Date: Wed, 8 Sep 1999 18:47:28 -0600 (CST)
Subject: Triangles & the history of degree measure for angles

Name: sandra
Who is asking: Student

Question: Are there any triangles which are not 180 degrees?

I am also in need of information on the history of degree measure for an angle.

Hi Sandra,

The answer is both yes and no.

  • Yes - triangles on a sphere.
    Take a globe. Take a triangle from the North pole to the equator, 1/4 of the way around the equator and back to the North pole. You will find THREE 90 degree angles!

  • No on the Eucdean plane, any triangle has an angle sum of 180. In fact, this property is equivalent to Euclid's fifth postulate (given the other four) about parallel lines etc.
Historically, people may not have measured angles on a sphere - but the same sets of measurements (and the same type of trigonometry) comes up in astronomy and navigation working with angles looking outwards to the sky!

Two places you might look for history part of your question are the Earliest Uses of Various Mathematical Symbols (look on the geometry page) and The MacTutor History of Mathematics archive

Walter Whiteley

Go to Math Central

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