Date: May 25, 2013 3:42 AM
Author: plutonium.archimedes@gmail.com
Subject: replacing Picketfence model with 2 pure triangle model Re: Maxwell<br> Equations as axioms over all of physics and math #9 Textbook 2nd ed. : TRUE<br> CALCULUS; without the phony limit concept

On May 25, 12:43 am, Archimedes Plutonium
<plutonium.archime...@gmail.com> wrote:
> Alright, I am learning more new things, for in this 2nd edition I have
> an alternative to the picketfence model. I have the pure and straight
> rectangle model and the pure and straight triangle. In the rectangle
> model we fill the dx of 10^-603 width and the height is y itself. In
> the pure triangle we have a right triangle on the leftside of the
> point of the graph and the same triangle on the rightside with its
> hypotenuse in the reverse direction as pictured like this:
>
>      /|
>   /   |
> / __|
>
> unioned with this triangle
>
> |\
> |  \
> |__\
>
> is the same area as the rectangle model of the point on the function
> graph.
>
> The problem, though, is that the angle of the hypotenuse does not like
> like the slope or tangent to the point of that function graph. So I
> need to see if that hypotenuse is related to the slope or tangent or
> derivative at that specific point. If it is, then, clearly we see how
> derivative is the inverse of integral, because both have the same area
> and the triangle hypotenuse would be the derivative. So instead of
> rectangles forming the integral we can take two triangles. So
> hopefully I can work this out in the 3rd edition which I plan to start
> in the next day or so.
>
> Alright, this is the 10th page of the 2nd edition and the last page. I
> want to devote the last page to showing how all this math is begot
> from the Maxwell Equations.
> Now on this last page I want to show how Calculus of its empty space
> between successive numbers is derived from the Maxwell Equations as
> the ultimate axiom set over all of mathematics. The Maxwell Equations
> derives the Peano axioms and the Hilbert axioms. But I want to show
> that the Maxwell Equations do not allow for the Reals to be a
> continuum of points in geometry but rather, much like the integers,
> where there is a empty space between successive integers.
> The Reals that compose the x-axis of 1st quadrant are these:
>
> 0,  1*10^-603,  2*10^-603,  3*10^-603, 4*10^-603, 5*10^-603,
> 6*10^-603 . . on up to 10^603
>
> Pictorially the Reals of the x-axis looks like this
> ...................>
> and not like this
> ____________>
>
> So in the Maxwell Equations we simply have to ask, is there anything
> in physics that is a continuum or is everything atomized with empty
> space in between? Is everything quantized with empty space in
> between?
>
> I believe the answer lies with the Gauss law of electricity, commonly
> known as the Coulomb law. The negative electric charge attracts the
> positive electric charge, yet with all that attraction they still must
> be separated by empty space. If there was a continuum of matter in
> physics, then the electron would be stuck to the proton. The very
> meaning of quantum mechanics is discreteness, not a continuum.
> Discreteness means having holes or empty space between two particles
> interacting of the Maxwell Equations.
> So if physics has no material continuum, why should a minor subset of
> physics-- mathematics have continuums. If Physics does not have
> something, then mathematics surely does not have it.
>
> Now I end with reminders for the 3rd edition:
>
>        REMINDERS:
> (1) First page talk about why Calculus exists as an operator  of
> derivative versus integral much the same way of add subtract or of
> multiply divide because in a Cartesian Coordinate System the number-
> points are so spaced and arranged in order that this spatial
> arrangement yields an angle that is fixed. So that if you have an
> identity function y = x, the position of points (1,1) from (2,2) is
> always a 45 degree angle. So Calculus of derivative and integral is
> based on this fact of Euclidean Geometry that the coordinates are so
> spatially arranged as to yield a fixed angle. Numbers forming fixed
> angles gives us Calculus.
>
> (2) Somewhere I should find out if the picketfence model is the very
> best, for it maybe the case that a rectangle model versus a pure
> triangle model may be better use of the empty space of 10^-603 between
> successive Reals (number points). The picketfence model is good, but
> it never dawned on me until now that there is likely a better model
> even yet-- pure rectangle versus two pure triangles. My glitch is to
> get the hypotenuse related to the derivative. If I can solve that
> glitch, I have a crystal clear understanding of the derivative,
> integral and why they are inverses.
>
> (3) I am really excited about that new method of arriving at the
> infinity borderline of Floor-pi*10^603 via Calculus. The first number
> which allows a half circle function to be replaced by a 10^1206
> derivatives of tiny straight line segments and still be a truncated
> regular polyhedra, is when pi has those 603 digits rightward of the
> decimal point. The derivative of half circles of any number smaller
> than Floor-pi*10^603 does not form a circle. And is that not what
> Calculus is all about in the first place-- taking curves and finding
> Euclidean straight line segments as derivative and area. Calculus is
> the interpretation of curved lines into straight line segments. So,
> onwards to 3rd edition.
>


I am not going to count this as the 11th page of a 10 page textbook,
but rather as a reply. I found out tonight that these hypotenuse of
right triangles of points on the graph of a function are related to
the slope or derivative of the function at that point.

So in my previous graph of the function y=x^2 in 10 grid:

.    .    .    .    .    . ?                         x ?.    .    .  
 .    .    . ?                    x ?.    .    .    x    .    .
.    .    .    .    .    . ?0  .1  .2  .3  .4   .5

at x=.3, y=.09
at x=.4, y =.16 ?at x=.5, y =.25
Now each of those intervals of .1 width has 2 pure
triangles as these two

     /|
/  |
?/ __|
unioned with this triangle

|\
|  \
|__\

So in the interval between .3 and .4 of a dx of .1 sits two triangles
where their hypotenuse cross one another and intersect at a point and
the same is true of the next dx =.1 interval of two triangles
intersecting and if we draw a line between the two intersections we
end up with the derivative. Sort of reminds me of the projective
geometry Desargues theorem.

But I need to confirm all of this.

The importance of this is that the picketfence model gets thrown out
and replaced by the pure 2 triangles aside each point of the graph of
a function and the 2 triangles determine the derivative and the
integral and it is easy to see how the derivative is the inverse of
integral.

--
More than 90 percent of AP's posts are missing in the Google
newsgroups author search archive from May 2012 to May 2013. Drexel
University's Math Forum has done a far better job and many of those
missing Google posts can be seen here:

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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