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Aziz Inan is fascinated by numbers.

(The University of Portland's The Beacon)

Aziz Inan is more interested in the mathematics of 3/14/15 than he is in the pie many will eat to celebrate Saturday.



He and Peter Osterberg, a fellow engineering professor at the University of Portland, ran the numbers and discovered a dozen facts about the day.



We spoke with Inan -- an animated, too-smart-for-journalists type -- about this once-in-a-century day. For more on the mysteries he has unraveled, check out his article at the end of the Q&A.



Q. When did you first hear about pi?



A. I don't remember exactly but most likely when I was in middle school, maybe in a geometry class.



Q. How do you explain the concept to those who barely made it through algebra?



A. Pi is an amazing number. It pops up in so many different places. It's not just in mathematics or engineering. It's a fascinating number. It's mysterious. It's irrational. It has non-stop digits. It's very magical. Sometimes it makes you think who created this number?



Q. But what is it exactly?



A. It is basically for every circle, it's the ratio of the perimeter or circumference -- I always get confused whether it's perimeter or circumference for a circle -- divided by its diameter. That's how people stumbled on it. This was almost three or four millennia ago. No matter how big the circle is, the circumference divided by its diameter is approximately the same number.



Q. How do you go about finding these hidden gems? Do you start experimenting?



A. For more than five years now, I have been fascinated with numbers. I look at calendar dates. I try to identify special calendar dates. You can write them as seven- or eight-digit numbers. I have stumbled on so many special calendar date numbers. That led to other things. I started looking at people's birthdays, including their birthday number and their age. I try to look for patterns or coincidences. Then I started looking at pi because I knew the special pi day was coming up. When I started looking at the digits of pi six months ago, I started seeing some patterns. That made me continue looking at more of relationships between the digits.



Q. What's your favorite discovery you made?



A. If you split the first six digits into two three-digit numbers, there are many connections. For instance, 314 is two times 157. Those two numbers are the prime factors of 314. One of the fascinations I have is palindrome dates. The neat thing about palindrome dates is I can read numbers from both directions. I took 159 and reversed it to 951. What 951 happens to be is three times 317. The difference of the prime factors of 951 yields 317 - 3 = 314, the first three digits of pi.



How nobody observed it for millenniums, that is fascinating to me. Those six digits are so well known, but nobody paid attention, split them into two three digit numbers and saw this prime factor connection. Fascinating! It's like somebody breaking a code.



Q. You write in your article that 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. Any idea how long mathematicians have been looking for hidden properties within the number?



A. People in the second millennium, up to year 2000, most of the time just tried to calculate pi more precisely. I don't think anybody did what I did.



Q. For most people who went through high school, pi is the longest number out there. Are there any numbers that are longer?



A. There is no end to it. It's infinite. Some scientists are still calculating it to more precise digits. There is another number called e. It also has infinite digits. Another one is the square root of 2. There are some numbers that consist of infinite digits.



Q. Pie companies celebrate this day, too. What's your favorite slice?



A. I like apple pie. One of my students who graduated a year ago, he sent me an email saying Dr. Inan I enjoyed your number connections. He told me, 'On that day I am going to eat my pie at 9:26:53 a.m. and 9:26:53 p.m.' I said, 'Ben, I am going to do the same thing.' This is not going to happen again in this century.





Inan and Osterberg's article:

Some Interesting Numerical Properties "Hidden" Within the Digits of Pi

Pi Day is celebrated around the world every year on March 14 (3/14, or simply 314) because 314 constitutes the first three digits of number pi. This year, Pi Day is expressed as 3/14/15 (31415) and is particularly unique since 31415 represents the first five digits of pi. This once-in-a-century Pi Day piqued our curiosity and motivated us to revisit the number pi, in search of finding some undiscovered interesting numerical properties "hidden" within its digits.



Historically, pi (or p), the ratio of any circle's circumference to its diameter, have fascinated and inspired mathematicians for four millennia [1-4]. Using basic experimentation, 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 16th and 17th centuries. Infinite series allowed mathematicians to compute pi with much greater precision than ever before.



