Epsilon

Epsilon (uppercase Ε, lowercase ε or lunate ; ) is the fifth letter of the Greek alphabet, corresponding phonetically to a close-mid front unrounded vowel . In the system of Greek numerals it has a value of 5. It was derived from the Phoenician letter He . Letters that arose from Epsilon include the Roman E and Cyrillic Ye.

The name "epsilon" (, "simple e") was coined in the Middle Ages to distinguish the letter from the digraph αι, a former diphthong that had come to be pronounced the same as epsilon.

The uppercase form of epsilon looks essentially identical to Latin E. The lowercase version has two typographical variants, both inherited from medieval Greek handwriting. One, the most common in modern typography and inherited from medieval minuscule, looks like an inverted "3". The other, also known as lunate or uncial epsilon and inherited from earlier uncial writing, looks like a semicircle crossed by a horizontal bar. While in normal typography these are just alternate font variants, they may have different meanings as mathematical symbols. Computer systems therefore offer distinct encodings for them.

Sound value

The initial sound value of Ε was determined by the vowel occurring in the Phoenician letter name He, which made it a natural choice for being reinterpreted from a consonant symbol to a vowel symbol denoting an sound. Besides its classical Greek sound value, the short phoneme, it could initially also be used for other -like sounds. For instance, in early Attic before c.500 B.C., it was used also both for the long, open , and for the long close . In the former role, it was later replaced in the classic Greek alphabet by Eta (Η), which was taken over from eastern Ionic alphabets, while in the latter role it was replaced by the digraph spelling ΕΙ.

Epichoric alphabets

Some dialects used yet other ways of distinguishing between various e-like sounds.

In Corinth, the normal function of Ε to denote and was taken by a glyph resembling a pointed B (), while Ε was used only for long close . The letter Beta, in turn, took the deviant shape .

In Sicyon, a variant glyph resembling an X () was used in the same function as Corinthian .

In Thespiai (Boeotia), a special letter form consisting of a vertical stem with a single rightward-pointing horizontal bar () was used for what was probably a raised variant of in pre-vocalic environments. This tack glyph was used elsewhere also as a form of "Heta", i.e. for the sound .

Glyph variants

After the establishment of the canonical classic Greek alphabet, new glyph variants for Ε were introduced through handwriting. In the uncial script (used for literary papyrus manuscripts in late antiquity and then in early medieval vellum codices), the "lunate" shape () became predominant. In cursive handwriting, a large number of shorthand glyphs came to be used, where the cross-bar and the curved stroke were linked in various ways. Some of them resembled a modern lowercase Latin "e", some a "6" with a connecting stroke to the next letter starting from the middle, and some a combination of two small "c"-like curves. Several of these shapes were later taken over into minuscule book hand. Of the various minuscule letter shapes, the inverted-3 form became the basis for lower-case Epsilon in Greek typography during the modern era.

{|class="wikitable" !Uncial !Uncial variants !Cursive variants !Minuscule !Minuscule with ligatures |- | | | | | |}

Uses

International Phonetic Alphabet

In the International Phonetic Alphabet, the Latin epsilon represents open-mid front unrounded vowel, as in the English word "pet" .

Symbol

The uppercase Epsilon is not commonly used outside of the Greek language because of its similarity to the Latin letter E.

Lower case

The Greek lowercase epsilon ε, the lunate epsilon symbol ϵ, or the Latin lowercase epsilon ɛ (see above) is used as the symbol for:

Math and science

In mathematics (particularly calculus), an arbitrarily small positive quantity is commonly denoted ε; see (ε, δ)-definition of limit.

*By analogy with this, the late mathematician Paul Erdős also used the term "epsilons" to refer to children (Hoffman 1998, p. 4).

In mathematics, Hilbert introduced epsilon terms $\backslash epsilon\; x.\backslash phi$ as an extension to first order logic; see epsilon calculus.

In mathematics, the Levi-Civita symbol.

In mathematics, to represent the dual numbers: a + bε, with ε² = 0 and ε ≠ 0.

In mathematics, sometimes used to denote the Heaviside step function.

In set theory, the limit ordinal of the sequence $\backslash omega,\backslash omega^\backslash omega,\backslash omega^\{\backslash omega^\backslash omega\},\backslash dots$.

