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Calculate the central angle of a regular dodecahedron

  1. May 1, 2004 #1
    A friend at work asked me to calculate the central angle of a regular dodecahedron. I think he was trying to stump me. :smile: Just to be sure we are talking the same thing, he was referring to the angle between any two radii drawn from a vertex of the dodecahedron to the center.

    At any rate, I did a quick calculation and came up with two answers: 180 degrees and 52.44 degrees. Before I present him with these answers, I just want to check - am I anywhere near close?
  2. jcsd
  3. May 1, 2004 #2
    Please remind me what is
    "regular dodecahedron." :eek:

    Thank you
    Moshe :smile:
  4. May 1, 2004 #3
  5. May 1, 2004 #4
    Thank you Warr for Wolfram web-site. Now i see . Hipasus was studding it's geometry when he first discover the existence of irrational number, but Euclid wrote in his 10th book the element only about the root of 2.

    Moshek :smile:

    "The discovery of incommensurrability by Hippasus of Metapontum" by Kurt von Frits (Ann of Math, 1945).
    Last edited: May 1, 2004
  6. May 1, 2004 #5
    Ooops - my two answers were 0 degrees and 52.44 degrees. I goofed up the sign of one answer initially. Sorry! So, that makes me a little happier with my results.
  7. May 1, 2004 #6
    Holy Mackerel! I found another error. My answers are now 0 degrees and 63.44 degrees. Lesson learned - never tackle a problem before your first cup of coffee in the morning!
  8. May 2, 2004 #7
    Geometer: Your lesson is great !

    Do you know what happend to Hipasus after his discovery
    about irrationality in the pentagon
    and what was his lesson from that?

    Moshek :smile:
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