# What is the true value of pi ?

May 4, 2017

The true value is $\pi$, an approximation would be $3.141592653589793238462643383279502884197169399$

#### Explanation:

$\pi$ is irrational and infinitely long, it never ends, so we can never write it's true value as a decimal number, it's true value can only be referred to as $\pi$

May 17, 2017

$\pi$ is the ratio between the circumference of a circle and its diameter.

#### Explanation:

$\pi$ is definable as the ratio between the circumference of a circle and its diameter.

It is an irrational number, a little over $3$. As such, it cannot be expressed in the form $\frac{p}{q}$ for any integers $p , q$ and its decimal expansion neither terminates nor repeats.

In fact, $\pi$ is a transcendental number. That is, it is not the root of any polynomial equation with integer (or rational) coefficients.

We can find some infinite series that we could use to find approximations to $\pi$. The most obvious is probably one of the least useful ones, in that it converges very slowly:

${\tan}^{- 1} x = x - {x}^{3} / 3 + {x}^{5} / 5 - {x}^{7} / 7 + \ldots$

and

$\tan \left(\frac{\pi}{4}\right) = 1$

So:

$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \frac{1}{11} + \ldots\right)$

There are much more effective methods.

About $1500$ years ago, a Chinese mathematician Zu Chongzhi using counting rods, effectively calculated the ratio between the perimeter of a polygon with more than 20000 sides and its diameter. He discovered the very accurate approximation:

$\pi \approx \frac{355}{113} \approx 3.1415929$

May 18, 2017

Pi (π) is the ratio of a circle’s circumference to its diameter. Pi is a constant number, meaning that for all circles of any size, Pi will be the same.

The diameter of a circle is the distance from edge to edge, measuring straight through the center. The circumference of a circle is the distance around.

If you're looking for what numbers there are in pi, it's below. It's just a shortened version. Look at http://www.piday.org/million/ for full.

#### Explanation:

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151557485724245415069595082953311686172785588907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676783744944825537977472684710404753464620804668425906949129331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992458631503028618297455570674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980742654252786255181841757467289097777279380008164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179049460165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848862694560424196528502221066118630674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745530506820349625245174939965143142980919065925093722169646151570985838741059788595977297549893016175392846813826868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388439045124413654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226

Dec 9, 2017

As you know, $\pi$ is the ratio between the circumference and the diameter of a circle. There are many approximations for $\pi$. Mine is a unique one.

#### Explanation:

In 1914, an Indian mathematician Ramanujan provided this expression as the approximation of $\pi$

$\sqrt[4]{{9}^{2} + \left({19}^{2} / 22\right)}$

Which is quite accurate.