An Even Simpler “Truly Elementary” Proof of Bertrand’s Theorem
نویسندگان
چکیده
منابع مشابه
A truly elementary proof of Bertrand’s theorem
Bertrand’s theorem is a surprising conclusion of Newtonian mechanics, which states that only the attractive linear and inverse-square forces can yield closed, if bounded, orbits. (For an English translation of Bertrand’s paper, see Santos et al.; for a near-transcription of Bertrand’s proof using modern notation, see Greenberg.) Since the harmonic potential cannot be physically extended over as...
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The fact that a continuous monotone function is differentiable almost everywhere was established by Lebesgue in 1904. Riesz gave a completely elementary proof of this theorem in 1932 by using his ’Rising Sun Lemma’. Other than Riesz’s, all the proofs of this theorem utilize measure theory. Also a geometric proof which involves measure theory and sets of measure zero was given by D. Austin. The ...
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ژورنال
عنوان ژورنال: Journal of Undergraduate Reports in Physics
سال: 2019
ISSN: 2642-7451
DOI: 10.1063/1.5129245