Pi in Binary

Pi in Binary

Take any circle, measure the length of its circumference then measure the length of its diameter and divide the two numbers. You get pi, probably the most famous number in all of mathematics and known for several thousand years.

pi=circumference/diameter

pi=3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132..

The decimal places go on forever and appear to be random.

But this is just one representation of the number, it's pi represented in base 10.

We can represent numbers in any base we please. In base 10 we have 10 symbols 0,1,2,3,...9 and in base n we have n symbols 0,1,2,3,...,(n-1)

The simplest base is base 2, because in that base we have only two symbols 0,1

Base 2 is also call "binary" and writing pi in base 2 makes it look like a computer data stream and even more mysterious. Here's pi in base 2..

pi=11.00100100 00111111 01101010 10001000 10000101 10100011 00001000 11010011 00010011 00011001 10001010 00101110 00000011 01110000 01110011 01000100 10100100 00001001 00111000 00100010 00101001 10011111 00110001 11010000 00001000 00101110 11111010 10011000 11101100 01001110 01101100 10001001 01000101 00101000 00100001 11100110 00111000 11010000 00010011 01110111 10111110 01010100 01100110 11001111 00110100 11101001 00001100 01101100 11000000 10101100 00101001 10110111 11001001 01111100 01010000 11011101 00111111 10000100 11010101 10110101 10110101 01000111 00001001 00010111 10010010 00010110 11010101 11011001 10001001 01111001 11111011 00011011 11010001 00110001 00001011 10100110 10011000 11011111 10110101 10101100 00101111 11111101 01110010 11011011 11010000 00011010 11011111 10110111 10111000 11100001 10101111 11101101 01101010 00100110 01111110 10010110..

What is this data stream encoding? Nobody knows.

Content written and posted by Ken Abbott abbottsystems@gmail.com