Chapter 6: Circle-Number Pi

What is this circle-number pi? How does it work? How accurate is it? How many decimal places does it have behind the comma? And what does that mean? Does the circle-number pi exist only in the mind of a human mathematician? Or does it exist also outside of mankind, independently of mankind? If so: why? What have scientists found out about this now?

Peter Mäder is Professor for Didactics of Mathematics at the National Seminary for School-Pedagogics in Freiburg, S.W. Germany. He says in the journal bild der wissenschaft, June 1993 p. 36, 38, under the heading "Number without an End":

"The facts, upon which this number is based, seem to be quite simple: If we, for example, rolled a round can once around itself, we shall find out, that the ratio between the circumference of this can, thus determined, and its diameter is always of the same size. This number lies between 3.1 and 3.2.

"The fraction c/d (circumference and diameter) is designated according to international custom, with the Greek letter pi. And this also enables us, to calculate the area of the circle: A = pi . r² (area A, radius r = half diameter). Verifying this is already more complicated.

"More than 1 billion figures behind the comma, mathematicians have discovered. Printed out with the computer, this results in a six meter high stack of paper. ... Only now they were sure, that the mathematicians would never come to an end with their pi: There are infinite places behind the comma, and also a period never appears. Still, one does not stop trying, to drive the number of the calculated places behind the comma further up."

"Computers encouraged these efforts. 1676 places behind the comma (calculating time: four hours and three minutes) one calculated in 1959 in Paris, eight years later already 500,000 (in 28 hours). In Tokyo in 1986 one came up to 16,000,000 places. At the beginning of 1988 Yasumasa Kaneda in Tokyo determined 201,326,000 places behind the comma of pi. The calculating time for this was nearly six hours, the result filled 40,266 printed pages."

"The brothers Gregory and David Chudnovsky during the summer of 1989 in New York then passed the billion: 1,001,196,691 places behind the comma of pi. This was the result of nearly three days of calculating time (on IMB-ES/3090), and the printed pile of paper was nearly six meters high." Mäder, P. (1993:38).

 

Pi with "only" 262 Places behind the Comma

The circle-number pi has no end. Prof. Peter Mäder published in bild der wissenschaft, 6/1993 pp. 36, 37, pi with 262 places behind the comma. It has the following numbers behind the figure 3 and its comma. I have separated them into groups of three, so that it will be easier, to read them:

3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844 609 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930 381 964 428 810 975 665 933 446 128 475 648 233 786 783 165 271 201 909 145 648 566 923 4..................

David V. Chudnovsky and Gregory V. Chudnovsky, Department of Mathematics at Columbia University, New York, report in their book Number Theory (1991:14): "Calculation of pi (decimal) expansion, and its analysis, has a long human history... Electronic calculations of pi were initiated by von Neumann and his team. The first 100,000 digit mark was passed by Shanks and Wrench nearly 30 years ago. The first million digit mark was passed in 1973 by Guilloud and Bonyer on CDC 7600 using classical arctan formulas for pi.

"The two million mark was passed in 1981 by Miyoshi and Kanada on FACOM M-200 and by Guilloud. Then Tamura and Kanada computed in 1982 4 million and 8 million digits of decimal expansion of π using HITAC M-280H. In 1983 Kanada and Tamura computed about 16 million digits on Hitachi S-810. Gospher in1985 computed over 17 million decimal digits of (and as many terms in the continued fraction expansion of pi) using only SYMBOLICS workstation. This was the first modern record that did not use supercomputer hardware. In early 1986 Bailey computed over 30 million digits of pi using a newly constructed CRAY 2. Then in 1987 Kanada computed 134 million digits on NEC SX-2 supercomputer. In 1988 Kanada raised his record to 201 million using Hitachi supercomputer S-820/80.

