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5th Degree Polynomial Wave Projection

Topic closed. 18 replies. Last post 9 years ago by JADELottery.

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The Quantum Master
West Concord, MN
United States
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December 7, 2001
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Posted: July 31, 2007, 5:29 am - IP Logged

kind of makes sense if your data plots with a nice sine wave...

red balls in powerball have a range of 1 to 42 every draw, a graph of that is a jagged sawtooth that appears to have no rhyme or reason....

you can limit sorted order whiteballs to observed range and cut the choices, but the red ones are as noisy as plotting DRAW ORDER data.

all we have to go on is past history, which is supposedly random (looks random to me, except how they always manage to avoid drawing the numbers on my ticket).

I was trying to apply some sort of "weight" to the possible outcomes based on observed history... such as

Higer/Lower... works ok near the range boundaries, less so in the middle

odd/even... proved useless

hot follower... covered less than 10% for each case

on white balls, my "weights" would put 3 of the 6 numbers I picked in the range most of the time... but a range still leaves ambiguity... my goal is always "one pick-DONE"

is there some other method or adaptation of this method that can focus more closely on a point rather than a range?

hypersoniq,

I have a basic process for finding the Wave Matrix for the Powerball Number 1 to 42. You'll have to goto the following link because the LP editor can't handle the load of information and the formatting.

Powerball Number Linear Regression, BMA and Wave Matrix

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.
Use at your own risk.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

    Fibonacci's avatar - Lottery-050.jpg
    New York, NY
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    May 16, 2006
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    Posted: July 31, 2007, 7:21 am - IP Logged

    Great stuff but after two pages we are yet to see anyone apply this to any set of numbers. 

    $$$

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      The Quantum Master
      West Concord, MN
      United States
      Member #21
      December 7, 2001
      3675 Posts
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      Posted: August 1, 2007, 2:14 pm - IP Logged

      Great stuff but after two pages we are yet to see anyone apply this to any set of numbers. 

      Fibonacci,

      Yes, you are right.

      Same goes for myself not posting more examples.

      However, I'm posting this information for those who know how to use the information.

      Also, when JADE LSG 2.0 is relased, all the topics I've posted will be a function in some form within the JADE LSG program.

      Presented 'AS IS' and for Entertainment Purposes Only.
      Any gain or loss is your responsibility.
      Use at your own risk.

      Order is a Subset of Chaos
      Knowledge is Beyond Belief
      Wisdom is Not Censored
      Douglas Paul Smallish
      Jehocifer

        JADELottery's avatar - MeAtWork 03.PNG
        The Quantum Master
        West Concord, MN
        United States
        Member #21
        December 7, 2001
        3675 Posts
        Offline
        Posted: August 5, 2007, 6:13 am - IP Logged

        I am curious, how the coefficients are chosen? Thanks.

        P.S. Just for grins I wonder if differentiating the equations and plotting against the original may give any valuable data from the intersects? Or possibly shifting the phase by introducing a sine, cosine, or cotangent function into the lower degrees of the polynomials.  I say this because the plot shown looks like 2.5 cycles of a dinged decay.  Just a thought.

        jarasan,

        I'd like to redirect on your earlier reply.

        Quote: "P.S. Just for grins I wonder if differentiating the equations and plotting against the original may give any valuable data from the intersects? Or possibly shifting the phase by introducing a sine, cosine, or cotangent function into the lower degrees of the polynomials.  I say this because the plot shown looks like 2.5 cycles of a dinged decay.  Just a thought."

        I have made another post related to this one topic, link: 1 to 11 Point - Polynomial Wave Projection Equations. It is an expansion of this topic.

        Ideally, you'd only want to use these Equations to project for the next data point. Once a new data point has been selected for the data you're analyzing, the calculations should be done again for the new point giving a new direction based on a new projection. The equations are set up that way to accommodate just the next possible point.

        You could apply the differential to a wave in the Wave Matrix, just as a suggestion. Or, even a differential of a differential; it could be interesting.

        The idea for this polynomial projection came from my study into the Taylor Series Expansion of the Sine and Cosine functions. Also, in the similarities to the Least Squares Fitting for finding a polynomial curve fit for plotted data. Below are the Taylor Series Expansion for a few terms of the Sine and Cosine functions.

        Taylor Series for Cosine and Sine
        Cos x = (x0 / 0!) - (x2 / 2!) + (x4 / 4!) - (x6 / 6!) + ...

        Sin x = (x1 / 1!) - (x3 / 3!) + (x5 / 5!) - (x7 / 7!) + ...

        Adding these two functions leads to an nth degree polynomial.

        Cos x + Sin x = (x0 / 0!) + (x1 / 1!) - (x2 / 2!) - (x3 / 3!) + (x4 / 4!) + (x5 / 5!) - (x6 / 6!) - (x7 / 7!) + ...

        Both Cosine and Sine can operate at different frequencies (a - Cosine, b - Sine) and magnitudes (A - Cosine, B - Sine). This gives the equation as follows:

        A Cos ax + B Sin bx = (A a0 / 0!) x0 + (B b1 / 1!) x1 - (A a2 / 2!) x2 - (B b3 / 3!) x3 + (A a4 / 4!) x4 + (B b5 / 5!) x5 - (A a6 / 6!) x6 - (B b7 / 7!) x7 + ...

        The coefficients are then as follows:

        a0 = (A a0 / 0!)
        a1 = (B
        b1 / 1!)
        a2 = (-A
        a2 / 2!)
        a3 = (-B
        b3 / 3!)
        a4 = (A
        a4 / 4!)
        a5 = (B
        b5 / 5!)
        a6 = (-A
        a6 / 6!)
        a7 = (-B
        b7 / 7!)
        .
        .
        .

        I needed a way to find A, B, a and b. Also, I only needed part of the equation because I would only need to estimate the next point and recalculate after a new data point was recorded. The Least Squares Fitting allowed for a similar polynomial equation to estimate for the a0 to an values rather than try to find A, B, a and b directly.

        The plots you are seeing in this topic are just generic. They are to show the basic concept and have no actual data associated with it. The frequencies and magnitudes of actual waves can vary greatly. Tweak the equations to suite your needs.

        Presented 'AS IS' and for Entertainment Purposes Only.
        Any gain or loss is your responsibility.
        Use at your own risk.

        Order is a Subset of Chaos
        Knowledge is Beyond Belief
        Wisdom is Not Censored
        Douglas Paul Smallish
        Jehocifer