7 Numbers That Are Just as Cool as Pi

We may be celebrate Pi Day here at io9 , but we would be irrational to deny that there ’s more to numerical interest than simply dividing an target ’s circumference by its diam . Here are seven figure we love as much as pi .

1 may be the solitary number , but it ’s the little act that could — the first non - zero integer that expose remarkable attribute of ego - trust . Aside from being the first whole number , it is its own square , cube , and factorial . It ’s also very unregenerate ; when you bring up 1 to any power — even a number as gamy as a googolplex ( 1 followed by 10 to the centesimal mogul , or 10^(10 ^ 100 ) ) — you still get 1 . It ’s the first and 2nd number in theFibonacci sequence . It is neither a composite bit , nor a prime number ( mathematicians rejected this idea because it complicates underlying theorems of arithmetic ) . It is , however , a unit ( like -1 ) . And it ’s the only positive bit that ’s divisible by on the button one positive bit .

Any figure that does n’t in reality exist , but is still useful , has to be see cool . Also called the imaginary unit , i is the square root of -1 ( i2 = -1 ) . This numeral can not live because no turn breed by itself can equal a negative number .

At first , imaginary number were considered useless ( an fanciful act is a number that , when squared , founder a damaging result ; for instance 5i = -25 ) . But by the Enlightenment Era , thinkers began to demonstrate its time value in maths and geometry , include Leonhard Euler , Carl Gauss , and Caspar Wessel ( who used it when working with complex planes ) . They ’re utile in that they can be used to find the square stem of a real negative number .

Today , i is used in signal processing , control hypothesis , electromagnetism , fluid dynamics , quantum grease monkey , cartography , and palpitation analysis . The figure j is often substituted in these field of battle , which is used to map the galvanizing field current . The notional number also appears in several pattern , include theEuler Identity .

As an aside , Isaac Asimov ’s short story “ The Imaginary ” ( 1942 ) featured the eccentric psychologist Tan Porus who explain the behavior of a cryptical species of calamari by using imaginary numbers in the equality which describe its psychology .

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merely put , this is the largest useful ( i.e. non - arbitrary ) figure do it to mathematicians . But it ’s an astoundingly large identification number . Named after Ronald Graham , it ’s the upper bound to a certain motion that involvesRamsey Theory(a branch of math that contemplate the condition under which order must appear ) . accordingly , it ’s the biggest number used for a serious numerical proof .

This number ’s “ root ” arises from the extreme addition , generation , and powering of threes . It ’s subsequently a very big power of three , and the number itself is considerably larger than a googolplex . In fact , Graham ’s phone number is so mindboggingly Brobdingnagian that it can not be expressed using established notational system of powers , and even powers of powers . It ’s so gravid , thatif all the material in the universe were turned into pen and ink it would not be enough to write the number down . therefore , mathematicians usea special notation devised by Donald Knuth to verbalise it .

It ’s so full-grown that it ’s physically out of the question for our Einstein to comprehend . AI theorist Eliezer Yudkowskyput it this way :

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Graham ’s act is far beyond my ability to grasp . I can name it , but I can not properly appreciate it … My sentiency of awe when I first encountered this number was beyond run-in . It was the sense of calculate upon something so much bombastic than the world inside my head that my design of the Universe was shattered and rebuilt to agree . All theologian should face a number like that , so they can in good order appreciate what they appeal by talking about the “ unnumerable ” word of God .

Interestingly , if not ironically , the lower bound to the Ramsey problem that gave birth to that phone number — rather than the upper spring — is belike six . short letter : A reader alarm me to thisstudy , which suggests a lower bound raised to 11 , and then to 13 .

The number 0 is totally taken for granted , which , when considering that it stage nothing , is jolly understandable . But it does serve some important functions , include as an empty place - value in our decimal number system . How else , for example , could we express the class 1906 in the decimal scheme without it ?

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Sure , the universe start to mellow when you endeavor to divide by it , but 0 can dish out some important roles in equation , including those that involve addition , multiplication , and subtraction . numbers game can also be raised by the power 0 , which will always produce the value of 1 . And if you raise 0 to power of anything , you still get 0 . But , if seek to do 0 ^ 0 , math goes all squirrely again and the answer becomes basically anything ( an “ indeterminate form ” ) .

last , the sum of 0 numbers is 0 , but the product of 0 number is 1 . And 0 is neither plus , nor negative . It ’s not a premier number , and it ’s not a unit — but it is an even number .

Yes , there ’s a number telephone ‘ e ’ , but it ’s also known as Euler ’s Number . Like pi , it ’s an significant numerical constant , an irrational number that goes like this : 2.71828182845904523536 …

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Named after Leonhard Euler ( 1707 - 1783 ) , it ’s the stand ofJohn Napier ’s Natural Logarithms — the log to the groundwork e , where e is an irrational and non - algebraical number ( what ’s foretell a transcendental unremitting , much like pi ) . Some people relate to it as the natural base . Euler machinate the following formula to calculate e :

e= 1 + 1/1 + 1/2 + 1/(2 x 3 ) + 1/(2 x 3 x 4 ) + 1/(2 x 3 x 4 x 5 ) + . . . ( alternately : 1 + 1/1 + 1/2 ! + 1/3 ! + 1/4 ! + 1/5 ! )

Mathematicians have calculated tocopherol to over a trillion digits of accuracy .

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Euler ’s interest in e come about when calculating continuously combine interestingness on a sum of money . And in fact , the demarcation line for compounding interest group can be evince by the constant e. So , if you put $ 1 at an interest rate of 100 % per year , and the involvement is compounded unceasingly , you will have $ 2.71828 ( or so ) at the end of the twelvemonth .

eastward also shows up in probability theory and theBernoulli trials process(which is helpful for calculating things like probabilities in gambling ) . Other applications let in derangements ( the so - calledhat - check problem ) , asymptotics ( when describing limit behavior , a useful construct in computer science ) , and calculus .

Tau is simply 2pi , or the constant that is equal to the proportion of a traffic circle ’s circumference to its spoke . Thus , tau is write out like 6.283185 …

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Tau is the 19th letter of the Greek first principle and was chosen as the symbol for 2pi by Michael Hartl , a physicist , mathematician , and generator of “ The Tau Manifesto , ” along with Peter Harremoës , a Danish information theorist ( who knew math could get so political ? ) .

Tau is considered by some to be more useful than pi for measuring circle because mathematician be given to use radians instead of degrees . fit in to Kevin Houston from the University of Leeds , the most compelling argument for tau is that it isa much more raw number to usein the fields of mathematics involve circles , like geometry , trig and even advance calculus .

What this means , of path , is that Tau Day should be celebrated on June 28 ( 6/28 ) .

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Also call the Golden Number , Phi ( rime with “ fly ” ) is an important mathematical figure that ’s written out as 1.6180339887 …

Unlike pi , which is a transcendental number , phi is the solvent to a quadratic equation . But like pi , phi is a proportion that ’s defined by geometric construction . Two quantities fit within the golden ratio if the proportion of the total of the quantity to the larger quantity is equal to the ratio of the great measure to the smaller one . Because of its unparalleled property , phi is used in maths , fine art , and architecture . The Greeks key out it as the dividing line in the extreme and mean ratio , and for Renaissance creative person it represented the Divine Proportion .

Phi also has interesting tantamount ratios when the turn one is introduced , like φ:1 is adequate to φ+1 : φ , or 1 : φ-1 . Also , two consecutive fibonacci numbers , when divided , produce a number close to phi . The further through the series , the more accurate ( or detailed ) phi becomes .

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