**Pi **, &pi, was, and still is, the** **sixteenth letter of the Greek alphabet. Its use as the ratio of the circumference to diameter of a circle is relatively modern. The Greeks more often used the letter to stand for **periphery**, the term they used for the circumference of a circle. They did, however, commonly use pi as a number. The Greek number system used 27 letters of the Greek alphabet (including three antiquated symbols) to represent the numbers from one to 900. This allowed them to express any number less than 1000 with only three "digits". In this system, &pi, used as a number would represent 80.

According to Antreas P. Hatzipolakis, the Greeks did not use any particular symbol for the ratio we now refer to with &pi, . In fact, neither did anyone else for a long time. According to Jeff Miller's web page on first usage, "Cajori writes that "perhaps the earliest use of a single letter to represent the ratio of the length of a circle to its diameter" occurs in 1689 in Mathesis enucleata by J. Christoph Sturm, who used e for 3.14159....

si diameter alicuius circuli ponatur a, circumferentiam appellari posse ea (quaecumque enim inter eas fuerit ratio, illius nomen potest designari littera e).Cajori cites a note by A. Krazer in Euleri opera omnia as a reference for the above. "

The first known use of the symbol &pi for its present purposes was in 1706 by William Jones, an English mathematician, although it was the use of the symbol by Euler that brought it its permanency. The St. Louis area Mathematics Educators have a web page for Pi Day that adds

The sixteenth letter of the Greek alphabet, &pi, was first used for the familiar value 3.1415… in the publication, “Synopsis Palmariorium Mathesios”, authored by William Jones in 1706.Teachers looking for activites for March 14th can find a good selection at the Pi Day website.

The Dr. Math FAQ pages have a wonderful link with loads of other information about Pi, its history, and relationship to many areas of mathematics. Here is a brief listing about the known accuracy of Pi Through the Ages as given in the MacTutor Math History site at St Andrews University in Scotland:

Ptolemy_________(c. 150 AD)______3.1416

Tsu Ch'ung Chi__(430-501 AD)_____355/113

al-Khwarizmi____(c. 800 )________3.1416

al-Kashi________(c. 1430)________14 places

Vičte___________(1540-1603)______ 9 places

Roomen__________(1561-1615)______17 places

Van Ceulen______(c. 1600)________35 places

Here is a link to a note about van Ceulen's monument which has his approximation to pi

The above reference also includes a reference to the idea that "The Bible says Pi = 3". Here is a excerpt from the critical parts.

A little known verse of the Bible reads "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about."(I Kings 7, 23)

The same verse can be found in II Chronicles 4, 2. It occurs in a list of specifications for the great temple of Solomon, built around 950 BC and its interest here is that it gives p = 3. Not a very accurate value of course and not even very accurate in its day, for the Egyptian and Mesopotamian values of 25/8 = 3.125 and 10 = 3.162 have been traced to much earlier dates: though in defence of Solomon's craftsmen it should be noted that the item being described seems to have been a very large brass casting, where a high degree of geometrical precision is neither possible nor necessary.

Here is a link to a more recent update of the Chronology of Pi from St Andrews.

So what about the state that passed a law that set Pi = 3? Well, it was in the paper, and on the internet, but it never happened, although it did get close once. A hoax article was printed and widely circulated (on April 1, 1998) that said that NASA engineers in Huntsville, Alabama were upset about the discovery that the Alabama legislature had just passed a law making Pi=3. When the perpetrators of the hoax realized that the article was being paraphrased (without all the hints that it was a joke, such as the authors name, April Holiday) and circulating as truth, they tried to circulate a notice of the hoax, but found the truth spread much more slowly than the sensational story. Here is a link to a site with a copy of the original article. And here is a little more about the real attempt to pass such a law in Indiana, which did NOT pass. Notice that in the proposed bill the idea was from a fellow who had already proved many of the impossible constructions of geometry, such as squareing the circle. Here is a another description of the bizarre incident by Cecil Adams from his web column, "Straight Dope":

It happened in Indiana. Although the attempt to legislate pi was ultimately unsuccessful, it did come pretty close. In 1897 Representative T.I. Record of Posen county introduced House Bill #246 in the Indiana House of Representatives. The bill, based on the work of a physician and amateur mathematician named Edward J. Goodwin (Edwin in some accounts), suggests not one but three numbers for pi, among them 3.2, as we shall see. The punishment for unbelievers I have not been able to learn, but I place no credence in the rumor that you had to spend the rest of your natural life in Indiana.

