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(2)-Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x

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  (2)-Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x  Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-09-10 15:37 -0700
    Re: Archimedes "Total Failure" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-09-11 03:00 +0000
    Re: (2)-Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x  Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x konyberg <konyberg@online.no> - 2018-09-19 11:32 -0700

#423329 — (2)-Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x

Newsgroups: sci.math
Date: Mon, 10 Sep 2018 11:30:16 -0700 (PDT)

Subject: Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x
 Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Mon, 10 Sep 2018 18:30:16 +0000

Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x

Now, you remember how we do the AP Polynomial functions-- they are all straight line segments over intervals. So they are all Y = mx+ b and we can do most of these in our head without resorting to the formula, unless the coefficients are too much to carry in the head.


For 2 coordinate points, (x0, y0) (x1, y1), we produce the 1st degree polynomial, a straightline or line segment 

P(x) = y0(x-x1) / (x0-x1) 
       + y1(x-x0) / (x1-x0) 

uptick wave 
(0,0) (1, .87) (1.57, 1) 


So, from 0 to 1 our first interval line segment is
Y = .87x for x=0 to x=1
next
(1-.87)/1.57-1) = .13/.57 = slope of .22
Y = .22x for x=1.01 to x= 1.57 (note, we could not say x=1 for that was in the last interval so in 10 Grid we substitute 1.01)

Now for the downtick portion of the Cycloid-Parabola Wave

and the downswing or downtick portion taking the complement of .94 to be .06

(1.57, 1) (2, .06) (3.14, 0) 

P(x) = y0(x-x1) / (x0-x1) 
       + y1(x-x0) / (x1-x0)

So, from 1.57 to 2 interval
(.06 - 1) / (2-1.57) = -.94/ .43 = -2.19 slope
Y = 4.45 - 2.19x for x = 1.571 to x= 2
1(x-2)/(1.57 -2) + .06(x-1.57)/ (2-1.57)
(x-2) / -.43   +  .06(x-1.57) / .43
-2.32x + 4.65 + .13x - .20
 Y = 4.45 - 2.19x close enough off by a little

From 2.01 to 3.14 interval
(0- .06) / (3.14 -2) = -.06/ 1.14 slope is -.05

Y = .157 -.05x close enough, off by a little

So, putting together all four line segments we have

Y = .87x
Y = .22x
Y = 4.45 - 2.19x
Y = .157 -.05x

Now, comparing that to the semicircle
Now instead of sawtooth sine periodic, let us do a flattened top. so I go from (0,0) to (.5,1) then a flat line segment Y = 1 over interval x=.5 to x=1.5 then back to a downward slope from 1.5 to 2 

Y = 2x for x from 0 to .5 
Y = 1 for x from .5 to 1.5 
Y = 4 - 2x for x from 1.5 to 2 

Notice how the 4-2x matches up nicely with the 4.45 - 2.19x

AP

Newsgroups: sci.math
Date: Mon, 10 Sep 2018 12:48:29 -0700 (PDT)

Subject: Cycloid-Parabola and Semicircle-Semicircle Waves have vertices Re:
 Cycloid-Parabola Function, replacing sine&cosine functions
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Mon, 10 Sep 2018 19:48:29 +0000

Cycloid-Parabola and Semicircle-Semicircle Waves have vertices Re: Cycloid-Parabola Function, replacing sine&cosine functions

- show quoted text -
Now I wish I could draw this into the post, but ascii art is limited. What I want to portray is the geometry of the wave of cycloid-parabola and where that wave is far superior to the semicircle wave or and sine wave. 

Superior in the sense that at the peak of the uptick we immediately do a downtick, and we could do this with a semicircle wave, only the downtick would be another semicircle inverted. And, if you flip a drawing of the Cycloid-Parabola Wave flip it over 180 degrees you have the same wave only the vertex points going in opposite directions. And one can nest two of these to form a rectangle that is interlocking. Something useful in Hund's rule as two electrons share a suborbital. 

But what is critically important, is that it appears the Cycloid-Parabola or the Semicircle-Semicircle Waves are the most simple of all waves-- even more simple than pure semicircle or any form of sine. 

And, one can take a Semicircle wave and assemble a SemiCircle-Semicircle Wave very similar to the Cycloid-Parabola, where the Semicircle-Semicircle vertex is more blunt and the Cycloid-Parabola vertex is more sharp, more hook like. 

Physics should love these new waves, for light waves and magnetic field waves are likely to be these type of waves. 

AP 

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#423338 — Re: Archimedes "Total Failure" Plutonium flunked the Math Test of a lifetime-generation test

Math Failure Archimedes Plutonium <plutonium.archimedes@gmail.com> fails:

> Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x 
> Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x

Have you decided whether the sine and cosine functions are a semicircle,
a cycloid or a parabola yet?

How about negative numbers? Do they exist or not?

You really can't seem to make up your mind lately. You have been failing
more and more. You post 8 stalker lists whenever you get all autistic
and post one of your stupid attack posts.  Get some help.

