Mathematical significance
σ(n) represents the sum of all positive factors of integer n. Let n decompose the prime factor into
, and then:
Extended data
The Greek alphabet originated from the Phoenician alphabet, which has only consonants and is written from right to left. The vowels in Greek were developed, and the Greeks added vowels. Because the Greek writing tool was a wax board, sometimes the first line was written from right to left, and the last line was written from left to right, which became the so-called "cultivated land" writing, and then gradually evolved into all writing from left to right. The direction of the letters is also reversed.
The Romans introduced the Greek alphabet, changed it into Latin alphabet with a little change, and it became popular all over the world. Greek letters are widely used in academic fields, such as mathematics. Cyrillic letters also evolved from Greek letters.
The English word alphabet (letter) comes from the alphabetum in vulgar Latin, and the alphabetum comes from the Greek word α λ φ α β ο ν (transliteration of Beton), which is the synthesis of the first two Greek letters α(Alpha) and β(Beta).
Greek letters have a far-reaching influence on Greek civilization and even western culture. In the New Testament, God said, "I am Alpha, I am Omega, I am the first, I am the last, I am the beginning and I am the end." (Revelation 22: 13). In the Greek alphabet, the first letter is "α, α", indicating the beginning, and the last letter is "ω, ω" ω, indicating the end. This is the trace of the New Testament written in Greek.
Greek letters used in mathematics, science and engineering.
The Greek alphabet is used in mathematics, science, engineering and other fields.
In mathematics, Greek letters are usually used to represent constants, special functions and some specific variables. In the field of mathematics, the meanings of uppercase and lowercase Greek letters are usually different and irrelevant.
Some capitalized Greek letters are the same or very similar to the corresponding Latin letters, so they are not used, such as: A, B, E, H, I, K, M, N, O, P, T, X, Y, Z. In addition, lowercase ι(iota), ο(omicron) and μ (up Sometimes, font variants of Greek letters have specific meanings in mathematics, such as φ(phi) and π(pi).
In financial mathematics, Greek letters are variables used to represent investment risks.
Mathematicians whose mother tongue is English don't read Greek letters with modern or ancient pronunciations, but read traditional English pronunciations. For example, the letter θ, these mathematicians will read it as [? θeit？ ]。 (In ancient times: [th^ε? Ta], nowadays: [? θita ])
Mathematical style and printing style
The Greek letters used in mathematics are usually different from those in Greek characters: the Greek letters used in mathematics are used independently and are not connected with other letters. In addition, some Greek letters used in mathematics use other styles, rather than those used in printing.
There is a label "mgrk" (mathematical Greek) in the OpenType font format, which can be used to mark that a Greek letter (not Greek) is used in mathematics.
The following table shows the differences between the Greek letters in TEX and HTML. TEX uses italics, because variables should be italics. Because Greek letters are generally used for variables in mathematical formulas, they appear in fonts similar to TEX, which are generally used in books about mathematics.
Baidu Encyclopedia-σ
Baidu Encyclopedia-Greek alphabet