14
$\begingroup$

Thales (circa 600BC—roughly 50 years before Pythagoras, 200 years before Plato, and 300 years before Euclid) certainly knew and reasoned with the concept of a planar angle. Are there earlier historical references to angles in a mathematical sense? Or is the origin of the notion lost in the mists of antiquity?

Improve this question
$\endgroup$
2
  • 6
    $\begingroup$ Almost certainly, the answer is no. There are "divisions of the circle into 360" in the Rigveda, to say nothing of clay tablets from the Babylonian and Sumerian periods. I'm not sure if this is MO-material, so if you want I can send explicit references by email. $\endgroup$
    – Vidit Nanda
    Commented Feb 6, 2014 at 1:22
  • 12
    $\begingroup$ I don't see anything very wrong with this question. $\endgroup$
    – Johan Wästlund
    Commented Feb 6, 2014 at 4:14

2 Answers 2

Reset to default
10
$\begingroup$

Just a few remarks:

  1. I doubt that we know that Thales "certainly knew" the concept of a planar angle. All we know about pre-Euclidean mathematics is basically based on histories written long after Euclid.

  2. There is no concept of angle in Sumerian or Old Babylonian mathematics. The division of the circle into 360 degrees came into being well after 700 BC in Chaldean astronomy. Of course the Babylonians (like Thales) knew what a right angle was, but they didn't even have a word for it.

Improve this answer
$\endgroup$
5
$\begingroup$

The division of a circle into 360 degrees may well have originated from ancient Babylonian mathematics (1800 BC), as evidenced by a clay tablet from Shush. Here is a quote from David Wallis, History of angle measurement:

See also A History of Pi (pages 21-22).

Improve this answer
$\endgroup$
2
  • 1
    $\begingroup$ This seems to be tablet TMS 2 (Friberg, A Remarkable Collection of Babylonian Mathematical Texts, p.218). Friberg does not observe any traces of the notion of an angle there. $\endgroup$
    – Franz Lemmermeyer
    Commented Dec 23, 2015 at 16:24
  • $\begingroup$ The picture of the clay tablet "from Shush" in Wallis's article is, of course, the famous Plimpton 322, which is believed to come from Larsa. There are no indications at all that it has to do with the division of a circle into 360 degrees. $\endgroup$
    – Franz Lemmermeyer
    Commented Dec 24, 2015 at 9:08

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .