Calculate the central angle of a regular dodecahedron

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Discussion Overview

The discussion revolves around calculating the central angle of a regular dodecahedron, specifically the angle between two radii drawn from a vertex to the center. The conversation includes attempts at calculation and clarification of terms related to the geometry of the dodecahedron.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Historical

Main Points Raised

  • One participant initially proposes two angles, 180 degrees and 52.44 degrees, as potential answers for the central angle.
  • Another participant requests clarification on what a "regular dodecahedron" is, indicating a need for conceptual understanding.
  • A participant mentions historical context, referencing Hippasus and his discovery related to the geometry of the dodecahedron and irrational numbers.
  • The initial participant corrects their earlier claims, stating their answers are actually 0 degrees and 52.44 degrees, later adjusting them again to 0 degrees and 63.44 degrees.
  • Another participant acknowledges the lesson learned about careful calculation, particularly in relation to timing and focus.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct central angle, as multiple calculations are presented and corrected without agreement on a final answer.

Contextual Notes

The discussion includes several corrections to initial calculations, indicating uncertainty in the mathematical steps taken. The definitions and properties of a regular dodecahedron are not fully explored, which may affect the clarity of the calculations.

Who May Find This Useful

This discussion may be of interest to individuals studying geometry, particularly those focused on polyhedra, as well as those interested in the historical context of mathematical discoveries.

geometer
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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?
 
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Please remind me what is
"regular dodecahedron." :eek:

Thank you
Moshe :smile:
 
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:
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.
 
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!
 
Geometer: Your lesson is great !

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


Moshek :smile:
 

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