Plimpton 322 Clay Tablet. Ancient spreadsheet.
I haven't actually printed this yet, but look forward to giving it a go.
An ancient cuneiform tablet. Created from a flat image using imagetostl.com
Below is an AI generated description with some more details.
The Plimpton 322 clay tablet, with each row of the table relating to a Pythagorean triple, is believed to have been written in Babylonia around 1800 BCE, around 1,000 years before the Greek mathematician Pythagoras was born.
Overview of Plimpton 322
Origin and Date: Plimpton 322 is a Babylonian clay tablet, believed to have been inscribed around 1800 BCE during the Old Babylonian period (circa 1894–1595 BCE). It hails from the region of ancient Mesopotamia, likely southern Iraq, and predates the Greek mathematician Pythagoras (circa 570–495 BCE) by approximately 1,000 years, challenging the notion that he was the first to explore Pythagorean triples.
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Discovery and Collection: The tablet is part of the Plimpton Collection at Columbia University, donated by publisher George A. Plimpton in 1936. It was likely excavated in the late 19th or early 20th century, though its exact find spot remains uncertain, with some speculation pointing to sites like Sippar or Nippur.
Physical Description: The tablet measures about 13 x 9 cm and is partially damaged, with a missing lower right corner. It features cuneiform script in the Old Babylonian dialect of Akkadian, arranged in a table with 15 rows and 4 columns, though only 13 rows are fully preserved.
Mathematical Significance
Pythagorean Triples: Each row of Plimpton 322 corresponds to a Pythagorean triple—three integers (a, b, c) that satisfy the equation a2+b2=c2a^2 + b^2 = c^2a^2 + b^2 = c^2
. Examples include (3, 4, 5), (5, 12, 13), and larger sets like (119, 120, 169). The tablet lists 15 such triples, with the largest involving numbers in the hundreds, suggesting a systematic method rather than trial and error.
Base-60 System: The Babylonians used a sexagesimal (base-60) numeral system, which is reflected in the tablet’s calculations. The numbers are written in cuneiform as regular sexagesimal fractions (combinations of powers of 2, 3, and 5), allowing precise representation of ratios.
Purpose Debate: Scholars have proposed several theories about its use:
Mathematical Exercise: Otto Neugebauer and Abraham Sachs, who first analyzed it in the 1940s, suggested it was a study of Pythagorean theorem solutions, possibly for training scribes or exploring number theory.