March 13, 2017

March 14 has been dubbed Pi Day. That’s because March 14 is often written 3/14, and a decimal approximation of pi is 3.14. But that’s only if you use decimals and our style of writing dates. In some countries, it is customary to list the date first followed by the month; for example, March 14 would be 14-3 in some places. Consequently, some places celebrate Pi Approximation Day on July 22, because that date can be written as 22-7, and a fractional approximation of pi is 22/7. What percentage of the year occurs between Pi Day and Pi Approximation Day? Express your answer to the nearest whole number.

There are 17 days in March after Pi Day. Then, there are 30 days in April, 31 in May, 30 in June and 22 in July, for a total of 130 days. So, 130/365 = 0.356, or roughly 36% of the year occurs between these two dates.

 

To twelve decimal places, pi is 3.141 592 653 589 793… What percent of the year has passed on 3/14 at 1:51:29 a.m.? Express your answer to the nearest tenth.

Until March 14 in a non-leap year, there are 31 + 28 + 13 days. The one hour until 1 a.m. is another 1/24 of a day, the additional 51 minutes is 51/(24 × 60) = 51/1440 of a day, and the 29 seconds is 29/(24 × 60 × 60) = 29/86,400 of a day. In total, then, that’s 72.07738 days, which is 72.07738/365 = 0.19747, or 19.7%, of the year.

 

Lisa Hoffman said that, “Love is like pi – natural, irrational, and very important.” And a famous quote asks, “How do I love thee? Let me count the ways.” In 2010, a computer built by Shigeru Kondo and Alexander Yee did just that – counted the number of ways to love pi. It calculated 5 trillion digits of pi in 90 days. How many digits is that every second?

We that 5 trillion is 5 × 1012, and 90 days is 90 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute = 7,776,000 seconds. So, the number of digits counted per second is 5 × 1012 ­÷ 7,776,000 643,004.

 

Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.
Page 2
contains ONLY PROBLEMS.