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Turner's Compendium: History of Trigonometry

Array ( [0] => HIST 3250 Fall 2017 [1] => no-show [2] => student exhibit )

A Brief History of Trigonometry

Timeline:

  • 1800 BCE -------------- Babylon -- Plimpton 322 Tablet contains a list of Pythagorean triplets more than a thousand years before Pythagoras and his formula
  • 1550 BCE -------------- Egypt ----- Rhind Mathematical Papyrus features example problems calculating the slope, or Seked, of a pyramid
  • 500s BCE ---------------Greece --- Pythagoras is said to have invented the famous theorem
  • 200 BCE to 200 CE -- Greece ---- Hipparchus, Menelaus, and Ptolemy each make additions and revisions to tables of chords for use in astronomy
  • 500 CE ----------------- India ------ First Sine Tables appear, begin to overtake chord tables
  • 1000 CE --------------- Islam ------ Mathematicians are using all six Trigonometric functions
  • 1765 CE --------------- England -- Turner publishes book on Trigonometry
Plimpton_322.jpg
The Plimpton 322 Clay Tablet, curently housed in the Plimpton collection at Columbia University.  
Rhind_Mathematical_Papyrus.jpg
The Rhind Mathematical Papyrus, currently located in the British Museum.

     Trigonometry traces its roots back to Ancient Babylon and Egypt.  This is because the oldest surviving pieces of evidence for trigonometry are the Plimpton Tablet #322 and the Rhind Mathematical Papyrus.  The Plimpton Tablet dates from around 1800 BCE and contains a table of Pythagorean triplets, or numbers that satisfy the sides of a right triangle [1].  The Rhind Papyrus, dating from around 1550 BCE, features problems solving the slope of a pyramid, called a Seked [2].

     The Ancient Greeks heavily contributed to trigonometry, with Hipparchus, Menelaus, and Ptolemy each living after one another and building off the chord tables of their predecessors [3].  Originally, the side of a triangle in question would be called a chord because it intercepted the arc of its corresponding angle.  The Greeks were mostly concerned with the sky and the heavens.  Therefore, Trigonometry started by studying the positions of the stars.  Hipparchus is said to be the founder of Trigonometry, and Ptolemy wrote the Almagest, an important work on the subject [4].  However, the first use of Sine tables was recorded instead in India in the 6th century and spread back west [5].  By the height of the Medieval Islamic World, mathematicians there were using the six trigonometric functions we know today, namely, the Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent [6].

Works Cited:
  1. Daniel F. Mansfield and N.J. Wildberger, "Plimpton 322 is Babylonian exact sexagesimal trigonometry," Historia Mathematica 44, no. 4 (Aug. 2017): 395, https://doi.org/10.1016/j.hm.2017.08.001.
  2. Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, (Princeton, NJ: Princeton University Press, 2009), 11.
  3. Morris Kline, Mathematical Thought from Ancient to Modern Times, (New York, NY: Oxford University Press, 1972), 119-122.
  4. Ibid.
  5. Van Brummelen, 95.
  6. David M. Bressoud, “Historical Reflections on Teaching Trigonometry,” The Mathematics Teacher 104, no. 2 (Sept. 2010): 110.
Image Sources:
  1. Unknown, Plimpton 322, 1800 BCE, Sept. 13, 2006, Wikimedia Commons, accessed Dec. 12, 2017, http://www.math.ubc.ca/~cass/courses/m446-03/pl322/pl322.html.
  2. Paul James Cowie, Rhind Mathematical Papyrus, 1550 BCE, June 4, 2017, Wikimedia Commons, accessed Dec. 12, 2017, https://commons.wikimedia.org/wiki/File:Rhind_Mathematical_Papyrus.jpg.