[bonanova]

Now that Bushindo has introduced us to the mysteries of the dodecahedron's dihedral angle,

can we determine the length of the dodecahedron edge for which the volume and surface

area have the same value?

[Glycereine]

napkin not good for keeping good decimal values.

I'm too tired for this

One thing that drove me nuts is that I'm solving for a unit-less side length.... lol.

Edited June 6, 2009 by Glycereine

[Guest]

Used calc and it gave me this: 2.6941667104173468292341373231142

(formulas from wiki, i did this calculation myself)

[Guest]

I have two questions..

1. What do you mean by same value?

2. Is it even possible for them to be the same?

[Glycereine]

Used calc and it gave me this: 2.6941667104173468292341373231142

(formulas from wiki, i did this calculation myself)

This is accurate from my calculations also but no real derivations on my own, same method as this poster.

[Glycereine]

I have two questions..

1. What do you mean by same value?

2. Is it even possible for them to be the same?

Same value meaning that for this given length of a side, The numeric value of Surface Area and Volume are the same. Units of course won't be.

You can take the two equations, for the surface area of a regular dodecahedron and the volume of that dodecahedron to be equal to each other and solve for the common variable in both equations, the length of a side.

[Guest]

Same value meaning that for this given length of a side, The numeric value of Surface Area and Volume are the same. Units of course won't be.

You can take the two equations, for the surface area of a regular dodecahedron and the volume of that dodecahedron to be equal to each other and solve for the common variable in both equations, the length of a side.

Thanks.

[bonanova]

I have two questions..

1. What do you mean by same value?

2. Is it even possible for them to be the same?

Spoiler for Suppose the edge of the solid is a centimeters.:

The Volume is some constant [say k₃] times a³ cm³ and

The Area is some other constant [say k₂] times a² cm².

The constants are the same regardless of the units.

We could have used meters, inches or miles.

When V and A have the same value, then k₃ a³ = k₂ a²

Dividing both sides by k₃ a² gives the desired value of edge length:

a = (k₂ / k₃)

Checking:

V = k₃ x (k₂ / k₃)³ = k₂³ / k₃²

A = k₂ x (k₂ / k₃)² = k₂³ / k₃²

So the puzzle basically asks to find k₂ and k₃.

The easiest solution is to Google it - they are complicated to calculate.

Like if you have no life, it would be a neat way to spend an hour.

[Guest]

Spoiler for Suppose the edge of the solid is a centimeters.:

The Volume is some constant [say k₃] times a³ cm³ and

The Area is some other constant [say k₂] times a² cm².

The constants are the same regardless of the units.

We could have used meters, inches or miles.

When V and A have the same value, then k₃a³ = k₂a²

Dividing both sides by k₃a² gives the desired value of edge length:

a = (k₂ / k₃)

Checking:

V = k₃ x (k₂ / k₃)³ = k₂³ / k₃²

A = k₂ x (k₂ / k₃)² = k₂³ / k₃²

So the puzzle basically asks to find k₂ and k₃.

The easiest solution is to Google it - they are complicated to calculate.

Like if you have no life, it would be a neat way to spend an hour.

Hey thanks. Never learned that stuff before. (an hour tho? try a day for me )