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40 is the natural number following 39 and preceding 41. In English, forty is the only number whose constituent letters appear in alphabetical order.

1 In mathematics

Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal numberA pentagonal pyramidal number is a number equal to the sum of the first few pentagonal numbers. The first few are 1, 6, 18, 40, 75, 126, 196, 288, 405, 550, 726, 936, 1183, 1470, 1800, 2176, 2601, 3078, 3610, 4200, 4851, 5566, 6348, 7200, 8125, and 9126.. It is a Harshad numberA Harshad number or Niven number is an integer that is divisible by the sum of its digits in a given number base. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997. All numbers between zer.

Given 40, the Mertens functionIn number theory, the Mertens function is : where μ(k) is the Mobius function. Because the Mobius function has only the return values -1, 0 and +1, it's obvious that the Mertens function moves slowly and that there is no x such that M ''x > x''. The Me 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 ProblemExample solution The eight queens puzzle is the problem of putting eight chess queens on an 8×8 chessboard such that none of them is able to capture any other using the standard chess queen's moves. Piece colour is ignored, and any piece is assumed to be solutions for n = 7.

2 In other fields

Forty is:

• the atomic numberThe atomic number Z is a term used in chemistry and physics to represent the number of protons found in the nucleus of an atom. In an atom of neutral charge, the number of electrons typically equals the atomic number. The atomic number originally meant th of zirconiumZirconium is a chemical element in the periodic table that has the symbol Zr and atomic number 40. A lustrous gray-white, strong transition metal that resembles titanium, zirconium is obtained chiefly from zircon and is very corrosion resistant. Zirconium.
• in Judaic, Christian and Islamic tradition: the tag Forty days and forty nights describes the period for which rain fell during Noah's flood, the period Moses spent on Mount Sinai receiving the Ten Commandments and the period Christ spent in the wilderness. In modern Western Christian practice, Lent consists of the 40 days preceding Easter
• the usual number of days in the time of mourning in Muslim cultures.
• the number of days after death for which the ghosts of the dead hang around the site of their death, according to Russian belief
• in the maxim " Life begins at forty".
• in the expression "Forty winks", meaning a short sleep.
• the number of years of marriage as the ruby wedding anniversary.
• the code for direct dial international phone calls to Romania.
• in the designation of Interstate 40, a freeway that runs from California to North Carolina.
• in the designation for U.S. Highway 40, the 800-mile highway that runs from Baltimore, Maryland, to Vandalia, Illinois, being synonymous with the National Highway.
• the year A.D. 40, 40 BC, or (for example) 1940.
• the title of a song by U2.
• in the title of the Food Network show $40 a Day.
• in the name of WD-40, a type of spray lubricant.
• in the name of the food additive FD & C Red Dye #40, commonly known as "Red 40" [1]
• the 40 ounce size used for liquor, typically fairly cheap malt beer
• in the UK, the A40 and M40 are important highways. 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.

Negative forty is:

• the temperature (in degrees) at which Celsius and Fahrenheit scales are equivalent (often referred to as minus forty or 40 below).