6). Pi is, therefore, on the level of philosophical discourse because many other mathematical problems elucidated by the ancients have since been solved. Arndt et al. claim that pi is “possibly the one topic within mathematics that has survived the longest,” (6). Initial pi explorations may have been prehistoric. Ancient Egyptians and Mesopotamians later developed systems of writing and mathematics that enabled rigorous investigations into crucial problems. In 1650 BCE, ancient Egyptian scribe Ahmes recorded what are likely the first formulas for pi. The formulas are written on what is referred to as the Egyptian Rhind Papyrus (Eymard, Lafon & Wilson).
The Ahmes formulas relate the circle to the square, foreshadowing further investigations into pi by the Greeks. The Egyptians were therefore the first to record attempts to “square the circle,” or relate the area of a square to that of a circle in search of a constant variable that could illuminate orders of magnitude. Squaring the circle served a practical function for the ancient Egyptians: accurate architectural engineering and surveying. The great pyramids of Giza are constructed in accordance with the pi ratio, even though the Egyptians never calculated pi to any specific amount. Instead, the Rhind Papyrus essentially reads, “Cut off 1/9 of a diameter and construct a square upon the remainder: this has the same area as the circle,” (cited by Blatner 2). Ahmes calculations were off by less than one percent (Blatner 2). The Babylonians and ancient Hebrews were far less accurate in their representations of the ratio (Blatner 2). Like the ancient Chinese, the Babylonians and Hebrews calculated only a rough approximation of pi, represented by the whole number 3.
However, the ancient Greeks catalyzed the study of mathematics in general, and pi in particular. Aristophanes was the first to articulate the squaring of the circle problem in 414 BCE. Pi was also of concern to Chinese mathematicians. Hippias, Dinostratus, Archimades, and a slew of other Greek mathematicians explored the role and relevance of pi and attempted calculations.
In the 5th century CE, Tsu Chhung-Chih came up with the “best pi approximation available for 800 years,” (Arndt et al. 5).
Research into pi came to a standstill throughout much of European history, partly because of political and religious constraints on science. Since the Enlightenment, mathematicians have managed incremental strides with pi. The discovery of the differential calculus made a big difference in how pi was studied. Mathematicians and astronomers in Europe and in Asia began computing pi to a greater and greater degree (Beckmann 102). It was not until the 18th century that the symbol for pi was represented by the Greek letter, chosen because it was the first letter in the Greek words for both periphery and perimeter.
Pi is a confounding constant that has been investigated at length by almost all the great civilizations in human history: from the Chinese and Indian to the Greek, Roman, and Mesopotamian. Investigating pi seems akin to a meditation on the potential patterns underlying the physical universe. Knowing pi is useful in practical as well as theoretical and analytical applications, and may also aid the study of theoretical physics too. Computing pi should be more than mere “digit hunting (Beckmann 102). In fact, chasing digits just for the sake of length is meaningless. Even calculated up to trillions of digits, a meaningful pattern in pi has yet to be revealed at least within the parameters of current number theories. The numerical sequence and any possible patterns are “still awaiting artistic representation,” (Arndt et al. 12).
Arndt, Jorg, Haenel, Christoph, Lischka, Catriona & Lischka, David. Translated by Catriona Lischka, David Lischka. Springer, 2001
Beckman, Petr. A History of Pi. Macmillan, 1971.
Berggren, Lennart, Borwein, Jonathan M. & Borwein, Peter B. Pi, A source book. Springer, 2004.
Blatner, David. The Joy of Pi. Walker, 1999.
Eymard, Pierre, Lafon, Jean Pierre, & Wilson, Stephen S. The number [pi]. AMS Bookstore, 2004.
Ivanov, Oleg A..