4

PI day again

Whatdya know ?! Its PI day again. I remember posting on this day, last year about the same event and now, here we are again ! And in case you didn’t know, today is also the birthday of ‘Dr. Einstein’ of the E=mc2 fame 😉
Here’s a tribute to this magic number, π:

History:

  • Biblical References: I Kings 7:23 II Chronicles 4:2
    In Kings, it states, “And he made a molten sea, ten cubits from one brim to the other: it was round all about, and a line of thirty cubits did compass it about.”
  • In 240 B.C, Archimedes of Syracuse, Sicily (287 – 212 BC) did the first theoretical calculation of . He used methods similar to the ones used by Euclid by inscribing a regular polygon inside a circle. He started with a hexagon and then polygons of 12, 24, 48, and finally 96 sides. He also used one of Euclid’s theorems to develop a numerical method for calculating the perimeter of the polygons. Archimedes obtained the approximation 223/71 < π < 22/7.
  • 150 A.D. Ptolemy found π to be approximately 377/120 (or 3.1416)
  • 480 A.D. In China, pi was found to be approximately equal to 355/113 or 3.1415929 …
  • 1150 Bhaskara (a Hindu) gave 3927/1250 as an accurate value of π
  • 1579 Viete used polygons having 393,216 sides to evaluate π correct to 9 places
  • 1610 Van Ceulen used 2^62 sides to compute π to 35 decimal places
  • 1949 ENIAC (first modern computer) spent 70 hours to compute π to 2,037 places
  • In September 2002, π was computed to 1,240,000,000,000 decimal places by Professor Yasumasa Kanada at the University of Tokyo. It took over 400 hours on a Hitachi Supercomputer.

Facts and interesting stuff:

  • All the digits of Pi can never be fully known.
  • William Jones, a self-taught English mathematician born in Wales, is the one who selected the Greek letter π for the ratio of a circle’s circumference to its diameter in 1706.
  • Thirty divided by ten gives a value of 3. However, it is interesting to note that the word circumference happens to be spelled with an extra letter. Since in Hebrew all letters are also numbers, if we take the ratio of the value for the word as it is written (111) to the normal spelled word (106) we get the number 1.047169811… If you multiply this number by 3 you get 3.141509434… An amazingly close approximation to π!
  • The 1983 Guinness Book of World Records lists Rajan Mahadevan from India as having recited 31,811 places of pi from memory !
  • PI poem by Lorreen Pelletier: The number of letters in each line corresponds to a digit in the number &#960, up to 35 decimal places.
  • The value of π can be computed using the fibonacci sequence ! Link.
  • How do you prove that the π exists ?? Here’s an interesting theory.
  • Can you decipher the digits of π using a Sanskrit sloka ? Here’s a demonstration. Interesting read !
  • Here’s π to 1000 digits:
    3. 14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 …
  • Here’s a palindrome for you : “I prefer PI” !!
  • e raised to the i*pi power equals -1 (e is the base of the natural logarithm and i is the imaginary number which is the sqare root of -1)

Alternate π addendum:

Book:
The life of PI – Here PI is an Indian guy’s name who gets stranded in the sea for more than 250 days. Its a good read although it has nothing to do with the π we are dealing with here. Just thought that might be an interesting trivia !
Movie:
PI – The movie starts with the line “When I was a little kid, my mother told me not to stare into the sun, so when I was six I did…”. Now with a line like that, how could i not watch it ! I’d recommend this movie to anyone who’s a little perceptive and frankly, a bit obsessed on math or anything for that matter. I watched the movie and loved it but few of my friends hated me for recommending the movie. So, there you go. But seriously, if you get some time, and are a math fan, watch it !

Links: