The symbol Sigma fly can se seen below and its meaning will be incorporated into the design/appearance of his logo. Some of the research I've been doing into the symbol can be seen below.

Typically the capital sigma symbol, Σ , is used to indicate summation, or the sum of the series of terms that follow. For example:

Σa_n = the sum of the values of "a_n" from some initial value of n to some ending value

Σa_n = a_0 + a_1 + a_2 + a_3 + ...

There are three sigma symbols, an upper case, a lower case and an end of the sentence case.

The capital letter case is used as summation.

The lower case is used to represent variance in statistics.

The lower case is also used to represent stress in mechanics and physics.

**Upper case**

Upper case Σ is used as a symbol for:

the summation operator

a class of baryons in particle physics

macroscopic cross sections in nuclear and particle physics

self-energy in condensed matter physics

the balance of the invoice classes and the overall amount of the debts and demands in economics

the set of symbols that form an alphabet in linguistics and computer science

the covariance matrix of a set of random variables in probability theory and statistics, sometimes in the form to distinguish it from the summation operator.

__Lower case__
Lower case σ is used for: sigma bonds in chemistry to represent an unknown angle in mathematics

__Sigma constant in science &__

**the sigma receptor in biology**

the standard deviation of a population or probability distribution in statistics

a quality model for business, Six Sigma, based on the standard deviation, often referred to as "6σ"

sigma-algebras, sigma-fields and sigma-finiteness in measure theory; more generally, the symbol σ serves as a shorthand for "countably", e.g. a σ-compact topological space is one that can be written as a countable union of compact subsets.

the generated sigma-algebra of a set is denoted

the sum-of-divisors function in number theory

the Stefan–Boltzmann constant

the "sigma factor" of RNA polymerase

a measure of electrical conductivity

the Surface charge density in electrostatics

Normal stress in continuum mechanics

volatility of a stock generally needed for options pricing

a syllable in phonology

the spectrum of a matrix , denoted as , in applied mathematics

surface tension

the unary operation of selection on a database relation in relational algebra

the Pauli matrices in quantum mechanics

a target's radar cross-section (RCS) in radar jamming or Electronic Warfare (EW)

the life span of a basic multicellular unit (BMU) in bone remodeling

the Damping Parameter in Signal processing

a millisecond in early 20th century physiology literature.

__Politics__
During the 1930s, an upper case Σ was in use as the symbol of the Ação Integralista Brasileira, a radical right-wing party in Brazil.

__CLAUDIAN LETTERS - WHERE SIGMA ORIGINATES FROM__
The Claudian letters were developed by, and named after, the Roman Emperor Claudius (reigned 41–54). He introduced three new letters:

Ↄ or ↃϹ/X (antisigma) to replace BS and PS, much like X stood in for CS and GS. The shape of this letter is disputed, however, since no inscription bearing it has been found. Franz Bücheler identified it with the variant Roman numeral Ↄ, but 20th century philologists, working from copies of Priscian's books, believe it to instead resemble two linked Cs (Ↄ+Ϲ), which was a preexisting variant of Greek sigma, and easily mistaken for X by later writers.

Ⅎ, a turned F or digamma (digamma inversum) to represent consonantal U ([w]/v).

Ⱶ, a half H. The value of this letter is unclear, but perhaps it represented the so-called sonus medius, a short vowel sound (likely [ɨ] or [ʉ]) used before labial consonants in Latin words such as optumus/optimus The letter was later used as a variant of y in inscriptions for Greek upsilon (as in Olympicus). It disappeared because the sonus medius itself disappeared from spoken language.

These letters were used to a small extent on public inscriptions dating from Claudius' reign, but their use was abandoned after his death. Their forms were probably chosen to ease the transition, as they could be made from templates for existing letters. He may have been inspired by his ancestor Appius Claudius the Censor, who made earlier changes to the Latin alphabet. Claudius did indeed introduce his letters during his own term as censor, using arguments preserved in the historian Tacitus's account of his reign, although the original proclamation is no longer extant.

After doing alot of research into the symbol sigma and starting to grasp what is means in terms of mathematics, it has given me alot of visual ideas I can translate into design. The sum of the series of terms that follow, is the main definition for simga, I plan on trying to play with this theory by using its definition to drive my design. A series of terms that follow could be communicated by characters following each other, imitating each other, appearing like a mathematic equation, using a serif typeface for the main branding to imitate Roman numerals and the Claudian Letterform.

The videos below explain Six simgma distribution curves, I'm going to plot my clients tracks across a distribution curve to be used across his CD and vinyl. This could also work in terms of using this distribution method to layout type or image, each point could correlate to a different position within a gridding system.

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__SUMMATION - WHAT SUMMATION IS AND HOW IT RELATES TO SIGMA__

Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well:vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid). For finite sequences of such elements, summation always produces a well-defined sum (possibly by virtue of the convention for empty sums).

Summation of an infinite sequence of values is not always possible, and when a value can be given for an infinite summation, this involves more than just the addition operation, namely also the notion of a limit. Such infinite summations are known as series. Another notion involving limits of finite sums is integration. The term summation has a special meaning related to extrapolation in the context of divergent series.

The summation of the sequence [1, 2, 4, 2] is an expression whose value is the sum of each of the members of the sequence. In the example, 1 + 2 + 4 + 2 = 9. Since addition is associative the value does not depend on how the additions are grouped, for instance (1 + 2) + (4 + 2) and 1 + ((2 + 4) + 2) both have the value 9; therefore, parentheses are usually omitted in repeated additions. Addition is also commutative, so permuting the terms of a finite sequence does not change its sum (for infinite summations this property may fail; see absolute convergence for conditions under which it still holds).

There is no special notation for the summation of such explicit sequences, as the corresponding repeated addition expression will do. There is only a slight difficulty if the sequence has fewer than two elements: the summation of a sequence of one term involves no plus sign (it is indistinguishable from the term itself) and the summation of the empty sequence cannot even be written down (but one can write its value "0" in its place). If, however, the terms of the sequence are given by a regular pattern, possibly of variable length, then a summation operator may be useful or even essential. For the summation of the sequence of consecutive integers from 1 to 100 one could use an addition expression involving an ellipsis to indicate the missing terms: 1 + 2 + 3 + 4 + ... + 99 + 100. In this case the reader easily guesses the pattern; however, for more complicated patterns, one needs to be precise about the rule used to find successive terms, which can be achieved by using the summation operator "Σ". Using this sigma notation the above summation is written as:

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The videos below explain Six simgma distribution curves, I'm going to plot my clients tracks across a distribution curve to be used across his CD and vinyl. This could also work in terms of using this distribution method to layout type or image, each point could correlate to a different position within a gridding system.

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The statistical representation of Six Sigma describes quantitatively how a process is performing. To achieve Six Sigma, a process must not produce more than 3.4 defects per million opportunities. A Six Sigma defect is defined as anything outside of customer specifications. A Six Sigma opportunity is then the total quantity of chances for a defect. Process sigma can easily be calculated using a Six Sigma calculator.

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