Define the intersection points of polynomials

bobbym · 2013-06-20 21:58:16

There could 3 intersections rather than 2.

Herc11 · 2013-06-20 22:02:54

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

bobbym · 2013-06-20 22:05:02

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

Herc11 · 2013-06-20 23:11:01

anonimnystefy,

do you agree with us?

Herc11 · 2013-06-20 23:24:33

How do you construct the polynomials?

MAthematica? I am not familiar with it..

bobbym · 2013-06-21 00:23:47

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

Herc11 · 2013-06-21 00:29:34

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

bobbym · 2013-06-21 00:42:41

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.

Herc11 · 2013-06-21 00:48:19

where is the data?

bobbym · 2013-06-21 00:50:37

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 )

Herc11 · 2013-06-21 00:57:49

Ok. Sorry!

bobbym · 2013-06-21 01:00:51

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?

Herc11 · 2013-06-21 02:17:57

Its

the respective of

bobbym · 2013-06-21 06:12:19

I am getting for a3

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

Herc11 · 2013-06-21 06:35:40

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

Last edited by Herc11 (2013-06-21 06:36:05)

bobbym · 2013-06-21 06:41:25

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

Herc11 · 2013-06-21 06:46:33

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

bobbym · 2013-06-21 07:34:12

Look at these two equations:

do you notice something different?

Herc11 · 2013-06-21 07:39:49

No.

bobbym · 2013-06-21 07:49:47

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

Herc11 · 2013-06-21 07:58:44

Yes

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

Herc11 · 2013-06-21 08:06:38

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

bobbym · 2013-06-21 08:18:40

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?

Herc11 · 2013-06-21 08:21:41

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.

anonimnystefy · 2013-06-21 08:25:58

Hi guys

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

Math Is Fun Forum

#126 2013-06-20 21:58:16

Re: Define the intersection points of polynomials

#127 2013-06-20 22:02:54

Re: Define the intersection points of polynomials

#128 2013-06-20 22:05:02

Re: Define the intersection points of polynomials

#129 2013-06-20 23:11:01

Re: Define the intersection points of polynomials

#130 2013-06-20 23:24:33

Re: Define the intersection points of polynomials

#131 2013-06-21 00:23:47

Re: Define the intersection points of polynomials

#132 2013-06-21 00:29:34

Re: Define the intersection points of polynomials

#133 2013-06-21 00:42:41

Re: Define the intersection points of polynomials

#134 2013-06-21 00:48:19

Re: Define the intersection points of polynomials

#135 2013-06-21 00:50:37

Re: Define the intersection points of polynomials

#136 2013-06-21 00:57:49

Re: Define the intersection points of polynomials

#137 2013-06-21 01:00:51

Re: Define the intersection points of polynomials

#138 2013-06-21 02:17:57

Re: Define the intersection points of polynomials

#139 2013-06-21 06:12:19

Re: Define the intersection points of polynomials

#140 2013-06-21 06:35:40

Re: Define the intersection points of polynomials

#141 2013-06-21 06:41:25

Re: Define the intersection points of polynomials

#142 2013-06-21 06:46:33

Re: Define the intersection points of polynomials

#143 2013-06-21 07:34:12

Re: Define the intersection points of polynomials

#144 2013-06-21 07:39:49

Re: Define the intersection points of polynomials

#145 2013-06-21 07:49:47

Re: Define the intersection points of polynomials

#146 2013-06-21 07:58:44

Re: Define the intersection points of polynomials

#147 2013-06-21 08:06:38

Re: Define the intersection points of polynomials

#148 2013-06-21 08:18:40

Re: Define the intersection points of polynomials

#149 2013-06-21 08:21:41

Re: Define the intersection points of polynomials

#150 2013-06-21 08:25:58

Re: Define the intersection points of polynomials

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