Buckminster Fuller

[modest]

Originally Posted by modest

Ummm... how would you solve the surface of a spherical tetrahedron without pi? How would you solve any spherical triangle without pi?

~modest

Originally Posted by Turtle

That explanation is in sections of Synergetics that precede the bit I brought forward.

Ok senor tortoise testudine. I've looked over the whole chapter top to bottom, back to front, insideness to outsideness.

His mannerismness of relating the area of the insideness of a spherical triangle to the angle sounds exactly like Girard's Theorem (he doesn't say this - it's just my guess). In which case, I think Fuller is technically correct. If you know the angles exactly of the 4 triangles making a circle then you can find the area without "using" pi.

This is a bit like saying "if you know the area of one hemisphere of a circle then you can find the area of the circle by multiplying by 2 and you have avoided the use of pi". Technically true - but to get the area of the hemisphere you must use pi and to get Girard's theorem, you must use pi.

I believe there is piness either way.

~modest

[Turtle]

Originally Posted by modest

Ok senor tortoise testudine. I've looked over the whole chapter top to bottom, back to front, insideness to outsideness.

His mannerismness of relating the area of the insideness of a spherical triangle to the angle sounds exactly like Girard's Theorem (he doesn't say this - it's just my guess). In which case, I think Fuller is technically correct. If you know the angles exactly of the 4 triangles making a circle then you can find the area without "using" pi.

This is a bit like saying "if you know the area of one hemisphere of a circle then you can find the area of the circle by multiplying by 2 and you have avoided the use of pi". Technically true - but to get the area of the hemisphere you must use pi and to get Girard's theorem, you must use pi.

I believe there is piness either way.

~modest

Velly nice! Now since this chapter is the 800 series and there are 7 preceding 'chapters' , I can only suggest that in those chapters Fuller shows how to get those exact angles of the 4 triangles & presumably without using pi. He implies as much in the passage it seems by referring to a 'sperical tetrahedron'?

Originally Posted by Fuller

812.06: ...Ergo, the area of a sphere's great circle equals the area of a spherical triangle of that sphere's spherical tetrahedron.

Well, it's a good start and kudos to you Sir for having a read. No books delivered here yet; I'm on tenderhooks. What do you think about my idea of a dedicated Synergetics thread in the Math/Physics forum? My plan is to go cover to cover.

[modest]

Originally Posted by Turtle

Velly nice! Now since this chapter is the 800 series and there are 7 preceding 'chapters' , I can only suggest that in those chapters Fuller shows how to get those exact angles of the 4 triangles & presumably without using pi.

Now that would be something

Originally Posted by Turtle

What do you think about my idea of a dedicated Synergetics thread in the Math/Physics forum?

That sounds good to me. It is a physics/math topic... and more than just a book as well... so, physics/math sounds right to me.

~modest

[Thunderbird]

Hey Turtlesan I did'nt want to take the thread "Synergetics Explorations" off track which sounds great, but I wanted to ask you if have heard of a guy named Dan Winter?

[Turtle]

Originally Posted by Thunderbird

Hey Turtlesan I did'nt want to take the thread "Synergetics Explorations" off track which sounds great, but I wanted to ask you if have heard of a guy named Dan Winter?

Who's da bird? You da bird! I have not heard of the guy; lay him on me. Over in the Synergetics thread, I plan to look a bit into some of the folks who played a roll in assisting Bucky.

[Thunderbird]

Originally Posted by Turtle

Who's da bird? You da bird! I have not heard of the guy; lay him on me. Over in the Synergetics thread, I plan to look a bit into some of the folks who played a roll in assisting Bucky.

I Warn you he is kinda koo koo but also I think he's kind of a genius too. EnjoyTHE PHYSICS OF Phi, Compression, Implosion, Gravity, Time, and Love

[Turtle]

Originally Posted by Thunderbird

I Warn you he is kinda koo koo but also I think he's kind of a genius too. EnjoyTHE PHYSICS OF Phi, Compression, Implosion, Gravity, Time, and Love

Interesting. However, I don't see any mention of Fuller and until I get Fuller's work internalized I am in no position to compare it to the work of others. I am of the general opinion that no matter the field, an ignorance of the principles of geometry laid out by Fuller is a considerable detriment.

[Turtle]

The co-author/collaborator with Bucky on Synergetics 1&2, one Mr. E. J. Applewhite, is a character I inteneded to address in the Synergetics thread. However, in the interest of sticking to the book over there, and answering a question posed here early on concerning the naming of the buckminsterfullerene, I have this informative link & quote. Sadly, Edgar Applwewhite moved on to the yet-unexperienced lower frequencies in 2005.

The Naming of Buckminsterfullerene by E.J. Applewhite | The Buckminster Fuller Institute

Originally Posted by Edgar Applewhite

...When Harry Kroto and Richard Smalley, the experimental chemists who discovered C60 named it buckminsterfullerene, they accorded to Richard Buckminster Fuller (1895-1985), the maverick American engineering and architectural genius, a kind of immortality that only a name can confer - particularly when it links a single historical person to a hitherto unrecognized universal design in the material world of nature: the symmetrical molecule C60. Smalley's laboratory equipment could only tell them how many atoms there were in the molecule, not how they were arranged or bonded together. From Fuller's model they intuitcd that the atoms were arrayed in the shape of a truncated icosahedron - a geodesic dome. Only after novel phenomenon or concept is named can it he translated into the common currency of thought and speech.
...
Fuller did not develop his peculiar geometry in order to build a dome. Of course, he delighted in building domes and built a great many of them (though all were replicable, no two of his prototypes were the same), and he succeeded admirably in containing a greater volume of space in an enclosed stable structure than any architect or engineer before him had ever done. (He had a dozen or so patents relating to his domes.) But I knew that Fuller was one of the most celebrated but least understood original thinkers of his day. Fuller did not develop his original great-circle coordinate geometry in order to build domes; he built domes because otherwise people would not understand the geometry - which rejected the XYZ coordinatesystem of standard mensuration. He advanced synergetics as nothing less than a new way of measuring experience and as a new strategy of design science which started with wholes rather than parts. ...

[Thunderbird]

It's shiny. It's weighty. It's geometrically... intense. And although it looks like something a Man In Black would use to store spare singularities, you can actually build it yourself.

And, if you get bored with it, rip it to bits and reassemble it into something else.

Amazing Magnets