Number pi

Puzzles, situation puzzles and recreational mathematics.

situation puzzles and recreational mathematics. Neuron juice
 
 
 

Neuron juice.

The important thing is not to stop questioning. (Albert Einstein.)

  
PI

The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a significant number of the most important mathematicians have contributed to its unfolding —directly or otherwise.

Pi is one of the few mathematical concepts whose mention evokes a response of recognition and interest in those not concerned professionally with the subject.  It has been a part of human culture and the educated imagination for more than twenty-five hundred years.

The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research." (From the introduction of "Pi: a Source Book", by L. Berggren, J. Borwein and P. Borwein.)

 

Definition of pi, by Wikipedia

The number π is a mathematical constant, the ratio of a circle's circumference to its diameter. It is used in mathematics, physics and engineering. The first ten decimals of pi are as follows: 3.1415926535...

 

And one of the definitions I have appreciated the most (thanks to Mr. Marcelo Juarez)

1) Take a cylindrical can.
2) Take some thread.
3) Cut the thread exactly like the perimeter of the cylinder (a complete turn)
4) Number pi means that the thread measures 3 times the diameter of the cylinder and there is a little bit left, which corresponds to 0.14... of the diameter.
That's why it is 3.14... I only got to understand the explanations of the teachers through this kind of examples.

 

History of number pi

The fist known reference to pi is from approximately 1650 BC in Ahmes's Rhind Mathematical Papyrus. It is a document written in a 6m-long and 33cm-wide piece of papyrus. It contains basic mathematical problems, fractions, area and volume calculation, progressions, proportional distribution, rule of three, linear equations and basic trigonometry.
The given value of pi is 28/34 ~ 3.1605.

One of the first approximations was the one given by Archimedes in 250 BC, who calculated its value between 3 10/71 and 3 1/7 (3.1408 y 3.1452) and used in his studies the value 211875/67441 ~ 3.14163.

Leonhard Euler began to use the popular symbol π in 1737 and it became immediately a standard notation.

In the computer age, one of the ways of verifying the effectiveness of a machine was to use it to calculate decimals of pi. In 1949, a ENIAC computer calculated 2037 decimals in 70 hours; in 1966 a IBM 7030 got to calculate 250,000 decimals in 8 hours and 23 minutes; and in the 21st century, in 2004, the supercomputer Hitachi spent 500 hours working to calculate 1.3511 trillion decimals.

 

How to calculate the value of pi

One of the ways of finding out the value of pi is calculating the perimeter of a polygon with many faces which is inside a circle of known diameter. The more faces has the polygon, the similar to the circumference it will look, and its perimeter will be closer to the length of the circumference.

 

Numerical value of pi

Being an irrational number, its value can't be calculated in a numerical way accurately, there will always be another decimal after the latest one. Just out of curiosity, here you have the first 1000 decimals of pi.

 

3.14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679 82148086513282306647093844609550582231725359408128 48111745028410270193852110555964462294895493038196 44288109756659334461284756482337867831652712019091 45648566923460348610454326648213393607260249141273 72458700660631558817488152092096282925409171536436 78925903600113305305488204665213841469519415116094 33057270365759591953092186117381932611793105118548 07446237996274956735188575272489122793818301194912 98336733624406566430860213949463952247371907021798 60943702770539217176293176752384674818467669405132 00056812714526356082778577134275778960917363717872 14684409012249534301465495853710507922796892589235 42019956112129021960864034418159813629774771309960 51870721134999999837297804995105973173281609631859 50244594553469083026425223082533446850352619311881 71010003137838752886587533208381420617177669147303 59825349042875546873115956286388235378759375195778 18577805321712268066130019278766111959092164201989