History Main / ArcNumber

** The number is prominently displayed along the sidelines of the football field.
** It's all over the basketball arena – a sign in the visitors' locker room in the basketball arena reads "Welcome to 7,220'. How's your oxygen?"; signs reminding visitors of the altitude are placed along their path from their locker room to the floor; and "7220[='=]" is painted on both sides of the court.

*** 3.14..., the ratio of a circle's circumference to its diameter, is known as Pi (π). There's also 2π, the ratio of a circle's radius to its circumference. There's a movement to start using that number (represented by Tau (τ)) instead. For example, e[[superscript:iτ]] = 1, sine and cosine both have a period of τ, etc.

*** i, or the square root of -1, is the fundamental constant that is the heart of complex analysis, which is a conduit for other important mathematical items such as the Reimann Zeta Hypothesis and the Fundamental Theorem of Algebra. The relation e[[superscript:iπ]] = -1, which is knwon as the Euler identity, iscalled the most beautiful relation in mathematics.

*** The Prime Numbers (2, 3, 5, 7, 11, 13, 17, 19...) are some of the most important numbers in all mathematics. They are integers whose only factors are 1 and themselves, and show up in numerous circumstances, most notably in The Fundamental Theorem of Arithmetic.
*** The Highly Composite Numbers (1, 2, 4, 6, 12, 24, 36...) are what one could consider "anti-prime" numbers. They have the special characteristic of having more divisors than any integer before them. They are often used in things such as timekeeping (e.g. 60 seconds in a minute, 60 mins in an hour, 24 hours in a day, which tends to get split into the 12 a.m. and 12 p.m. hours) and measurements (12 inches in a foot, 360 degrees in a circle). Then there were historical examples, 12 pennies in a shilling and the Ancient Babylonian Base 60 number system, and Plato specifically mentioning 5040 as a good number to choose for things that would often be split up into groups (land areas, populations, etc.)

*** 1.618..., otherwise known as Phi (Φ), the number at the heart of the Golden Ratio. The Golden Ratio (1.618... or (1+(√5))/2) to 1) can be found everywhere in nature. It really is freaky when you learn more about it. Phi is the ratio where a portion of a line is to another portion as the whole is to the first portion, i.e. (Φ+1)/Φ=Φ. Additionally, Φ[[superscript:2]] =Φ+1 and Φ[[superscript:-1]] (or 1/Φ)=Φ-1.

*** i, or the square root of -1, is the fundamental constant that is the heart of complex mathematics, which is a conduit for other important mathematical items such as the Reimann Zeta Hypothesis and the Fundamental Theorem of Algebra
*** By the way, e[[superscript:iπ]] = -1.

*** By the way, e[[superscript:iπ]] = -1.

** 12. Its a highly composite number, there's the fact that both a set of 12 and the number 144 (12[[superscript:2]]) have specific names (dozen and gross respectively) attached to them, there's 12 notes in the Western Chromatic Scale, and base-12 often referenced as a good choice for an alternative to base-10 due to its highly composite nature

*** By the way, e[[superscript:iπ]] = -1.

*** The Highly Composite Numbers (1, 2, 4, 6, 12, 24, 36...) are what one could consider "anti-prime" numbers. They have the special characteristic of having more divisors than any integer before them. They are often used in things such as timekeeping (e.g. 60 (5*12) seconds in a minute, 60 mins in an hour, 24 (2*12) hours in a day, which tends to get split into the 12 a.m. and 12 p.m. hours) and measurements (12 inches in a foot, 360 (12*30) degrees in a circle). Then there were historical examples, 12 pennies in a shilling and the Ancient Babylonian Base 60 number system, and Plato specifically mentioning 5040 as a good number to choose for things that would often be split up into groups (land areas, populations, etc.)

*** By the way, e[[superscript:iπ]] = -1.

** The first Feigenbaum constant, 4.669 201 609(...). It turns up in all sorts of chaotic systems and fractals, for example in the ratio of diameters of circles in the well-known Mandelbrot set. The discovery of the number's universality was key in the development of chaos theory.

** 12. Already noted as a highly composite number, but in addition there's the fact that both a set of 12 and the number 144 (12[[superscript:2]]) have specific names (dozen and gross respectively) attached to them, there being 12 notes in the Western Chromatic Scale, and base-12 often referenced as a good choice for an alternative to base-10 due to its highly composite nature

*** Euler's number e, or 2.718... And i, or the square root of -1. By the way, e[[superscript:iπ]] = -1.

*** Not necessarily a number, but the [[http://en.wikipedia.org/wiki/Fibonacci_number Fibonacci sequence]] (1, 1, 2, 3, 5, 8, 13, 21...) appears just as much in nature as Phi (which makes sense seeing as they're related).

