Plimpton 322 is a cuneiform clay tablet with the catalog number 322 in the G.A. Plimpton Collection at Columbia University. Probably the most well known mathematical tablet, it was written in the Old Babylonian period between 1900 and 1600 B.C.E. and shows the most advanced mathematics known before the development of the Greek mathematics. It was originally thought that Plimpton 322 was one of many tablets that recorded inventories of food and merchandise. However, in 1946 Otto Neugebauer and A. J. Sachs, historians of mathematics, discovered that the numbers in the table were computations and not just records of quantity.Plimpton 322 is written sexigesimally (in base 60) w ...view middle of the document...
The first column of Plimpton 322 is interesting because each number is a perfect square and subtracting one from each leaves a perfect square. This table is usually related to Pythagorean triples. In interpreting it, the second column is considered a, one side of a right triangle or the width of a rectangle. The third column is considered c, the hypotenuse of the right triangle or the diagonal of the rectangle. The other side of the triangle or rectangle, b, does not appear on the table. In this interpretation the first column is then (c/b)2 = 1 + (a/b)2 . Neugebauer and Sachs confirmed that the columns were computations by assigning lengths of a side (width) and hypotenuse (diagonal) of a right triangle to the numbers in columns 2 and 3. When the lengths were computed, calculations gave way to the Pythagorean theorem, a2 + b2 = c2. There are exceptions to this, 4 rows, but Neugebauer and Sachs explained them as errors made by the Scribe of the tablet.Plimpton 322 proves that the Old Babylonians used sophisticated mathematics and knew the Pythagorean theorem more than 1000 years before Pythagoras' birth! They had no proof for the theorem, but there are ample examples of its use in various problems of that time period.References:Holt, Rinehart and Winston, Geometry, pages 321-322, 638, 686-687; 2001Joyce, David, Plimpton 322 Tablet, Clark University, Department ofMathematics and Computer Science, 1995http://aleph0.clarku.edu/~djoyce/mathhist/plimpnote.htmlOtero, Daniel, Plimpton 322, Xavier University, 2000 (modified 1/2002)http://cerebro.xu.edu/math/math300/02s/plimpton2.html
