Classical Values :: Geometry

July 11, 2007

Geometry

I have had to get in rather deeper into geometry than is my usual for the past 30 or so years (since my dome building daze - I built 3 or 4 and even lived in Bucky's Dome in Carbondale - he was no longer a resident alas) because of my design work on the Bussard Fusion Reactor which is ongoing at the IEC Fusion Technology blog and on the IEC Fusion Newsgroup.

There is a plan for the design of the second demonstration reactor to change from a cubical arrangement of magnets to an arrangement that forms a dodecahedron. Which got me doing some research on the matter of edge lengths vs radius and other such questions in order to work out the geometry.

In doing my research I came across an extraordinary book on the platonic solids. It explains how the cube is related to the dodecahedron. Through the magic of computers this is the clearest explanation of the connection I have yet come across. In other words - pretty pictures.

Another thing that makes this interesting is that it is an e-book. I recently blogged about a friend of mine (Sgt. Mom) in Plan B From Outer Space who is going a similar route although in her case an actual book will be delivered. I wonder how the ISBN system will cope?

Book selling and buying is going to face an earthquake from this direction. Or to mix the metaphors, this train is just starting to get up some steam.

Cross Posted at Power and Control and at The Astute Bloggers

posted by Simon on 07.11.07 at 12:44 AM

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Comments

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eric · July 11, 2007 12:59 AM

That geometry was way over my head (I wouldn't be able to enter Plato's academy: ἀγεωμέτρητος μηδεὶς εἰσίτω, literally 'Let no one un-geometrical enter').

But how can this blacktygrrrr guy hope to win a blog award when he can't even tell the difference between blog comments and e-mail, and in confusing the two resorts to spam?

Dennis · July 11, 2007 07:28 AM

Dennis,

I actually checked out his blog. He is very "right". However, he does not write worth a damn.

If you want good rants Protein Wisdom is the place to go.

M. Simon · July 11, 2007 11:51 AM

I thought there was something in Bussard's Google presentation (which is about the extent of my knowledge on this) about needing an even number of edges entering each vertex, presumably to balance charges/polarities, which is why he went with the shape he did (rhombicuboctahedron, IIRC). Two questions: how does a dodecahedron satisfy this requirement, and what's wrong with an octahedron?

Aaron Davies · July 11, 2007 12:33 PM

Aaron,

I have never gotten a satisfactory answer to that question.

One thing to keep in mind is that because of the open cusps (corners) whatever solid that is used is in effect truncated.

If the physics can be proved so that the technology is seen as viable money will pour in and proper simulations or test reactors will be built to explore all this further.

Since the cubic structure is deemed adequate to prove the physics I'm doing what any conservative engineer would do. Sticking with a known design.

M. Simon · July 11, 2007 01:30 PM