Does any one have a view on the possiblity that Fermat's and Wilson's Theorem might be the background cause of Pythagoras all around us?
Can you be specific. What do you mean by "background cause"? Which theorem by Fermat? Fermat's Little Theorem? Fermat's Last Theorem (I see it is tagged in the question, but not stated above)?
If you mean Fermat's Little Theorem (or the Last Theorem) and Wilson's Theorem from Number Theory (as tagged), can you elaborate your question a bit more, especially what you mean by "cause of Pythagoras all around us"? What about Pythagoras? Be specific and precise.
This may help people answer this question.
Thank you Daniel. Yes I do mean the Theorem you guessed. The question I am trying ask is: Do the Pythagorean properties of Euclidean space ultimately derive from the Fermat and Wilson Theorem, not allowing any alternative?
I stumbled across this question and find the Pythagorean aspect interesting and understand the relation to Fermat's LAST theorem. But in reading about Wilson's theorem, it appears related only to Fermat's LITTLE theorem, which seems to me to have nothing to do with the LAST theorem.
While waiting for clarification I'll venture my opinion. I have thought about the occurrences of Pythagorean related formula extensively, especially in relativity theory. They occur in the Pythagorean form, which is the power 2 form of the Fermat LAST theorem, regardless of the dimensionality of the problem. Therefore, I do not think there is a relation. It is only coincidence that the power 2 is integer solvable. I have not seen any need for integers in any of these applications, which further supports my conclusion.
Indeed, I have a similar feeling, but I can not, of course, prove it. I think a similar idea underlies (for Pytaghor) the undelivered "simple and amazing" proof of the Great theorem of Fermat. As far as we studied, the Pythagoreans believed that the basis of nature are the numbers even wrote poems about it. Today we witness the coloring with millions of colors obtained by numbers. Greetings: Anna Tomova.
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