In computing, the precision of a numeric data type and floating-point machine epsilon.

In computer science, the empty string, though different writers use a variety of other symbols for the empty string as well, including the upper-case Greek letter lambda.

In physics, the permittivity of a medium.

In physics and electronics, the emf of a circuit

In physics, the strain of a material (a ratio of extensions).

In automata theory, a transition that involves no shifting of an input symbol.

In astronomy, the fifth-brightest star in a constellation (see Bayer designation).

In astronomy, Epsilon is the name for Uranus' most distant and most visible ring.

In chemistry, the molar extinction coefficient of a chromophore.

In economics, ε refers to elasticity.

In statistics, to refer to error terms.

In agriculture, to represent the "photosynthetic efficiency" of a particular plant or crop.

Fictional names

In the popular web series "Red vs. Blue", Epsilon is the name of Agent Washington's AI, possessing memories from the breaking of the Alpha AI by Project Freelancer.

Epsilon in Malaysian Pale is the name of the second solo album released by Tangerine Dream leader Edgar Froese in 1975.

Epsilon is also an Australian light-powered female-looking robot that fought Pluto in an episode of Astro Boy.

Epsilon Eridani III is the planet that the spacestation Babylon 5 orbited in the eponymous sci-fi television series.

E-104 Epsilon is also the name of a robot in Sonic Adventure.

Epsilon is an otherworldy being in the book The Riddles of Epsilon by Christine Morton-Shaw.

"Epsilon 9" is the name of the Federation space station consumed by the V'ger cloud in .

Epsilon is the name of an unlockable creature in the game Monster Rancher 2.

In Greek it is used for Epsilon Team.

"Epsilon Mirror" is the name of one of Aika's moves in the video game Skies of Arcadia.

Epsilon is the leader of the Rebellion in .

"The Epsilon Program" is a mysterious cult in the video game by Game Developer Rockstar North. This cult is thought to be based on Scientology.

The Epsilon Project is a fictional experiment mentioned in the Dreamcast and Xbox versions of Dead or Alive 2 and is based on cloning.

Epsilon is the lowest of five social castes in the Aldous Huxley novel Brave New World.

"Plan Epsilon" was one of many plans to restore Doctor Doom to life in the event of his death, as shown in Fantastic Four issue no. 246, written by Stan Lee.

Epsilon-Eagle is the name of the protagonist in the Sega Mega Drive game Alien Soldier.

Epsilon was the name given to one of the ground support teams in the Sony Playstation game G-Police.

Epsilon is the name of the newly resurrected Yuri Faction in the Yuri's Revenge mod Mental Omega.

Epsilon was one of the warriors of Asgard in the Anime series Saint Seiya, Fenrir Epsilon, The Northern Wolf, when Dragon Shiryu had to fight for his life against him on his way to rescue Hilda.

Epsilon was the name of the chef dog in the Pixar movie Up when Carl and Russell are in Muntz's lair.

"Epsilon Knight" is the name of a racer in the Extreme-G racing game series who, if controlled by the computer, always happened to finish 5th.

Epsilon was a man-made God in the game AdventureQuest.

Other uses

"Epsilon" is the name used by General Motors for the post-2003 Epsilon platform.

Epsilon Euskadi, a carmaker and EpsilonEuskadi LMP1 car.

Barazi-Epsilon, a manufacturer in the 2009 Superleague Formula season for the Olympique Lyonnais car.

Hurricane Epsilon, a storm of the 2005 Atlantic hurricane season.

Epsilon TB-30 is a training aircraft made by Socata and used by the French, Portuguese, Senegalese and Togo airforces. Introduced in 1984 it provides basic and intermediate training, and has a 300 hp lycoming engine.

Stars Epsilon Eridani and 40 Epsilon.

Epsilon is a multi-platform Emacs-like programmer's text editor by Lugaru Software Ltd

Epsilon is used in the "reverse cat-face" emoticon.

Unicode

Initial

References

Further reading

Hoffman, Paul; The Man Who Loved Only Numbers. Hyperion, 1998. ISBN 0-7868-6362-5.

Category:Greek letters Category:Vowel letters