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Cuchulainn
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Re: what did the painter do wrong?

June 1st, 2018, 1:58 pm

@"Compute [$]\sqrt{7}[$] by hand to two decimal positions accuracy. And make it snappy."

sqrt(64) - 1/2/sqrt(64) = 8 - 1/16 \approx 3*sqrt(7) => sqrt(7) \approx  127/16/3
And as a number?
2.646 - it's easy to obtain by hand.
using fixed point above
[$]n, a_{n}[$]
////////////////////
1, 4
2, 2.875
3, 2.6548
4, 2.6457
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Cuchulainn
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Re: what did the painter do wrong?

June 1st, 2018, 2:07 pm

There is hope according to Vico

During the Renaissance, imagination prevailed and many wonderful things were accomplished. Since then, Western civilization has gradually devolved into what we see today. We are close to the next turning point.  All societies undergo similar periods of evolution and devolution, as well. 
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Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
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katastrofa
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Re: what did the painter do wrong?

June 1st, 2018, 2:40 pm

Sorry, the fraction 127/16/3 is precisely 2.6458(3). You required two decimal points and accidentally my method sufficed. It's not a robust method of estimating decimal values of square roots, obviously.
 
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Cuchulainn
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Re: what did the painter do wrong?

June 1st, 2018, 3:51 pm

Sorry, the fraction 127/16/3 is precisely 2.6458(3). You required two decimal points and accidentally my method sufficed. It's not a robust method of estimating decimal values of square roots, obviously.
This discrepancy can possibly be attributed to the fact that CF has convergence rate bounded by CF for Golden Ratio, i.e. 0.3819.. (Corollary 1.5).
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf
The fixed-point algo has (at most) linear convergence as we can see. Aitken acceleration gives 2nd order acceleration.
http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
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Re: what did the painter do wrong?

June 1st, 2018, 5:12 pm

Any conclusion yet? closing in on the light? or still in the darkness? any word from the jury yet?  needs another  over-painting or not?

few can paint light like that! one light on, another off...
Image
 
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katastrofa
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Re: what did the painter do wrong?

June 1st, 2018, 6:59 pm

Sorry, the fraction 127/16/3 is precisely 2.6458(3). You required two decimal points and accidentally my method sufficed. It's not a robust method of estimating decimal values of square roots, obviously.
This discrepancy can possibly be attributed to the fact that CF has convergence rate bounded by CF for Golden Ratio, i.e. 0.3819.. (Corollary 1.5).
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf
The fixed-point algo has (at most) linear convergence as we can see. Aitken acceleration gives 2nd order acceleration.
Which leads T4As to the proof that it's a Cauchy sequence :-)
 
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Cuchulainn
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Re: what did the painter do wrong?

June 1st, 2018, 10:59 pm

Sorry, the fraction 127/16/3 is precisely 2.6458(3). You required two decimal points and accidentally my method sufficed. It's not a robust method of estimating decimal values of square roots, obviously.
This discrepancy can possibly be attributed to the fact that CF has convergence rate bounded by CF for Golden Ratio, i.e. 0.3819.. (Corollary 1.5).
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf
The fixed-point algo has (at most) linear convergence as we can see. Aitken acceleration gives 2nd order acceleration.
Which leads T4As to the proof that it's a Cauchy sequence :-)
Image
http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik
 
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Re: what did the painter do wrong?

June 1st, 2018, 11:19 pm

This discrepancy can possibly be attributed to the fact that CF has convergence rate bounded by CF for Golden Ratio, i.e. 0.3819.. (Corollary 1.5).
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf
The fixed-point algo has (at most) linear convergence as we can see. Aitken acceleration gives 2nd order acceleration.
Which leads T4As to the proof that it's a Cauchy sequence :-)
Image
and when fate hands you demons, make a Demonade. Maxwell's Demonade!  Is it vegan or not?
 
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Traden4Alpha
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Re: what did the painter do wrong?

June 1st, 2018, 11:37 pm

Which leads T4As to the proof that it's a Cauchy sequence :-)
Image
and when fate hands you demons, make a Demonade. Maxwell's Demonade!  Is it vegan or not?
Who knows if it's vegan but at least the beverage always stays cold no matter what the conditions.
 
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katastrofa
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Re: what did the painter do wrong?

June 2nd, 2018, 1:07 am

Definitely vegan in that case. I'm always cold - except in the middle of the summer in Italy when temperatures go above 30C. My hands and feet are still cold though. Anyway, doesn't one also need some sugar for the lemonade? Or is this another (sugar) tax avoidance scheme?
 
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Traden4Alpha
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Re: what did the painter do wrong?

June 2nd, 2018, 1:39 am

Definitely vegan in that case. I'm always cold - except in the middle of the summer in Italy when temperatures go above 30C. My hands and feet are still cold though. Anyway, doesn't one also need some sugar for the lemonade? Or is this another (sugar) tax avoidance scheme?
That sounds like Raynaud's Syndrome.
 
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Cuchulainn
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Re: what did the painter do wrong?

June 2nd, 2018, 1:41 pm

Any conclusion yet? closing in on the light? or still in the darkness? any word from the jury yet?  needs another  over-painting or not?
yes! See Kevin Spacey' blackboard QED
http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik
 
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Cuchulainn
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Re: what did the painter do wrong?

June 2nd, 2018, 3:22 pm

The [$]\sqrt 7[$] identity is wrong. The continued fraction should be the golden ratio with the only radical being [$]\sqrt 5[$]. So the two side cannot be equal.
so he messed up that also? 
well supposedly he forgot the ln in front of 2, so they had to add "ln" above the 2 later on, can be seen from the painting kind off. And now u say one more error, I need to tell them and ask if they can fix it. this is what happen when one hire painters/artists with no math skills?

or a math-smart painter putting in math errors on purpose? wanting people to think...?
What yer Norwegian artist (like Kevin Spacey) wanted to say was that every algebraic number such as [$]\sqrt n[$] for each [$]n \in \mathbb{Z} [$] has a continued fraction expansion (but there was not enough space on the margin).  So, can we close this discussion by saying that each algebraic number can be characterised by Cauchy sequence of continued fractions?
Last edited by Cuchulainn on June 2nd, 2018, 3:45 pm, edited 1 time in total.
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http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik
 
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Cuchulainn
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Re: what did the painter do wrong?

June 2nd, 2018, 3:34 pm

The artist knew his Joyce

Image
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Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
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Re: what did the painter do wrong?

June 2nd, 2018, 5:27 pm

Any conclusion yet? closing in on the light? or still in the darkness? any word from the jury yet?  needs another  over-painting or not?
yes! See Kevin Spacey' blackboard QED
"Grattan-Guinness 1970 has suggested that Cauchy "stole" this and other ideas from Bolzano's paper of 1817."  
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