- Cuchulainn
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I also wondered how Leonhard Euler arrived at all those formulae and equations. In many cases he did a finite difference on the problem and then let h -> 0. Clever. Euler-Lagrange QuoteIn solving optimisation problems in function spaces, Euler made extensive use of this `methodof finite differences'. By replacing smooth curves by polygonal lines, he reduced the problem offinding extrema of a function to the problem of finding extrema of a function of n variables, andthen he obtained exact solutions by passing to the limit as n ! 1. In this sense, functions canbe regarded as `functions of infinitely many variables' (that is, the infinitely many values of x(t)at different points), and the calculus of variations can be regarded as the corresponding analog ofdifferential calculus of functions of n real variables.

Last edited by Cuchulainn on February 11th, 2015, 11:00 pm, edited 1 time in total.

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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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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

- Cuchulainn
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QuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.

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

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

- Traden4Alpha
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QuoteOriginally posted by: CuchulainnQuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.Without electricity, it would not have done him much good.We may stand on the shoulders of giants but giants stand on the rising gravel pile of every-day enabling technologies.

- Cuchulainn
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QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.Without electricity, it would not have done him much good.We may stand on the shoulders of giants but giants stand on the rising gravel pile of every-day enabling technologies.True. They also did not have coffee.

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

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

- Traden4Alpha
**Posts:**23951**Joined:**

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.Without electricity, it would not have done him much good.We may stand on the shoulders of giants but giants stand on the rising gravel pile of every-day enabling technologies.True. They also did not have coffee.They did not need it. They had all those exciting table entries to compute!

- Cuchulainn
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QuoteHis colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems",[15] and Erdős drank copious quantities (this quotation is often attributed incorrectly to Erdős,[16] but Erdős himself ascribed it to Rényi[17]).

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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..

R. van Gulik

- Cuchulainn
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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..

R. van Gulik

- Traden4Alpha
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One write an ODE to maths day, what?

- Cuchulainn
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Good idea!One write an ODE to maths day, what?

Or maybe the 57th way to compute [$]e^5[$]. I'm clean out of ideas.

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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..

R. van Gulik

- Traden4Alpha
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Twas a valiant effort and at least you got above [$]e^4[$] ways, what?Good idea!One write an ODE to maths day, what?

Or maybe the 57th way to compute [$]e^5[$]. I'm clean out of ideas.

- Cuchulainn
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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..

R. van Gulik

- Traden4Alpha
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And later mathematicians Taylored a polynomial for this purpose, what?You can blame it all on a German mathematician(*), Carl Friedrich Gauss, who started the futuristic "mega-trend" back in 1809: He showed us how to "train" a straight line to pass nicely through a cloud of unruly, scattered data points. To find, in effect, a path of least embarrassment.

- Cuchulainn
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The solutions are manifold, what about Gauss' student Riemann?And later mathematicians Taylored a polynomial for this purpose, what?You can blame it all on a German mathematician(*), Carl Friedrich Gauss, who started the futuristic "mega-trend" back in 1809: He showed us how to "train" a straight line to pass nicely through a cloud of unruly, scattered data points. To find, in effect, a path of least embarrassment.

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

- Traden4Alpha
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He made math tensor.The solutions are manifold, what about Gauss' student Riemann?And later mathematicians Taylored a polynomial for this purpose, what?You can blame it all on a German mathematician(*), Carl Friedrich Gauss, who started the futuristic "mega-trend" back in 1809: He showed us how to "train" a straight line to pass nicely through a cloud of unruly, scattered data points. To find, in effect, a path of least embarrassment.

what would the interpretation of the square root of a probability be? something in particular, something we can imagine in the "real" world? or just useful as math in intermediate calculations?

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