Just as people today have a hard time accepting the idea that the speed of light is the speed limit of the universe, Goodwin and Record apparently couldn't handle the fact that pi was not a rational number. "Since the rule in present use [presumably pi equals 3.14159...] fails to work ..., it should be discarded as wholly wanting and misleading in the practical applications," the bill declared. Instead, mathematically inclined Hoosiers could take their pick among the following formulae:

(1) The ratio of the diameter of a circle to its circumference is 5/4 to 4. In other words, pi equals 16/5 or 3.2

(2) The area of a circle equals the area of a square whose side is 1/4 the circumference of the circle. Working this out algebraically, we see that pi must be equal to 4.

(3) The ratio of the length of a 90 degree arc to the length of a segment connecting the arc's two endpoints is 8 to 7. This gives us pi equal to the square root of 2 x 16/7, or about 3.23.There may have been other values for pi as well; the bill was so confusingly written that it's impossible to tell exactly what Goodwin was getting at. Mathematician David Singmaster says he found six different values in the bill, plus three more in Goodwin's other writings and comments, for a total of nine.

Lord knows how all this was supposedly to clarify pi or anything else, but as we shall see, they do things a little differently in Indiana. Bill #246 was initially sent to the Committee on Swamp Lands. The committee deliberated gravely on the question, decided it was not the appropriate body to consider such a measure and turned it over to the Committee on Education. The latter committee gave the bill a "pass" recommendation and sent it on to the full House, which approved it unanimously, 67 to 0.

In the state Senate, the bill was referred to the Committee on Temperance. (One begins to suspect it was silly season in the Indiana legislature at the time.) It passed first reading, but that's as far as it got. According to The Penguin Dictionary of Curious and Interesting Numbers, the bill "was held up before a second reading due to the intervention of C.A. Waldo, a professor of mathematics [at Purdue] who happened to be passing through." Waldo, describing the experience later, wrote, "A member [of the legislature] then showed the writer [i.e., Waldo] a copy of the bill just passed and asked him if he would like an introduction to the learned doctor, its author. He declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know."

The bill was postponed indefinitely and died a quiet death. According to a local newspaper, however, "Although the bill was not acted on favorably no one who spoke against it intimated that there was anything wrong with the theories it advances. All of the Senators who spoke on the bill admitted that they were ignorant of the merits of the proposition. It was simply regarded as not being a subject for legislation."

Tennessee is also frequently mentioned as a state that "passed a pi=3 bill" but that seems to come from a reference by Robert Heinlein in __Stranger in a Strange Land__.

Pi also appears to have made its way into slang expressions according to the note I received from Mary O'Keeffe:

I just encountered the following item in Harry E. Wedeck's Short Dictionary of Classical Word Origins (Philosophical Library, NY, copyright 1957).

I ad Graecum Pi: This Latin phrase means Go to the Devil or Go and hang yourself! Literally, Go to the Greek pi. Because the Greek letter pi looks like a gallows.(I assume that this refers to the alternate upper case version of pi, which does indeed look like a gallows. Unfortunately, that's not the version that mathematicians usually use. Still, I thought your students and visitors to your website might enjoy it!)

Mary

When Mary wrote this, I inserted the current symbol for uppercase pi, &Pi, , thinking that was what she meant (although I didn't get the connection to gallows). Later Mary, always patient with me, provided the following additional information (I have added a few symbol graphics).

It appears that the classical Greeks used a symbol for pi which looks like the backwards version of the symbol which we today use for uppercase gamma, &Gamma, . At other times in its evolution, the symbol for pi flipped over to look like a dead ringer for the symbol we currently use for uppercase gamma.Here is a link I found for those interested in the evolution of alphabets from the ancient cuniform, thorugh the Phoenicians, Greeks, and Latins to modern times.

The uppercase pi symbol which we use today, &Pi, , (for example in the notation for "product") was a later development in an Oscan (or Italian) version of Greek. So I think the reference to "Graecum Pi" or "Greek Pi" is a reference to the classical Greek form of uppercase pi, which looks much more like a gallows than the form of the letter modern mathematicians typically use today.

My thanks to Mary for her continued assistance in getting this information correct.