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#423857

tirsdag 11. september 2018 00.38.06 UTC+2 skrev Archimedes Plutonium følgende:
> Newsgroups: sci.math
> Date: Mon, 10 Sep 2018 11:30:16 -0700 (PDT)
> 
> Subject: Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x
>  Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Mon, 10 Sep 2018 18:30:16 +0000
> 
> Cycloid-Parabola Function, replacing sine&cosine functions// Y = .87x Y = .22x Y = 4.45 - 2.19x Y = .157 -.05x
> 
> Now, you remember how we do the AP Polynomial functions-- they are all straight line segments over intervals. So they are all Y = mx+ b and we can do most of these in our head without resorting to the formula, unless the coefficients are too much to carry in the head.
> 
> 
> For 2 coordinate points, (x0, y0) (x1, y1), we produce the 1st degree polynomial, a straightline or line segment 
> 
> P(x) = y0(x-x1) / (x0-x1) 
>        + y1(x-x0) / (x1-x0) 
> 
> uptick wave 
> (0,0) (1, .87) (1.57, 1) 
> 
> 
> So, from 0 to 1 our first interval line segment is
> Y = .87x for x=0 to x=1
> next
> (1-.87)/1.57-1) = .13/.57 = slope of .22
> Y = .22x for x=1.01 to x= 1.57 (note, we could not say x=1 for that was in the last interval so in 10 Grid we substitute 1.01)
> 
> Now for the downtick portion of the Cycloid-Parabola Wave
> 
> and the downswing or downtick portion taking the complement of .94 to be .06
> 
> (1.57, 1) (2, .06) (3.14, 0) 
> 
> P(x) = y0(x-x1) / (x0-x1) 
>        + y1(x-x0) / (x1-x0)
> 
> So, from 1.57 to 2 interval
> (.06 - 1) / (2-1.57) = -.94/ .43 = -2.19 slope
> Y = 4.45 - 2.19x for x = 1.571 to x= 2
> 1(x-2)/(1.57 -2) + .06(x-1.57)/ (2-1.57)
> (x-2) / -.43   +  .06(x-1.57) / .43
> -2.32x + 4.65 + .13x - .20
>  Y = 4.45 - 2.19x close enough off by a little
> 
> From 2.01 to 3.14 interval
> (0- .06) / (3.14 -2) = -.06/ 1.14 slope is -.05
> 
> Y = .157 -.05x close enough, off by a little
> 
> So, putting together all four line segments we have
> 
> Y = .87x
> Y = .22x
> Y = 4.45 - 2.19x
> Y = .157 -.05x
> 
> Now, comparing that to the semicircle
> Now instead of sawtooth sine periodic, let us do a flattened top. so I go from (0,0) to (.5,1) then a flat line segment Y = 1 over interval x=.5 to x=1.5 then back to a downward slope from 1.5 to 2 
> 
> Y = 2x for x from 0 to .5 
> Y = 1 for x from .5 to 1.5 
> Y = 4 - 2x for x from 1.5 to 2 
> 
> Notice how the 4-2x matches up nicely with the 4.45 - 2.19x
> 
> AP
> 
> Newsgroups: sci.math
> Date: Mon, 10 Sep 2018 12:48:29 -0700 (PDT)
> 
> Subject: Cycloid-Parabola and Semicircle-Semicircle Waves have vertices Re:
>  Cycloid-Parabola Function, replacing sine&cosine functions
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Mon, 10 Sep 2018 19:48:29 +0000
> 
> Cycloid-Parabola and Semicircle-Semicircle Waves have vertices Re: Cycloid-Parabola Function, replacing sine&cosine functions
> 
> - show quoted text -
> Now I wish I could draw this into the post, but ascii art is limited. What I want to portray is the geometry of the wave of cycloid-parabola and where that wave is far superior to the semicircle wave or and sine wave. 
> 
> Superior in the sense that at the peak of the uptick we immediately do a downtick, and we could do this with a semicircle wave, only the downtick would be another semicircle inverted. And, if you flip a drawing of the Cycloid-Parabola Wave flip it over 180 degrees you have the same wave only the vertex points going in opposite directions. And one can nest two of these to form a rectangle that is interlocking. Something useful in Hund's rule as two electrons share a suborbital. 
> 
> But what is critically important, is that it appears the Cycloid-Parabola or the Semicircle-Semicircle Waves are the most simple of all waves-- even more simple than pure semicircle or any form of sine. 
> 
> And, one can take a Semicircle wave and assemble a SemiCircle-Semicircle Wave very similar to the Cycloid-Parabola, where the Semicircle-Semicircle vertex is more blunt and the Cycloid-Parabola vertex is more sharp, more hook like. 
> 
> Physics should love these new waves, for light waves and magnetic field waves are likely to be these type of waves. 
> 
> AP

Just for fun: https://xkcd.com/2048/

KON

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