* 3.14..., the ratio of a circle's circumference to its diameter, is known as Pi (π). There's also 2π, the ratio of a circle's radius to its circumference. There's a movement to start using that number (represented by Tau (τ)) instead. For example, e[[superscript:iτ]] = 1, sine and cosine both have a period of τ, etc.
* 1.618..., otherwise known as Phi (Φ), the number at the heart of the Golden Ratio. The Golden Ratio (1.618... or (1+(√5))/2) to 1) can be found everywhere in nature. It really is freaky when you learn more about it. Phi is the ratio where a portion of a line is to another portion as the whole is to the first portion, i.e. (Φ+1)/Φ=Φ. Additionally, Φ[[superscript:2]] =Φ+1 and Φ[[superscript:-1]] (or 1/Φ)=Φ-1.
* Not necessarily a number, but the [[http://en.wikipedia.org/wiki/Fibonacci_number Fibonacci sequence]] (1, 1, 2, 3, 5, 8, 13, 21...) appears just as much in nature as Phi (which makes sense seeing as they're related).
* The Prime Numbers (2, 3, 5, 7, 11, 13, 17, 19...) are some of the most important numbers in all mathematics. They are integers whose only factors are 1 and themselves, and show up in numerous circumstances, most notably in The Fundamental Theorem of Arithmetic.
* Number e, or 2.718... And i, or the square root of -1. By the way, e[[superscript:iπ]] = -1.
* The first Feigenbaum constant, 4.669 201 609(...). It turns up in all sorts of chaotic systems and fractals, for example in the ratio of diameters of circles in the well-known Mandelbrot set. The discovery of the number's universality was key in the development of chaos theory.
* Averted in programming, where repeatedly using a number whose significance may not be obvious is known as using "magic numbers" or "magic constants"; this is generally thought to be bad style, making code harder to understand. The alternative is to declare a constant, tying a unique name to the number that can be used in place of it.
* Played straight with programing limits, where anyone who didn't know better would wonder why the numbers like 8, 256, and 1024 show up so much. The answer is since data is binary (1 or 0) the amount of data that can be stored in any given number of bits, n, is 2[[superscript:n]]. It also has the effect of causing [[UsefulNotes/PowersOfTwoMinusOne numbers that are]] 2[[superscript:n]] -1 showing up a lot.[[note]]The extra place is reserved for 0.[[/note]] And if one of the bits are being used as a sign bit, you also see -(2[[superscript:n-1]]) and 2[[superscript:n-1]] -1 very often. Note that there are 8 bits in a byte, so n tends to be a multiple of 8. These numbers are most apparent in old {{RPG}}s where the limit to a stat would be 255 a lot.
* While powers of 2 are extremely important to computers, one in particular -- 64 -- gets a lot of attention outside of its numeric meaning. A 32-bit addressing space is limited to only handling 4GB of data in total; 64 bits is the most practical next step and ups that limit to 16 ''exabytes'' [[note]]17 ''million'' terabytes, although most systems only use the lower 48 bits, limiting them to a measly 256 terabytes[[/note]], so it's an important milestone for any given computer architecture to cross. AMD put this into their branding, with the "[=AMD64=]" architecture and "Athlon 64" processors. Even today, modern [=PCs=] are often referred to as "amd64" or "x64" machines to differentiate them from the 32-bit processors of yore. [[note]]The Platform/Nintendo64 got this number from the same place, but it really had no use for the addressing space and just wanted the marketing value of calling itself "64 bit".[[/note]]
* Early PC [=CPUs=] were typically named something-86, after Intel's standard-setting 8086, which was followed by the 286, 386, and 486. While Intel stopped the trend officially with the first Pentiums, AMD and Cyrix continued the tradition for a while with "5x86" and "6x86" processors.

* 10, as the base of the most widely-used number system.
* While not a single number, multiples of 12 are also common due to the fact that 12 is highly divisible without being very large. (e.g. 60 (5*12) seconds in a minute, 60 mins in an hour, 24 (2*12) hours in a day, which tends to get split into the 12 a.m. and 12 p.m. hours, 12 inches in a foot, 360 (12*30) degrees in a circle. Plus the fact that both a set of 12 and the number 144 (12*12) have specific names (dozen and gross respectively) attached to them.) Then there were historical examples, 12 pennies in a shilling and the Ancient Babylonian Base 60 number system.

