextel Cup Series number for Chip Ganassi Racing
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. Most chefs bring it in under. (For holidays they are given $80).
Rigveda : The total number of syllables in Rigveda, the most sacred and ancient scripture of the Hindu Religion, equal to the total Muhurtas or the ‘auspicious time’ n 40 years. There are 432,000 syllables in Rigveda. In each day, we have 30 Muhurtas. The total number of days in a year as per the Hindu calendar is 360 days. This works out to 40 years. The number 40 is an important number in the Hindu tradition. ..... Shrikant V Soman
the M40 (field protective mask), a United States military gas mask