Alexander Bogomolny

Freelance mathematician and educational web developer. I am a proud Israeli American, with love and respect for both countries.

[Alexander Bogomolny @CutTheKnotMath]

Probability in triangle #FigureThat #math #probability

[Alexander Bogomolny @CutTheKnotMath]

Lorian Saceanu's Inequality for All Triangles https://t.co/hpnqx3PJac #FigureThat #math #geometry #inequality

[Alexander Bogomolny @CutTheKnotMath]

@gsramos_ @_felopen @fernandals No, quite irrelevant

[Alexander Bogomolny @CutTheKnotMath]

Probability in triangle #FigureThat #math #probability

[Republic of Mathematics @republicofmath]

#FF for math @CutTheKnotMath @jamestanton @JohnAllenPaulos @GlobalMathProj @stevenstrogatz @monsoon0 @aussiemath @mathyawp @octonion @MathforLove @k8nowak @maanow @Derektionary @jamesgrime @peterrowlett @JohnDCook @mathematicsprof @Mathgarden @ilana_horn @MrHonner @wilderlab

[Alexander Bogomolny @CutTheKnotMath]

Here's a couple of solutions https://t.co/yAAFspFiwR https://t.co/eZRJvPDvkt

[Alexander Bogomolny @CutTheKnotMath]

Probability in triangle #FigureThat #math #probability

[Alexander Bogomolny @CutTheKnotMath]

@KriteeshP What this shows is that "P interior to KLM" => "P interior to the medial traingle" But this is trivial because the former is inscribed in the latter.

[Alexander Bogomolny @CutTheKnotMath]

@KriteeshP Not certain how it all applies that P is interior to KLM

[Alexander Bogomolny @CutTheKnotMath]

@KriteeshP I've nothing against (I am all for) the Indians' pride in their culture and history. But, for crying out loud, did anybody hear the word probability c. 600 BCE.

[Alexander Bogomolny @CutTheKnotMath]

@dennismhunter This is incorrect

[Alexander Bogomolny @CutTheKnotMath]

Seeking problems with 4/7 probability being involved. E.g., Diminishing Hopes II #FigureThat #math #probability https://t.co/Sx6j9Q2dB0

[Alexander Bogomolny @CutTheKnotMath]

@JohnAllenPaulos I am still undecided.

[Alexander Bogomolny @CutTheKnotMath]

@giohio That would be a contribution

[Alexander Bogomolny @CutTheKnotMath]

Every one can take part in this statistical research. Every one is invited https://t.co/3ryHCkuxgA

[Rolf Degen @DegenRolf]

You won't believe what great sh*t a psychologist managed to plant on a predatory journal. https://t.co/i6kCxCeIm7
h/t @maltoesermalte

[Alexander Bogomolny @CutTheKnotMath]

@nntaleb @dasanil @gcfr20 Interesting. But this would be rather upending my intention, not to mention the designation

[Alexander Bogomolny @CutTheKnotMath]

Let {x_k} be uniformly distributed on say, [-1,1] with the mean=0. Is that true that the variance is at least the square of the median? #FigureThat #math #probability

[Alexander Bogomolny @CutTheKnotMath]

@dasanil @nntaleb @gcfr20 That is right. I now examples of statements whose "normal" proofs are rather convoluted, while, with a probabilistic interpretation, you have something short and elegant. E.g., https://t.co/9FMWx88L1V

[Alexander Bogomolny @CutTheKnotMath]

@antfilfon @nntaleb @gcfr20 But there's also a coefficient 1/(2n-1)

[Alexander Bogomolny @CutTheKnotMath]

@dasanil @nntaleb @gcfr20 I think you are trying to prove the inequality; I only asked about its possible probabilistic interpretation. Honestly, I indeed thought of using this interpretation for proving the inequality. Your ideas may be the right way of pursuing that goal

[Alexander Bogomolny @CutTheKnotMath]

@antfilfon @nntaleb @gcfr20 With the sign "-"?

[Alexander Bogomolny @CutTheKnotMath]

@nntaleb @gcfr20 I have a proof for this inequality. There is no doubt that the inequality holds under the stated condition. I was curious whether it admits a probabilistic interpretation

[Alexander Bogomolny @CutTheKnotMath]

@nntaleb @gcfr20 Note that you never used (attached). If you did, you would not have any mildly misleading minus signs on the right