40 (number)

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

Though the word is related to "four" (4), the spelling "forty" replaced "fourty" in the course of the 17th century and is now the standard form.

In mathematics

*Forty is a composite number, a refactorable number, an octagonal number, and—as the sum of the first four pentagonal numbers: $1 + 5 + 12 + 22 =40$—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 with exactly nine solutions to the equation Euler's totient function $\varphi (x)=n$.
*Forty is the number of -queens problem solutions for $n=7$.
*Forty is a repdigit in ternary (1111, ''i.e.'', $3^ + 3^ + 3^ + 3^$, or, in other words, $\frac$) and a Harshad number in decimal.

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

*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

In religion

The number 40 is found in many traditions without any universal explanation for its use. In Jewish, Christian, Islamic, and other Middle Eastern traditions it is taken to represent a large, approximate number, similar to " umpteen".

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, lake water (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.

Judaism

* In the Hebrew Bible

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