"Our pi computations in December 1988. CRAY 2 computations proceeded at the Minnesota Supercomputer Center in Minneapolis. Computations on IBM 3090 were conducted at the IBM T.J. Watson Research Center at Yorktown Heights. Computations were conducted in shared environments over a period of 6 months. By the end of July, 1989 we had computed over 1,011,000,000 digits of pi on IBM-3090 VF. We stopped our calculations in September, 1989 with over 1,130,000,000 decimal digits of pi.

"These last computations were performed at the T.J. Watson IBM Research Center, Yorktown Heights, on IBM - 3090/200 and IBM - 3090/600. The largest announced Japanese calculation of pi was Kanada’s of 1,073,741,799 digits on S-820-80 (November 1989)." - Chudnovsky, D. and G. (1991:14).

Pi: How Accurate

How accurate is the circle-number pi? How accurate is pi, when using only 4 decimal places behind the comma, 10 decimals, 15 decimals, and 100 decimals?

Heinrich Tietze is Professor for Mathematics at the University of Munich, S. Germany. He states in his book Famous Problems of Mathematics (1965:100) about the circle-number pi: "What does one know about this number pi? That is, about the ratio of a circle-area to the square area with the radius at its side? It is a ratio, which shows us, that it is also the ratio of the circle’s circumference to the circle’s diameter for every circle.

"Four decimal places will suffice for determining the circumference of a circle to within 1 mm, if the radius is 30 meters or less. If the radius is as large as that of the earth, 10 are sufficient. If the circle has a radius as large as the distance of the earth to the sun, 15 places are enough to determine the circumference to within millimeters.

"In order to show the incredible exactitude obtainable with 100 places of pi, consider the following problem: Take a sphere with our earth as its center and extending to Sirius (since the speed of light is 186,000 miles per second, it would take 8.75 years to reach the surface of the sphere from the earth); fill this sphere with microbes, so that every cubic millimeter contains a trillion (1,000,000,000,000) microbes. Now if all these microbes are spread out in a straight line, so that the distance between successive microbes is equal to the distance from the earth to Sirius, and the distance from the first to the last is taken as the radius of a circle, then the error in calculating the circumference of this circle using 100 decimal places of pi, will be less than 1/10 of a millionth of a millimeter."

Present Universe: Its Size

Our universe is now about 12 billion years old. Hence it has now a radius of 12 billion light-years, and a diameter of 24 billion light-years, up to its "Cosmic Horizon", according to Prof. L. M. Krauss (1999:40).

At 100 decimal places behind the comma of pi, the circumference of this circle will have then an error of less than 10/1,000,000 mm. - What does that prove? - It proves to me, that the circle-number pi is able to make a circle, with a radius, enclosing now our whole physical universe. This circle, whose circumference has an error of less than 10/1,000,000 mm (at 100 decimals behind the comma), is thus, able, to contain our whole universe.

Still more Accurate

When using 100 decimal places behind the comma of pi, the mistake made then, when calculating the circumference of this circle, will be then less than 10/1,000,000 mm = 0.0000001. - How large will be then the mistake, when using still more decimal places behind the comma? - I have calculated over 10,000 places behind the comma of pi, to find this out:

At 101 decimal places behind the comma of pi, the mistake made, when calculating the circumference of this huge circle (containing the whole universe within itself), will be 1.10-08 mm. - At 102 decimal places behind the comma of pi, the mistake, when calculating the circumference of this circle, will be then 1.10-09 mm, and so on. This means: With each decimal place behind the comma of pi, the mistake made, when calculating the circumference of this huge circle, will be 1/10 less.

When using 200 decimal places behind the comma of pi, the mistake made, when calculating the circle’s circumference, will be less than 10-106 mm. - When using 500 decimal places behind the comma of pi, the mistake made, when calculating the circle’ circumference, will be less than 10-406 mm.

When using 1,000 decimal places behind the comma of pi, the mistake made, when calculating the circle’s circumference, will be then 10-906 mm. - When using 2000 decimal places behind the comma of pi, the mistake made, when calculating the circle’s circumference, will be less than 10-1754 mm.

