Calculate the central angle of a regular dodecahedron

In summary, the conversation was about a friend asking the speaker to calculate the central angle of a regular dodecahedron, to which the speaker responded with two different answers. They also clarified the definition of a regular dodecahedron and discussed its connection to the discovery of irrational numbers. The speaker made some initial mistakes in their calculations but eventually arrived at the correct answer. The conversation ended with a question about what happened to Hipasus after his discovery and what lesson he learned from it.
  • #1
geometer
195
0
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?
 
Mathematics news on Phys.org
  • #2
Please remind me what is
"regular dodecahedron." :eek:

Thank you
Moshe :smile:
 
  • #3
 
  • #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:
  • #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.
 
  • #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!
 
  • #7
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:
 

1. How is the central angle of a regular dodecahedron calculated?

The central angle of a regular dodecahedron can be calculated by dividing 360 degrees by the number of faces, in this case 12. Therefore, the central angle of a regular dodecahedron is 30 degrees.

2. What is the significance of the central angle in a regular dodecahedron?

The central angle in a regular dodecahedron is important because it helps determine the orientation and symmetry of the object. It also plays a role in understanding the relationships between the different faces and angles of the dodecahedron.

3. Can the central angle of a regular dodecahedron be measured in radians?

Yes, the central angle of a regular dodecahedron can be measured in radians. In fact, the central angle of a regular dodecahedron is equivalent to 1/12 of a full rotation in radians, which is approximately 0.5236 radians.

4. How does the central angle of a regular dodecahedron relate to its other angles?

The central angle of a regular dodecahedron is equal to all of its other angles. This is because a regular dodecahedron is a platonic solid, meaning all of its faces are identical regular polygons, and therefore all of its angles are also equal.

5. Can the central angle of a regular dodecahedron be calculated using a formula?

Yes, the central angle of a regular dodecahedron can be calculated using the formula 360/n, where n is the number of faces. This formula can also be used to calculate the central angle of other regular polygons.

Similar threads

MHB What are the angles of isosceles triangle ABC?
    • General Math
Replies
1
Views
721
I Can the same argument be used for both radians and degrees in the sine function?
    • General Math
Replies
3
Views
733
MHB Degree Measure of Central Angle
    • General Math
Replies
4
Views
1K
A Regular vs stable orbits in spherically symmetric potentials
    • Mechanics
Replies
4
Views
618
MHB Calculating angles for a physical regular icosahedron
    • General Math
Replies
2
Views
3K
B Reprise: Calculate the distance between two points without using a coordinate system
    • General Math
Replies
1
Views
192
I Spherical Angle Math: Pyramid Angles Constant?
    • General Math
Replies
2
Views
975
MHB Find unknown angles of a triangle
    • General Math
Replies
6
Views
3K
MHB Left or Right Angles ( + or - ) of adjoining vectors
    • General Math
Replies
2
Views
1K
I don't understand how this equation calculates angle for hexagons
    • General Math
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top