Do You Know What’s Hidden Inside That There Pi?

 
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Do You Know What’s Hidden Inside That There Pi? Tau Bate engineering professors Aziz S. Inan, Ph.D., and Peter N\. Osterberg, Ph.D., look at the numerical properties within the digits involved i Day is celebrated around the world every year on March 14 (3/14, or simply 314) be¬ cause 314 constitutes the first three digits of number pi. In 2015, Pi Day expressed as 3/14/15 (31415) was particularly unique since 31415 represents the first five digits of pi. In addition, this next Pi Day (3/14/16 or 31416) is also in¬ teresting since 3.1416 is the value of pi “rounded off’ to 5 significant digits. These two once-in-a-century Pi Days piqued our curios¬ ity and motivated us to revisit the number pi, in search of finding some undiscovered interesting numerical proper¬ ties “hidden” within its digits. Historically, pi (or л), the ratio of any circle’s cir¬ cumference to its diameter, has fascinated and inspired mathematicians for four millennia [1-4]. Using basic ex¬ perimentation, many mathematicians in early civilizations figured out that the length of a rope wound around the circumference of a circle is equal to approximately three times the length of its diameter. The calculation of the digits of pi was revolutionized by the development of infinite series techniques during the 16"' and 17"' centuries. Infinite series allowed mathemati¬ cians to compute pi with much greater precision than ever before. Irrational Number Pi is an irrational number, meaning that it cannot be written as the ratio of two integers. Since л is irrational, it has an infinite number of digits and does not appear to settle into a repeating pattern of digits. U sing powerful computers, mathematicians are now able to compute the value of pi to billions of digits, but still, no one has ever found any evidence that calculating more and more digits of pi will reveal that there is a regular pat¬ tern that exists within its digits. A number consisting of an infinite number of digits is called normal when all possible sequences of digits of any given length appear equally often. The conjecture that pi is normal has not yet been proven or disproven. In this article, numerous “hidden” number connections are revealed between the early digit s of pi. The authors discovered most of these number connections by splitting the digits of pi into groups of three consecutive digits. The following table lists the first 45 digits of pi in groups of three digits. 3.14 159 265 358 979 323 846 264 338 327 950 288 419 716 939 Hidden Properties Revealed The following “hidden” properties were observed: 1 . The prime factors of the first three digits of pi, 314, add up to 2 + 157 = 159, the next three digits of pi. (The prime factors of a positive integer are the prime numbers that divide this integer exactly. For example, 314 = 2 x 157, where 2 and 157 are prime numbers.) 2. The reverse of the next three digits of pi, 159, is 951. Interestingly enough, the difference of the prime fac¬ tors of 951 yields 317 - 3 = 314, the first three digits of pi. (Figure below7 demonstrates how7 the prime factors of the first three digits of pi produce the next three digits of pi and vice versa.) 3. The sum of 314 and 951 (which is the reverse of 159) yields 1265, where the rightmost three digits are 265, corresponding to the next three digits (7"' to 9"') of pi. 4. The product of 159 and the reverse of 265 (562) yields 89358, where the rightmost three digits (358) are the next three digits (10"' to 12"') of pi. Also, interestingly enough, if 89358 is split into numbers 893 and 58, these tw7o numbers add up to 951, which is reverse of 159. In addition, 159 + 265 = 8 x 53, where if numbers 8 and 53 are put side-by-side as 853, the reverse of this number is also 358. 5. If the 5"' to 12"' digits of pi (59265358) are split as 59, 265, and 358, the sum of 59, the reverse of 265 (562), Winter 2016 ф The Bent of tau beta pi 23