When using 5000 decimal places behind the comma of pi, the mistake will be less than 10-4833 mm. - When using 8000 decimal places behind the comma of pi, the mistake will be less than 10-8084 mm.

When using 10,000 decimal places behind the comma of pi, the mistake made, when calculating the circle’s circumference, will be less than 10-10 003 mm. That is, when calculating the circumference of the circle, enclosing our whole physical universe.

 

Size of circle

Decimals of number pi behind comma

Error, when calculating the circle’s circumference, mm

30 meter (or less)

4

1

Radius of earth

10

1

Radius from earth to sun

15

1

Radius 8 ¾ light-years

100

One ten millionth of a millimeter

Present universe, diameter 24 billion light-years

100

Less than 10/1,000,000

dito

101

1.10-08

dito

102

1.10-09

dito

200

10-106

dito

500

10-406

dito

1000

10-906

dito

2000

10-1754

dito

5000

10-4833

dito

8000

10-8084

dito

10 000

10-10 003

 

Result

The circle-number pi (3.131592653.....) determines the ratio of the circumference of the circle to its diameter. Pi has an infinite number of decimals. By the end of July 1989, mathematicians have determined 1,130,000,000 decimal places of pi. - How accurately is pi working?

Pi: Its Information Content

The circle-number pi = 3.131592653... is an endless number (from the human point of view). And a period (= an identical row of numbers) never appears in it. In November 1989 Japan’s Kanada reached 1,073,741,799 digits. And in September 1989, David and Gregory Chudnovsky, at Columbia University, New York, reached over 1,130,000,000 digits of pi.

Let us look now briefly at the over 1,130,000,000 decimal places of pi, determined in New York. - What we would like to find out now: What does one need, to think out this number, and to put each figure at the right place, in the right order? We are not just talking here about so and so many decimal places of zeros; but about decimal places, where each one has its specific number. In other words: What are its sequence alternatives?

One needs only 4 decimal places of pi, to determine the circumference of a circle to within 1 mm, if the radius is 30 m (or less). If the circle is as large as the radius of the earth, 10 decimals will be enough, to determine the circumference of this circle to within 1 mm. And if the radius of the circle has a distance from the earth to the sun, 15 decimals of pi will be enough, to determine its circumference to within 1 mm.

100 decimals of pi will determine the circumference of a circle, that contains our whole physical universe, with its diameter of 24 billion light-years, with an error of less than 10/1,000,000 mm. When using 10,000 decimals of pi, the circumference of the circle will have an error of less than 10-10 003 mm.

1,000,000,000 (109) decimals of pi, behind the comma, have 10600 million sequence alternatives, and just as many bits of information. In other words: 10600 million bits of information were needed, to put the first 1,000,000,000 decimals behind the comma of pi in the right order.

Bernd-Olaf Küppers (1986:96), a leading German evolutionist, uses only ca. 109 nucleotide pairs, when calculating the sequence alternatives of the human genome (DNA-chain). - What was needed, to think out and to make this human genetic code?

Bernd-Olaf Küppers reports: The human genome, with ca. 109 (= 1,000,000,000) nucleotides, has 10600 million sequence alternatives. That is a 1 with 600 million zeros. And each one of these sequence alternatives is a "yes" or "no" decision, or 1 bit of information. This means: 1,000,000,000 decimal digits of the circle-number pi do have just as many bits of information, as the human DNA-chain, when calculated at only 1,000,000,000 nucleotide pairs. We should remember here: There are only some 1078 hydrogen atoms within the whole observable universe!

Pi makes the circles and spheres of the macro-cosmos, of the atoms, nuclei, and interacting particles. It makes them instantaneously, across billions of light-years. Pi is a universal constant. It makes and preserves the spatial and temporal order of the universe. It does not change with time. The circle-number pi exists independently of mankind. Man has only found it and understood it (a little). He has not made it. It has been there already for some 12 billion years. Its mathematics has a non-material, spiritual source: the Creator. It clearly disproves the doctrine of evolution.