Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > sci.physics > #714385

Re: 3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure?

Show all headers | View raw

Newsgroups: sci.math
Date: Fri, 23 Nov 2018 18:31:07 -0800 (PST)

Subject: looking at tetrahedron density versus torus // conjecture if torus is
 maximum density is tetrahedron minimum density?
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sat, 24 Nov 2018 02:31:08 +0000

looking at tetrahedron density versus torus // conjecture if torus is maximum density is tetrahedron minimum density?

- hide quoted text -
On Friday, November 23, 2018 at 3:30:31 PM UTC-6, Archimedes Plutonium wrote: 
> Circle density is perimeter*area = 2(pi^2)r^3 
> 
> That does not remind me of any volume of some figure 
> 
> Unless perhaps some polyhedra come close to that 

Alright, so, let me apply this new found knowledge to look for the Smallest Geometry figure density. I would guess a regular tetrahedron. 

So the density of a tetrahedron would be (surface-area)*volume. That would be (sqrt3)s^2 times (sqrt2)(1/12)s^3 = (sqrt6)(1/12)s^5 

If the torus is a maximum density and the regular tetrahedron a minimum density, we do not see a inverse of a prefix factor. Tetrahedron prefix factor is .20.... and torus prefix factor is 777.69.... 

Torus density is 8(pi^4)R^2r^3 

If it were a inverse relation of 8 to 1/8 would be 8 to .125, although .2 is rather close to .125. 

Now as for Perimeter*Area density for equilateral triangle we have 3s * (sqrt3)(1/4)s^2 = 3(sqrt3)(1/4)s^3 = 1.299...s^3. 

So still looking for link-ups,,,, 

AP 

Back to sci.physics | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure? Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-11-23 13:17 -0800
  Re: 3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure? Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-11-23 18:59 -0800
  Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-11-24 14:13 +0000

csiph-web