dodecahedron

[geometer]

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?

[moshek]

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

Thank you
Moshe :smile:

[Warr]

Dodecahedron (http://mathworld.wolfram.com/Dodecahedron.html)

[moshek]

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).

[geometer]

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.

[geometer]

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!

[moshek]

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: