Right angled triangle combinations(3,4,5....)

[Turtle]

Originally Posted by sebbysteiny

Seeing as things are getting so agro, I thought I might join in the fireworks.

Technically speaking, no 3,4,5 triangle (or other entirely whole number sided triangles) actually exist. We are living in a 4 dimensional universe in curved space time and the angles of triangles do not add up to exactly 180 degrees and therefore, a triangle of length 3 cm and 4cm will not have a hypotonuse of exactly 5 cm. If we were living in a flat 4 dimensional universe, or even a 3 dimensional universe, maybe it would, but we are not.

If you read a bit of Buckminster Fuller's geometry in Synergetics you will see it is you who is 180 out of phase as no lines exist save straight lines.
http://www.rwgrayprojects.com/synerg...nergetics.html

[TheBigDog]

On a sphere a right triangle can be 1,1,1 with three right angles.

Bill

[Turtle]

Originally Posted by TheBigDog

On a sphere a right triangle can be 1,1,1 with three right angles.

Bill

Mmmm...processing.
Here is the page concerning triangles on spheres I couldn't find earlier from Fuller:
http://www.rwgrayprojects.com/synerg.../plate01z.html

[Qfwfq]

What does "straight" mean?

Geodetic is the term, in a general manifold.

[Turtle]

Originally Posted by Qfwfq

What does "straight" mean?

Geodetic is the term, in a general manifold.

That ain't a lot, but it's more commentary on something Fuller-esque than I have seen here in 6 months. Care to expound on that geodetic in a general manifold?

[Qfwfq]

I don't know what Fuller says about them, but in differential geometry it is a curve such that parallel transport along it brings the tangent vector at the initial point onto the tangent vector at the final point, for any pair of points. It can also be described more simply as giving the briefest path between any two of its points.

[sebbysteiny]

On a sphere a right triangle can be 1,1,1 with three right angles.

Maybe so, but again, we are not living in a 3 dimensional sphere. At best, the Universe can be approximated by a sphere, but not a real sphere. a 4d sphere that we cannot immagine (although we can calculate for). To be deadly accurate, you must include the curviture caused by every mass in the Universe all at one value of time.

[cwes99_03]

Delete. Re checking my work

[Turtle]

Originally Posted by Qfwfq

I don't know what Fuller says about them, but in differential geometry it is a curve such that parallel transport along it brings the tangent vector at the initial point onto the tangent vector at the final point, for any pair of points. It can also be described more simply as giving the briefest path between any two of its points.

Excellent Q; shortest distance between 2 points it is. Moreover, I can't let a direct comment on Fuller slip through my grasp. Since you forget very little Q, may I presume you haven't read Fuller's Synergetics? Setting aside Fuller's quirky aspects, he was a master geometer by the standard convention, what with inventing the Geodesic Dome & the Dymaxion Map Projection. Just wondering what gives with no one knowing what Fuller says (said RIP).

[Turtle]

Originally Posted by Turtle

If you read a bit of Buckminster Fuller's geometry in Synergetics you will see it is you who is 180 out of phase as no lines exist save straight lines.

Er...well, Fuller said no straight lines exist apparently, but he used those non-existing straight lines to good effect.

http://www.gap-system.org/~history/Q...ns/Fuller.html

Originally Posted by BuckminsterFuller

Everything you've learned in school as 'obvious' becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There's not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines.