From π (PI) to Paradox of a Circle

Kaan Özkordağ/ March 26, 2015

"Makale yi Türkçe okumak için tıklayınız."

PI in Mathematics

As known the constant  π (PI) would be called as Archimedes constant or Ludolph number. We use this constant to find out the length of the perimeter of the circle or area basically .  And the number π (PI) has infinite  digits after comma.  And that is why this constant is so interesting for mathematicians , it is endless .  We can show the first 1000 digits as below and  it goes on …

3,14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679 82148086513282306647093844609550582231725359408128 48111745028410270193852110555964462294895493038196 44288109756659334461284756482337867831652712019091 45648566923460348610454326648213393607260249141273 72458700660631558817488152092096282925409171536436 78925903600113305305488204665213841469519415116094 33057270365759591953092186117381932611793105118548 07446237996274956735188575272489122793818301194912 98336733624406566430860213949463952247371907021798 60943702770539217176293176752384674818467669405132 00056812714526356082778577134275778960917363717872 14684409012249534301465495853710507922796892589235 42019956112129021960864034418159813629774771309960 51870721134999999837297804995105973173281609631859 50244594553469083026425223082533446850352619311881 71010003137838752886587533208381420617177669147303 59825349042875546873115956286388235378759375195778 18577805321712268066130019278766111959092164201989…


The Eternity Between Two Dots

Another interesting side of π (PI) is that it doesn’t include any  iterative bunch of digits  . This means that we have a number with an infinite number after comma that has infinite digits of numbers that comes together by infinite combination.

Now ; if we are clear on that; we can talk about the paradox of the circle;

A circle’s perimeter ,  – which has a diameter  value is  one unit –  ,  is  π (PI).  If we must show the perimeter of the circle as a line on a ruler it will show us a number between 3 and 4 units. But if we look closer  to the digits after the coma of π (PI) we could obtain the constant π by adding every digits infinite times as  ; “π= 3 + 0,1 + 0,04 + 0,001 ….”  endless times for every digit.  So if we are adding  a positive number  to another positive number  for  infinite times  then can we say this number goes to infinite as value. And then could we say the perimeter  of the circle goes to infinite or not ?

This circle paradox has an answer:

Of course π  does not go to infinite , just the digits after 3 goes to infinite . So every rate of rational number that forms π goes to 0(zero) . So π goes to 4 but never reaches to 4 . It is not important how long or how short ,basically ,  a line consists of infinite number of dots.  And you can never show the real π number on a ruler. Because it continuously moves to 4 😉

See you  …

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