Description:
Mathematical discussions and pursuits.
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Billiards
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Hello, suppose to have a ball on a smooth rectangular billiard table. When the particle hits the boundary it reflects from it without loss of speed. I have two questions. (I) Given a point P on the billiard table, and a positive integer M, does there exist a trajectory P(t), with P(0)=P, such that the ball passes again... more »
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bijective tetration ?
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is there an analytic bijective tetration known ? details : 1) bijective from A <-> B where A is the complex plane with real part > -2 and B is the complex plane apart from at most a finite set of complex numbers. 2) analytic on A. (see 1) ) 3) with tetration i mean base e tetration with f(-2)= -oo, f(-1) = 0 , f(0) = 1 and f(x+1) = exp(f(x)).... more »
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I choose three (#2)
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Here are three blogs on science and physics (except for one) that I found interesting today. [link] (pseudo-science to the extreme, but this guy has lots of followers who are nearly as nutty as the cranks usenet. =) [link] [link] (I love that show)... more »
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proof that a + b is unique for any cardinal numbers a,b
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Definition: given sets A, B, C, where A and B have no elements in common, we write a + b = c when there is a one to one correspondence between the elements of C and the totality of elements of A and B. Prove that for any cardinal numbers a, b, a + b is a unique cardinal number. suppose we have the sets A, B, C, D where... more »
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When t^4-z^4=d*w^p
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Given t,z are odd integers, t>z. When t^4-z^4 is representable in the form of d*w^p, where d is integer, w is integer >1, p is prime >=7?
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Math/CompSci Interview Question - Thoughts?
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I was posed the following question in a technical interview for a Software Engineering position by a major multinational NASDAQ company: [Paraphrasing] "You are given an array of 1,000,000 32-bit integers. One int value x occurs 500,001 times or more in the array. Specify an algorithm to determine x."... more »
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I found this interesting stuff with Riemann's ZF
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RZF --> Zeta Function While working with integrals of fractional parts, I came out with this... which I haven't quite seen before (on the internet, or books that I own)... Namely, the equation RZF(n) = 1/(n-1) - integral _1 ^oo 1/r^(1/n) dr 0 < n < 1, n belongs to N I myself am doubtful about the correctness of this equation... But I... more »
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5*z^4 - 11*z^3 + K*z^2 - 11*z + 5
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f[z,K]=5*z^4 - 11*z^3 + K*z^2 - 11*z + 5 where K is a real number. Show that all roots zj of f[z,K]=0 lie on the unit circle the complex plane if and only if ____________. (condition of K)
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Monica Pignotti to Call for Excoriation of LiveJournal?
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Recently, the journal operated by "wayward radish" was deleted. Among other things, this journal contained unsubstantiated and defamatory claims of therapeutic abuse. When WordPress blogs operated by "wayward radish" were deleted, both Monica Pignotti and Larry Sarner spoke out against them. Will history... more »
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