Chinese numerologySome numbers are believed by some to be auspicious or lucky (吉利, ) or inauspicious or unlucky (不吉, ) based on the Chinese word that the number sounds similar to. The numbers 2, 3, 6, and 8 are generally considered to be lucky, while 4 is considered unlucky. These traditions are not unique to Chinese culture, with other countries with a history of Han characters also having similar beliefs stemming from these concepts. The number 0 (零, ) is the beginning of all things and is generally considered a good number, because it sounds like 良 (pinyin: liáng), which means 'good'.
72 (number)72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen (i.e., 60 in duodecimal). Seventy-two is a pronic number, as it is the product of 8 and 9. It is the smallest Achilles number, as it's a powerful number that is not itself a power. 72 is an abundant number. With exactly twelve positive divisors, including 12 (one of only two sublime numbers), 72 is also the twelfth member in the sequence of refactorable numbers.
Japanese numeralsThe Japanese numerals are the number names used in Japanese. In writing, they are the same as the Chinese numerals, and large numbers follow the Chinese style of grouping by 10,000. Two pronunciations are used: the Sino-Japanese (on'yomi) readings of the Chinese characters and the Japanese yamato kotoba (native words, kun'yomi readings). There are two ways of writing the numbers in Japanese: in Arabic numerals (1, 2, 3) or in Chinese numerals (一, 二, 三).
14 (number)14 (fourteen) is a natural number following 13 and preceding 15. In relation to the word "four" (4), 14 is spelled "fourteen". Fourteen is the seventh composite number. It is specifically, the third distinct Semiprime, it also being the 3rd of the form (2.q) , where q is a higher prime. It has an aliquot sum of 8, within an aliquot sequence of two composite numbers (14,8,7,1,0) to the Prime in the 7-aliquot tree. 14 is the first member of the first cluster of two discrete semiprimes (14, 15) the next such cluster is (21, 22).
Unary numeral systemThe unary numeral system is the simplest numeral system to represent natural numbers: to represent a number N, a symbol representing 1 is repeated N times. In the unary system, the number 0 (zero) is represented by the empty string, that is, the absence of a symbol. Numbers 1, 2, 3, 4, 5, 6, ... are represented in unary as 1, 11, 111, 1111, 11111, 111111, ... Unary is a bijective numeral system.
PrimorialIn mathematics, and more particularly in number theory, primorial, denoted by "#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers. The name "primorial", coined by Harvey Dubner, draws an analogy to primes similar to the way the name "factorial" relates to factors. For the nth prime number pn, the primorial pn# is defined as the product of the first n primes: where pk is the kth prime number.
Unit fractionA unit fraction is a positive fraction with one as its numerator, 1/n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc. When an object is divided into equal parts, each part is a unit fraction of the whole. Multiplying two unit fractions produces another unit fraction, but other arithmetic operations do not preserve unit fractions.
Squared triangular numberIn number theory, the sum of the first n cubes is the square of the nth triangular number. That is, The same equation may be written more compactly using the mathematical notation for summation: This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE). Nicomachus, at the end of Chapter 20 of his Introduction to Arithmetic, pointed out that if one writes a list of the odd numbers, the first is the cube of 1, the sum of the next two is the cube of 2, the sum of the next three is the cube of 3, and so on.
Centered hexagonal numberIn mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal numbers: {|style="min-width: 325px;"| ! 1 !! !! 7 !! !! 19 !! !! 37 |- style="text-align:center; color:red; vertical-align:middle;" | +1 || || +6 || || +12 || || +18 |- style="vertical-align:middle; text-align:center; line-height:1.
Square pyramidal numberIn mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes. As well as counting spheres in a pyramid, these numbers can be described algebraically as a sum of the first positive square numbers, or as the values of a cubic polynomial.
