Proving Fermat's principle without calculus?

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Discussion Overview

The discussion centers around the historical and mathematical aspects of Fermat's principle, particularly how Fermat formulated his ideas without the use of calculus, which was developed later by Newton and Leibniz. Participants are interested in exploring the challenges Fermat may have faced and the historical context surrounding the development of Snell's law.

Discussion Character

  • Exploratory, Historical, Conceptual clarification

Main Points Raised

  • One participant suggests discussing the methods Fermat used to prove his principle without calculus and the problems he encountered due to the absence of modern mathematical notation.
  • Another participant expresses a need for clarification on the historical sequence of events related to Fermat's work.
  • A moderator notes that the thread has been moved to a more appropriate forum, highlighting the dual nature of the topic as both mathematical and physical.
  • A participant mentions that despite the lack of modern notation, historical figures had methods to express their calculations, referencing an original paper by Leonhard Euler as an example of how mathematical ideas can be conveyed differently over time.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specific methods Fermat used or the historical context, and multiple views on the relevance of the topic to different fields remain evident.

Contextual Notes

The discussion acknowledges limitations related to the absence of modern mathematical notation and the potential challenges in interpreting historical texts.

Nikhil Kumawat
According to me this topic must be raised and discussed how fermat did it without calculus.What problems he faced since calculus was developed afterwards by Newton leibniz.

http://aapt.scitation.org/doi/10.1119/1.1514235

Moderator's edit: File substituted by link due to potential copyright violation.
 
Last edited by a moderator:
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I need help over this topic too...and a clarification over how the series of events went in history..
 
@Nikhil Kumawat thread is being moved to General Math - the New Member forum is for introductions not questions.
 
I moved it to Classical Physics as there might be better chances of an answer. Although it is about mathematical techniques, it is a physical law at its heart. The historical aspect of it is also about the history of Snell's law.

@Nikhil Kumawat please remind me to move it back to mathematics in case you won't get answers here. Both subforums are suited, so the question where it belongs to has no unique answer.

The fact, that there was none of our modern notations doesn't imply they haven't had methods to deal with. There have been several wordings around which actually describe the calculations, simply in other terms. I've recently read an original paper from Leonhard Euler about the gamma function and couldn't identify even the function from this. This doesn't affect the fact, that it nevertheless contained the statement which we nowadays write down in a completely different manner.
 
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