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:

http://mathforum.org/kb/profile.jspa?userID=499986

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