Description:
Mathematical discussions and pursuits.
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Cevian triangles
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Conjecture: If a triangle with integer side lengths a,b,c is such that, for some interior point P of the triangle, the 3 Cevians through P partition the triangle into 6 smaller triangles with integer side lengths, then gcd(a,b,c) > 1.
quasi
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Infinitesimal Slope
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Hello All,
Don't know if this idea has been considered before.
Given the greatest integer function, [Xn] = n for non-negative real Xn, let Yn = Xn - n. Plot this on a rectangular coordinate system and you will get a series of isomorphic saw teeth for n <= Xn < n+1. For an integer N = 0 drop... more »
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Matheology § 018
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Feferman and Levy showed that one cannot prove that there is any non-
denumerable set of real numbers which can be well ordered. Moreover,
they also showed that the statement that the set of all real numbers
is the union of a denumerable set of denumerable sets cannot be
refuted.
[Abraham A. Fraenkel, Yehoshua Bar-Hillel, Azriel Levy: "Foundations... more »
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Einstein and Socratus.
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Einstein and Socratus.
=.
Einstein, you was mistaken using your Gravitation theory
to the all Universe as a whole.
The Gravitation theory doesn’t work in the Universe as a whole.
The Gravitation theory is a local theory.
Why?
Because the detected material mass of the matter in the
Universe ( the cosmological constant / the critical density)... more »
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On the definition of Mathematics and its completeness
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In post titled "mathematics is" I had presented a definition of
mathematics, to re-iterate:
Mathematics is the investigation of behaviors that are formalizable in
consistent formal systems extending logic.
Although the concept is correct yet it is immense. There are
infinitely many consistent formal systems that can extend logic, and... more »
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Contour integral
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Greetings all,
This is probably an easy question, but it's been decades since I've
done much complex analysis.
Pursuant to recent questions here and in other newsgroups, I've
been reviewing my understanding of basic quantum mechanics, and in
one of my texts I've come across this integral over the reals:... more »
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EINSTEIN WRESTLING WITH AN UNSOLVABLE PROBLEM
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[link] John Stachel: "But here he ran into the most blatant-seeming contradiction, which I mentioned earlier when first discussing the two principles. As noted then, the Maxwell-Lorentz equations imply that there exists (at least) one inertial frame in which the speed of light is a constant regardless of the motion of the light source. Einstein's version of the relativity principle (minus the ether) requires that, if this is true for one inertial frame, it must be true for all inertial frames. But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair."... more »
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