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  •  » Define the intersection points of polynomials

#126 2013-06-21 19:58:16

bobbym
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Re: Define the intersection points of polynomials

There could 3 intersections rather than 2.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#127 2013-06-21 20:02:54

Herc11
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Re: Define the intersection points of polynomials

Yes. this is true. So the unknown variables will be six (the 3 intersection points)
So we need 6 cubics etc etc....

#128 2013-06-21 20:05:02

bobbym
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Re: Define the intersection points of polynomials

Yes, you will need 6 equations when there are 3 points of intersection.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#129 2013-06-21 21:11:01

Herc11
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Re: Define the intersection points of polynomials

anonimnystefy,

do you agree with us?

#130 2013-06-21 21:24:33

Herc11
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Re: Define the intersection points of polynomials

How do you construct the polynomials?

MAthematica? I am not familiar with it..

#131 2013-06-21 22:23:47

bobbym
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Re: Define the intersection points of polynomials

There is a better tool for constructing them because it is dynamic. It is called Geogebra.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#132 2013-06-21 22:29:34

Herc11
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Re: Define the intersection points of polynomials

Ok, and for solving the system you use Mathematica or the afore mentioned tool?

#133 2013-06-21 22:42:41

bobbym
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Re: Define the intersection points of polynomials

Mathematica will solve the system and geogebra will construct it.

Here is a good one that I will provide all the data for and leave it as a challenge.


Uploaded Images
View Image: 2013-06-21_041359.gif      


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#134 2013-06-21 22:48:19

Herc11
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Re: Define the intersection points of polynomials

where is the data?

#135 2013-06-21 22:50:37

bobbym
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Re: Define the intersection points of polynomials

Putting it together now. it will take some time to post it. Please hold.

a3 = 1  , point ( 4,18 )

a3 = -0.142857142857141, point ( -4 , 10 )

a3 = 0.017482517482521 point (14 , 40)

a3 = -0.018939393939392 point ( 9 , -10 )

a3 = 0.066137566137551 point ( 10 , 50 )

a3 = -1.111111111111111 point ( 4 , -20 )


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#136 2013-06-21 22:57:49

Herc11
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Re: Define the intersection points of polynomials

Ok. Sorry!

#137 2013-06-21 23:00:51

bobbym
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Re: Define the intersection points of polynomials

No problem, I am filling in post #135

A question about the formula in post #99. It has a P(xi) that the formula in post #98 did not have. What is it?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#138 2013-06-22 00:17:57

Herc11
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Re: Define the intersection points of polynomials

Its

the respective of

#139 2013-06-22 04:12:19

bobbym
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Re: Define the intersection points of polynomials

I am getting for a3



you are saying that P(x3) is y3 which makes sense.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#140 2013-06-22 04:35:40

Herc11
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Re: Define the intersection points of polynomials

Yes I think what you write in #139 is correct.

Last edited by Herc11 (2013-06-22 04:36:05)

#141 2013-06-22 04:41:25

bobbym
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Re: Define the intersection points of polynomials

Okay, I will see if I can solve the problem I posted in post 133 - 135.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#142 2013-06-22 04:46:33

Herc11
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Re: Define the intersection points of polynomials

I think that it will be solved as you have 6 equations and 6 unknowns..x0---y3

#143 2013-06-22 05:34:12

bobbym
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Re: Define the intersection points of polynomials

Look at these two equations:





do you notice something different?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#144 2013-06-22 05:39:49

Herc11
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Re: Define the intersection points of polynomials

No.

#145 2013-06-22 05:49:47

bobbym
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Re: Define the intersection points of polynomials

The a3 has coefficients in it, a0, a1, a2. While the formula for a2 does not have any coefficients in it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#146 2013-06-22 05:58:44

Herc11
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Re: Define the intersection points of polynomials

Yes


So you have only to replace the coefficients with the are equals

#147 2013-06-22 06:06:38

Herc11
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Re: Define the intersection points of polynomials







So, if you now look a_3 you have six unknows. Using 6 cubics I think can leed to a soultion.

#148 2013-06-22 06:18:40

bobbym
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Re: Define the intersection points of polynomials

Yes, if you wanted to solve for the a's too. But you can substitute for those a's with earlier terms can you not?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#149 2013-06-22 06:21:41

Herc11
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Re: Define the intersection points of polynomials

What do you mean?

It is the same thing. You have only to solve the set of equations of a3. \

Afterwards, you know the x0-y3. If you wish you can compute a0-a2, but there is no need.

Of course you can substitute. Either you solve for a0 to a2 or for x0-y3 its the same.

#150 2013-06-22 06:25:58

anonimnystefy
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Re: Define the intersection points of polynomials

Hi guys

Sorry about not posting all day. has the interpolation worked to reduce the number of needed equations?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
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