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March 5th, 2017, 12:39 PM   #1
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High-order root-approximating methods for children

Hi All,

Hope you find of some interest how to teach children on high-order root-approximating methods (at any desired convergence rate) based on the generalized mediant which is well-known operation for Number theorists.
No derivatives, no Trial-Error checks, No Geometry, but just the Simplest Arithmetic.

Kindly take a look at the introduction on the new high-order methods for children at:
https://domingogomezmorin.wordpress.com/


Best Regards,
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March 5th, 2017, 01:24 PM   #2
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are children generally in need of high-order root-approximating methods?
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March 5th, 2017, 02:40 PM   #3
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Yes, talented children certainly do:

MATHPATH
Program for middle school students showing high promise in mathematics:
Cube roots via mediants

Last edited by skipjack; March 5th, 2017 at 04:50 PM.
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March 5th, 2017, 03:52 PM   #4
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Nevermind. OP is basically spam. Totally not for children. It's a link to his book.

Last edited by Maschke; March 5th, 2017 at 04:25 PM.
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March 5th, 2017, 05:12 PM   #5
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Quote:
Originally Posted by Maschke View Post
Nevermind. OP is basically spam. Totally not for children. It's a link to his book.,
which spam I have seen on other sites.
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March 5th, 2017, 05:15 PM   #6
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Quote:
Originally Posted by romsek View Post
are children generally in need of high-order root-approximating methods?
Absolutely. Every time I visit kindergarten, I am asked about the third real root of 11. Aren't you? Few kindergarteners are high on complex roots. But the REAL roots? HUGE deal among 5 and 6 year olds.
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Last edited by JeffM1; March 5th, 2017 at 05:17 PM.
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March 5th, 2017, 05:19 PM   #7
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Quote:
Originally Posted by arithmo View Post

Yes, talented children certainly do:

MATHPATH
Program for middle school students showing high promise in mathematics:
Cube roots via mediants
Please, let young students find their way. Freedom.

Press News: ┬┤The Irish Independent┬┤ Dublin, Irlanda
January 24, 2004. Irish student awarded for his work based on some of the new methods shown in this book.

Boffins of the future gunning for glory - Independent.ie
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March 5th, 2017, 07:22 PM   #8
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Originally Posted by JeffM1 View Post
which spam I have seen on other sites.
I figured I'd see a mention of gnomons somewhere in the preview text....
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March 7th, 2017, 02:16 AM   #9
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Quote:
Originally Posted by arithmo View Post
Hi All,

Hope you find of some interest how to teach children on high-order root-approximating methods (at any desired convergence rate) based on the generalized mediant which is well-known operation for Number theorists.
No derivatives, no Trial-Error checks, No Geometry, but just the Simplest Arithmetic.

Kindly take a look at the introduction on the new high-order methods for children at:
https://domingogomezmorin.wordpress.com/


Best Regards,
There is an exact method via recoursive difference... pls search in my old post.

Given a $P\in\mathbb{N+}$, to have it's cubic root

Start from X=1, make the recoursive difference rising X using:

M_3(x)=3X^2-3X+1

Example: P=27

27-1=26
26-7=19
19-19=0 3 is the cubic root of 3
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March 7th, 2017, 12:09 PM   #10
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Quote:
Originally Posted by complicatemodulus View Post
There is an exact method via recoursive difference... pls search in my old post.
Given a $P\in\mathbb{N+}$, to have it's cubic root
Start from X=1, make the recoursive difference rising X using:
M_3(x)=3X^2-3X+1
Example: P=27
27-1=26
26-7=19
19-19=0 3 is the cubic root of 3
ok. thanks.
What about, say, the cube root of 2

Last edited by greg1313; March 7th, 2017 at 12:41 PM.
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