Sigma

Sigma is the eighteenth letter of the Greek alphabet. It looks like a large capital "S" in its uppercase form (Σ), and it has a smaller form (σ) that changes at the end of words to look like a smaller "s" (ς).

In a system called Greek numerals, sigma stands for the number 200. In math, the uppercase sigma (Σ) is a symbol that means "add up" or "sum." It tells us to add together a group of numbers.

The letter sigma also influenced other alphabets. The Latin letter "S" comes from sigma, and the Cyrillic letter "Es" (С) comes from an older, rounded version of sigma. This shows how one letter can affect many writing systems around the world.

History

The Greek letter sigma (Σς) is shaped like an old letter called shin from the Phoenician alphabet.

Early Greeks may have called sigma san, but it later became known as sigma. Some think the name comes from a Phoenician letter called samekh, while others think it was named for the "hissing" sound it makes.

During the Hellenistic period (4th–3rd century BC), writers changed sigma to a C-like shape, called the lunate sigma. This shape is still used in special fonts in Greece, especially in religious writing and old Greek texts. Different forms of lunate sigma were used as special marks in ancient books and documents.

Uses

Language and linguistics

In both Ancient and Modern Greek, the sigma makes a special sound. In Modern Greek, this sound changes based on the letters that follow it.

The big letter Σ was borrowed into the Latin alphabet to help create new letters. In studying languages, σ helps count syllables. In studying old languages, Σ helps describe ancient sounds.

Science and mathematics

Mathematics

In math, lowercase σ often shows angles or is a short way to say “countably.” The big Σ is used for adding numbers together.

In logic, Σ shows groups of statements with certain rules. In statistics, σ stands for how spread out numbers are. In topology, σ-compact means a space can be made from smaller simple pieces. In math and chance, σ-algebra is a way to group sets.

In number theory, σ is part of functions that add up divisors of numbers. In applied math, σ shows the range of options for maps. In complex math, σ is used in special functions. In chance and statistics, Σ shows relationships between changing values. Spectral analysis also uses σ for spread.

Biology, physiology, and medicine

In living things, σ receptors are special parts on cells. In the study of body chemicals, the σ factor helps with making RNA. In bone study, the sigma period is an old term for how long bones change. In old body studies, σ was used for very short time pieces.

Business, finance, and economics

In money matters, σ shows how much prices change. In keeping money records, Σ shows totals of debts. In big money studies, σ is used in equations to show how easy it is to switch between things. In making things, Six Sigma is a way to make very few mistakes.

Chemistry

In chemistry, σ bonds are the strongest way atoms stick together. In chemistry of organs, σ shows a value in special equations. In old chemistry magic, Σ was sometimes used for sugar.

Engineering and computer science

In computer study, Σ shows all the symbols in a set. In relating things, σ helps pick out certain parts. In learning machines, σ is part of a special curve formula. In radar trickery or electronic fighting, σ shows how big a target looks on radar. In handling signals, σ shows how much a system slows down. In thinking about computers, Σ is a very busy function. In building, σ shows pressure on materials.

Physics

In nucleus and small part physics, σ shows how big targets are, while Σ shows big targets per length. Σ also shows a constant in heat and light. σ often means how well things carry electricity. In static electricity, σ shows how much charge is on a surface. In studying how materials move and stretch, σ shows normal pressure. In crowded matter physics, Σ shows extra energy. Σ can also show how much things pull apart on surfaces. In tiny world physics, σ shows special math tables. In star studying, σ shows how much things move apart. In star studying, Σ is used to name pairs of stars. In small part physics, Σ stands for a group of baryons.

Organizations

In the 1930s, a big Σ was used by a political group in Brazil. The company Sigma Corporation uses the name but not the letter itself. Sigma Aldrich uses both the name and the letter in its logo.

Unicode

The Greek letter Sigma has many forms used in writing and math. Each form has a special code, called a Unicode number. This helps computers know which symbol to show. Some of these include symbols for capital and small Sigma, bold and italic styles, and special math signs used for adding numbers together.