Pi is an irrational number, meaning that it cannot be written as the ratio of two integers. Since p is irrational, it has an infinite number of digits, and does not appear to settle into a repeating pattern of digits.



Using 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 pattern 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 p is normal has not yet been proven or disproven.



In this article, numerous "hidden" number connections are revealed between the digits 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.

The following "hidden" properties were observed:

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.)

The reverse of the next three digits of pi, 159, is 951. Interestingly enough, the difference of the prime factors of 951 yields 317 - 3 = 314, the first three digits of pi.

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 (7th to 9th) of pi.

The product of 159 and the reverse of 265 (562) yields 89358, where the rightmost three digits (358) are the next three digits (10th to 12th) of pi. Also, interestingly enough, if 89358 is split into numbers 893 and 58, these two 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.

If the 5th to 12th digits of pi (59265358) are split as 59, 265, and 358, the sum of 59, the reverse of 265 (562), and 358 equals 979, which is the next three digits (13th to 15th) of pi.

Subtracting twice 314 from 951 (the reverse of 159) yields 323, the next three digits (16th to 18th) of pi. Also, the reverse of 323 plus 1 equals 3 times 141, where 3 and 141 side-by-side constitutes the first four digits of pi.

323 plus 1 times 2 yields 648, the reverse of which is 846, which corresponds to the next three digits (19th to 21st) of pi. Also, 141 (the 2nd to 4th digits of pi) times the sum of its digits yields 846.

265 minus 1 yields 264, the next three digits (22nd to 24th) of pi, and since 264 equals 33 times 8, 33 and 8 put side-by-side makes 338, which constitutes the next three digits (25th to 27th) of pi.

Numbers 846, 264, and 338 (which side-by-side as 846264338 constitute the 19th to 27th digits of pi) are numerically connected in an interesting way: Reverse of 264 (462) multiplied by reverse of 338 (833) yields 384,846 where the rightmost three digits are 846. In addition, if 384,846 is split in the middle as 384 and 846, 846 minus 384 results in 462, which is the reverse of 264.

979 (which corresponds to the 13th to 15th digits of pi) plus 2 divided by 3 yields 327, the next three digits (28th to 30th) of pi.

One less than 951 (the reverse of 159, the 4th to 6th digits of pi) is 950, the next three digits (31st to 33rd) of pi. In addition, 723 (which is the reverse of 327, the 28th to 30th digits of pi) plus the reverse of one less than 723 also equals 950. Also, 592 (the 5th to 7th digits of pi) plus 358 (the 10th to 12th digits of pi) yield 950.

The difference of 626 (the 21st to 23rd digits of pi) and 338 (the 25th to 27th digits of pi) is 288, the next three digits (34th to 36th) of pi. Also, 338 plus twice 288 yields 914, the reverse of which is 419, corresponding to the next three digits (37th to 39th) of pi. (Also, note that 914 equals 626 plus 288.)

Twice 358 (the 10th to 12th digits of pi) yield 716, the next three digits (40th to 42nd) of pi.

Three times half of the difference of the reverse of 419 (the 37th to 39th digits of pi) and 288 (the 34th to 36th digits of pi) yields 939, the next three digits (43rd to 45th) of pi. And, 939 minus 2 results in 937, which constitute the next three digits (46th to 48th) of pi. Also, interestingly enough, 937 is the 159th (the 4th to 6th digits of pi) prime number.

The authors find these "hidden" properties fascinating. And there probably exist many more interesting undiscovered properties hidden within the number p which the authors will continue to investigate. And, who knows, maybe the findings of this article will someday lead mathematicians to make a "breakthrough" to prove or disprove, once and for all, if p is a normal irrational number. And, by the way, next year's Pi Day (3/14/16 or 31416) is also interesting since 3.1416 is the value of pi "rounded off" to 5 significant figures.

-- Casey Parks

503-221-8271

cparks@oregonian.com; @caseyparks