https://www.sciencedirect.com/science/article/pii/S0315086017300691

JavaScript is disabled on your browser. Please enable JavaScript to
use all the features on this page. [1696201312] Skip to main content
Skip to article
Elsevier logo

  * Journals & Books

  * 
  *  Search

RegisterSign in

  * View PDF
  * Download full issue

Search ScienceDirect[                    ]
Elsevier

Historia Mathematica

Volume 44, Issue 4, November 2017, Pages 395-419
Historia Mathematica

Plimpton 322 is Babylonian exact sexagesimal trigonometry

Author links open overlay panelDaniel F. Mansfield, N.J. Wildberger
Show more
Share
Cite
https://doi.org/10.1016/j.hm.2017.08.001Get rights and content
Under a Creative Commons license
open access

Highlights

  * *

    Plimpton 322 contains a fragment from a proto-trigonometric
    table.

  * *

    The Babylonians discovered exact sexagesimal trigonometry at
    least 1500 years before the ancient Greeks discovered
    trigonometry.

  * *

    Babylonian exact sexagesimal trigonometry uses exact ratios and
    square ratios instead of approximation and angles.

Abstract

We trace the origins of trigonometry to the Old Babylonian era,
between the 19th and 16th centuries B.C.E. This is well over a
millennium before Hipparchus is said to have fathered the subject
with his 'table of chords'. The main piece of evidence comes from the
most famous of Old Babylonian tablets: Plimpton 322, which we
interpret in the context of the Old Babylonian approach to triangles
and their preference for numerical accuracy. By examining the
evidence with this mindset, and comparing Plimpton 322 with Madhava's
table of sines, we demonstrate that Plimpton 322 is a powerful, exact
ratio-based trigonometric table.

  * Previous article in issue
  * Next article in issue

MSC

01A17

Keywords

Plimpton 322
Trigonometry
Old Babylonian
Tablet
Pythagorean triples
Recommended articles

Cited by (0)

Daniel Mansfield is an Associate Lecturer in the School of
Mathematics and Statistics at UNSW, Sydney. He worked as a Software
Engineer before obtaining his doctorate in pure mathematics from UNSW
in 2014. His research interests include dimension and ergodic theory.

Norman Wildberger is an Associate Professor in the School of
Mathematics and Statistics at UNSW, Sydney. He graduated from the
University of Toronto and did doctoral work at Yale University, and
has also taught at Stanford University and the University of Toronto.
His research interests include harmonic analysis, representation
theory of Lie groups, hypergroups and hyperbolic geometry. He is also
a keen YouTuber, with several hundred maths videos on his channel
Insights into Mathematics.

(c) 2017 The Authors. Published by Elsevier Inc.

Recommended articles

No articles found.

Article Metrics

View article metrics
Elsevier logo with wordmark

  * About ScienceDirect
  * Remote access
  * Shopping cart
  * Advertise
  * Contact and support
  * Terms and conditions
  * Privacy policy

We use cookies to help provide and enhance our service and tailor
content and ads. By continuing you agree to the use of cookies.

All content on this site: Copyright (c) 2023 Elsevier B.V., its
licensors, and contributors. All rights are reserved, including those
for text and data mining, AI training, and similar technologies. For
all open access content, the Creative Commons licensing terms apply.

RELX group home page