Buckminster Fuller

[Dark Mind]

Originally Posted by Turtle

...___I still find it curious none of you science folk have voiced your opinion on the scientific content & value of Fuller's geometrics (other than UncleAl ) So again; what gives?

Does UncleAl count?

So again, starting tonight .

[Turtle]

___Everyone counts.
___I have read through section 100.30 now. Fuller laid a foundation for a corpuscular view of "somethings", established the tetrahedron as the minimum stable structure of a "something", & now begins the disections of the tetrahedron into component parts which in their rearrangements form cubes, dodecahedra, & other geometric solids.
___I may have to make some little paper models for myself to better get a handle on this.

[Buffy]

Originally Posted by Turtle

Fuller...established the tetrahedron as the minimum stable structure of a "something"....

Sounds Principia Mathematica-like: spending hundreds of pages just to get to "1+1=2"... Have you ever sat on a one or two-legged stool? They're the only structures with fewer parts than a tetrahedron (a three-legged stool for those of you who are not topologists or geometers), and they're obviously not very stable.... This is why I think lots of folks have trouble absorbing Bucky....

Cheers,
Buffy

[Turtle]

___Indeed; but a journey worth taking. I go at a turtle's pace so following me is not inherently dangerous. I have my first little paper tetrahedron now & a few more laid out. I have the pattern I used in the Science Gallery/Member's Categories/Turtle:
http://hypography.com/gallery/showimage.php?i=415&c=3
___I plan to try chopping them up as Bucky describes in order to better see for myself. No worries.

[Buffy]

Originally Posted by Turtle

I go at a turtle's pace so following me is not inherently dangerous.

Yeah, normally, but infamous is behind me in his hot rod and I'm not sure about the state of his brake pads....

Tetrahedra are fun! So are Icosahedra (can you make one out of tetrahedra? do they tesselate in 3-D?). I like truncated polyhedra too: try truncating your tetrahedra while you're at it....

Polymorphically,
Buffy

[Turtle]

Originally Posted by Buffy

Yeah, normally, but infamous is behind me in his hot rod and I'm not sure about the state of his brake pads....

Tetrahedra are fun! So are Icosahedra (can you make one out of tetrahedra? do they tesselate in 3-D?). I like truncated polyhedra too: try truncating your tetrahedra while you're at it....

Polymorphically,
Buffy

___No problem on the braking if we widen the road.
___I haven't managed through all the reconstructions of polyhedra Fuller exposits as I still haven't fully explored the disections. I do recall he has mentioned the truncated tetrahedron in one of the diagrams. Also, they made one of crystal, frosted some faces, & when you look inside it you see an icosahedron.
http://www.rwgrayprojects.com/synerg...gs/f00120.html
____I didn't mean to imply above I read the Principia Mathematica; I have read exerpts & studied the calculus in texts that refer to it. Fuller in his Synergetics does not take 100 pages to get to the geometry. It's a little hard to tell how many pages on the online version, but I'd say no more than 15 pages to get us to the tetrahedron.
___One other point Fuller makes in the begiining of the work is an argument for adopting a generalist approach as opposed to a specialist approach. As a generalist myself, I like it very much & I suspect the specialists feel otherwise. I start to get the sense this may have some bearing on Fuller's lack of popularity.

[Buffy]

Originally Posted by Turtle

I didn't mean to imply above I read the Principia Mathematica; I have read exerpts & studied the calculus in texts that refer to it....

Anyone who claims they have read all of it is either a liar or has a doctorate in mathematics....

Cheers,
Buffy

[Dark Mind]

[Turtle]

___So I have 3 paper tetrahera & one disected in the manner of the rightmost illustration here:
http://www.rwgrayprojects.com/synerg...gs/f00103.html
___Usually after this much cutting with an Exacto blade I have a severe laceration somewhere on the left hand. I procede with the turtle's caution & the spider's intent.

[Turtle]

___As I proceded with my paper disections, I thought double perpendicular bisections of the regular tetrahedron yielded the dissections here:
http://www.rwgrayprojects.com/synerg...igs/f1301.html
It is not the case.
___I seem to recall not getting this diagram well when I first read this years ago; I do now. What I posted in the Science Gallery & called a "paper pattern" , Fuller calls a "planar net". The diagram linked to above has the planar net (paper pattern) to build a specific irregular tetrahedron called "A Quanta Module". The disections leading to this do however run along the perpendicular equators, whose intersection all of the A Quanta Modules share. I may not have the patience to print, cut out & fold the 24 required to build a regular tetrahedron, but I see it now.
___If you do have the patience, note that 12 lefts & 12 rights of the A Quanta Module make the regular tetrahedron; fold 12 planar nets with the lettering inside & the other 12 with the lettering outside to get the left/right correct.

PS I did take the time to print,cut, fold & assemble 1 A Quanta module. I added tabs to the planar net before I cut, & used glue rather than tape to hold it together. It's worth the time.