Prev: Need help understanding some wf
Next: I Think Therefore I Am - rebuttal
From: Archimedes Plutonium on 13 Mar 2010 03:20


Archimedes Plutonium wrote:
> Well I have been simmering or stewing or brewing over this question of
> whether Physics
> has some examples of whether the number (i) is actually a 60 degree
> arc rotation
> and not a 90 degree rotation, for two days now. And I landed on a
> likely candidate.
>
> --- quoting Wikipedia on Least Action Principle ---
> In physics, action is an attribute of the dynamics of a physical
> system. It is a functional which takes the trajectory (also called
> path or history) of the system as its argument and returns a real
> number as the result.
>
> It has units of energy × time (joule-seconds in SI units). Planck's
> constant is the quantum of action.
>
> Generally, the action takes different values for different paths.
> Classical mechanics postulates that the path actually followed by a
> real physical system is that for which the action is minimized (or,
> more strictly, is stationary). The classical (differential) equations
> of motion of a system can be derived from this principle of least
> action.
>
> The stationary action formulation of classical mechanics extends
> readily to quantum mechanics in the Feynman path integral formulation,
> where a physical system follows simultaneously all possible paths with
> amplitudes determined by the action.
>
> --- end quoting Wikipedia on Least Action Principle ---
>
> Now if (i) were truly a 60 degree rotation and not a 90 degree, then
> the Least
> Action Principle should be able to decide between the two rotations.
>
> And the way I see a proof of this is to consider given any closed
> figure drawn in
> 2D and asked what regular geometrical object is able to tile that
> closed figure the best?
>
> Now we have to stipulate that the area of the tiling objects have to
> be the same. So that
> if we chose a square as the unit tiler, then someone else choses a
> triangle, then the
> areas of the unit tilers are equal.
>
> So now we ask, what tiler is the best, and by best we mean is able to
> tile with more of its
> units than any other tiler. So this is a rather theoretical equivalent
> of the Least Action Principle.
>
> Now some may want to chose a circle of unit area for their tiler.
> Another will chose a square
> as their unit tiler. I think the very best or maximum unit tiler,
> remember, all the tilers are of the
> same unit area.
>
> I think the best tiler is an equilateral triangle whose angles are all
> 60 degrees.
>
> By best, given any random shaped object in 2D, that the equilateral
> triangle, because of its
> sharp pointed ends is able to squeeze more triangles into any given
> random shaped object,
> than any other tiler.
>
> So if that is true, then in a sense, the Principle of Least Action in
> physics is tied up with
> the equilateral triangle and its 60 degree angles. If squares or
> parallelograms or circles or
> right-triangles or hexagons all of unit area were the best tilers then
> i would be 90 degrees if
> a square was the best tiler. But if equilateral triangle is the best
> tiler than (i) is 60 degree
> rotation.
>
> Funny how noone in mathematics has ever thought of this Conjecture.
>
> Conjecture: given any 2D shaped object and asked to tile it with a
> unit tiler. The best
> tiler is a equilateral triangle

That conjecture is vague. What I meant to say is given a large
collection of randomly
shaped 2D objects, and given a choice of a unit tiler, the best choice
to make is a
equilateral triangle.

The above conjecture is false when I say given any 2D shaped object
since if someone
handed me a square that was area of 4 square units then a unit square
would be the best
tiler and not a unit equilateral triangle.

So the conjecture that I want, says more of given a large collection
of random shaped 2D
objects then the best choice of a tiler is a unit equilateral
triangle.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
 | 
Pages: 1
Prev: Need help understanding some wf
Next: I Think Therefore I Am - rebuttal