p is the ratio of the cirumference of a circle to its diameter. Interestingly, p shows up in all kinds of places. There are many nifty ways to compute p on a handheld calculator. p also shows up in the formula for the famous "bell curve" (officially called a normal distribution). This curve explains all kinds of stuff: sizes of animals, IQ scores, levels of various chemicals in our blood, even coin tosses. Yes -- p actually has something to do with coin tossing! Below you'll find a silly quiz about p.
There's also some information on approximations to p.
from MathCounts, published in quality papers around the world.
Let me Count the Ways. . .
Lisa Hoffman said "Marriage is like p--natural, irrational and very important." Some might draw the analogy between love and p, too, in that both go on forever. Valentine's Day just passed, and every year this holiday is celebrated on February 14. Math folks celebrate p Day, which occurs on March 14. (Admittedly, fewer cards are sent on p Day than on Valentines' Day.)
On average, how many hours pass between Valentines' Day and p Day?
To this, let me add a second question.
Why is March 14 p Day?
Before proceeding to the solutions, let's review the history of p. Here are the best known approximations to the value of p for a variety of dates. Strikethrough is used at the first place in error.
|Date (source, if available)||Approximate value of p|
|1650 B.C. (Rhind Papyrus)||(4/3)4 = 3.1
|approx. 250 B.C. (Archimedes of Syracuse)||Between 3.14103 and 3.14271|
|Bible (1 Kings vii 23)||3.
|approx 150 (Ptolemy)||3.1416...|
|approx 500 (Tsu Ch'ung-chih)||355/113 = 3.141592
|1621 (van Ceulen)||3.1415926535897932384626433832795028
|1699 (Abraham Sharp)||3.14159265358979323846264338327950288419716939937510582097494459230781640
|1706 (John Machin)||3.1415926535897932384626433832795028841971693993751058209749445923078164062865089986280348253421170679...
(Correct to 100 places)
|1873 (Shanks)||Correct to 527 places.|
|1946 (Ferguson)||Correct to 710 places.|
|1947 (Wrench)||Correct to 808 places.|
|Here marks the beginning of the age of the computer. From this point on computers have been used to obtain approximations for p. The first value below was obtained by the ENIAC computer, programmed by the U.S. Army.|
|1949||Correct to 2037 places.|
|1959||Correct to over 16,000 places.|
|1966||Correct to over 250,000 places.|
|1980||Correct to over 500,000,000 places.|
|Today||Correct to about 1,000,000,000,000 places? Anybody know how many? E-mail me if you do. Anybody know what they are? Want to type them onto a web page?|
There probably is no application in the world that requires an approximation any better than the 1424 version; the rest is all overkill in a practical sense.
Now, the solutions.