# Calculate the central angle of a regular dodecahedron

1. May 1, 2004

### geometer

A friend at work asked me to calculate the central angle of a regular dodecahedron. I think he was trying to stump me. 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. May 1, 2004

### moshek

Please remind me what is
"regular dodecahedron."

Thank you
Moshe

3. May 1, 2004

Dodecahedron

4. May 1, 2004

### 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

"The discovery of incommensurrability by Hippasus of Metapontum" by Kurt von Frits (Ann of Math, 1945).

Last edited: May 1, 2004
5. May 1, 2004

### 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.

6. May 1, 2004

### 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!

7. May 2, 2004

### 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