* Played straight with programing limits, where anyone who didn't know better would wonder why the numbers like 8, 256, and 1024 show up so much. The answer is since data is binary (1 or 0) the amount of data that can be stored in any given number of bits, n, is 2^n. It also has the effect of causing [[UsefulNotes/PowersOfTwoMinusOne numbers that are]] 2[[superscript:n]] -1 showing up a lot.[[note]]The extra place is reserved for 0.[[/note]] And if one of the bits are being used as a sign bit, you also see -(2[[superscript:n-1]]) and 2[[superscript:n-1]] -1 very often. Note that there are 8 bits in a byte, so n tends to be a multiple of 8. These numbers are most apparent in old {{RPG}}s where the limit to a stat would be 255 a lot.

* Played straight with programing limits, where anyone who didn't know better would wonder why the numbers like 8, 256, and 1024 show up so much. The answer is since data is binary (1 or 0) the amount of data that can be stored in any given number of bits, n, is 2^n. It also has the effect of causing [[UsefulNotes/PowersOfTwoMinusOne numbers that are (2[[superscript:n]])-1 showing up a lot.]][[note]]The extra place is reserved for 0.[[/note]] And if one of the bits are being used as a sign bit, you also see -(2[[superscript:n-1]]) and (2[[superscript:n-1]]) -1 very often. Note that there are 8 bits in a byte, so n tends to be a multiple of 8. These numbers are most apparent in old {{RPG}}s where the limit to a stat would be 255 a lot.

* 3.14..., the ratio of a circle's circumference to its diameter, is known as Pi (π). There's also 2π, the ratio of a circle's radius to its circumference. There's a movement to start using that number (represented by Tau (τ)) instead. For example, e^(i*τ)=1, sine and cosine both have a period of τ, etc.

* Number e, or 2.718... And i, or the square root of -1. By the way, e[[superscript:(iπ)]] = -1.

* Played straight with programing limits, where anyone who didn't know better would wonder why the numbers like 8, 256, and 1024 show up so much. The answer is since data is binary (1 or 0) the amount of data that can be stored in any given number of bits, n, is 2^n. It also has the effect of causing [[UsefulNotes/PowersOfTwoMinusOne numbers that are (2^n)-1 showing up a lot.]][[note]]The extra place is reserved for 0.[[/note]] And if one of the bits are being used as a sign bit, you also see -(2^(n-1)) and (2^(n-1))-1 very often. Note that there are 8 bits in a byte, so n tends to be a multiple of 8. These numbers are most apparent in old {{RPG}}s where the limit to a stat would be 255 a lot.

* 3.14..., the ratio of a circle's circumference to its diameter, is known as Pi (π). There's also 2*pi, the ratio of a circle's radius to its circumference. There's a movement to start using that number (represented by Tau (τ)) instead. For example, e^(i*τ)=1, sine and cosine both have a period of τ, etc.
* 1.618..., otherwise known as Phi (Φ), the number at the heart of the Golden Ratio. The Golden Ratio (1.618... or (1+(√5))/2) to 1) can be found everywhere in nature. It really is freaky when you learn more about it. Phi is the ratio where a portion of a line is to another portion as the whole is to the first portion, i.e. (Φ+1)/Φ=Φ. Additionally, Φ^2=Φ+1 and Φ^-1 (or 1/Φ)=Φ-1.

* Number e, or 2.718... And i, or the square root of -1. By the way, e^(i*pi)=-1.

* Music theory is heavily rooted in mathematics, resulting in nigh everything having a specific number associated with it. Of particular note is [[CommonTime 4/4]], and the 7 notes of every major and minor scale.

** Magic rings come in sets of 3, 7, 9, or 1. There are 5 wizards. ''Literature/TheHobbit'' has 13 dwarves (plus one hobbit, picked for the lucky number). ''Literature/TheSilmarillion'' has 7 gods plus 7 goddesses, and 3 Silmarilli. Tolkien sure liked prime numbers. Also, 9.

* Music theory is heavily rooted in mathematics, resulting in nigh everything having a specific number associated with it. Of particular note is [[CommonTime 4/4]], and the 8 notes of every major and minor scale.