Olivier's interests

Olivier's posts

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In answer to Antti, it is sometimes beneficial to renormalize

sequences to check if the features one imagines remain.

The first version is (A003959 - x)/x

Others are the log of this.

sequences to check if the features one imagines remain.

The first version is (A003959 - x)/x

Others are the log of this.

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2014-11-17

3 Photos - View album

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Since Jess Tauber brought up recently the subject on the seqfan mailing list recently here are two variations on +Harlan Brothers' idea for finding a relation between the binomial triangle and the constant

A) Let's consider the limit of the n*(n-1)/2 -th root of the product of all binomial coefficients of order n.

(see first formula image)

It seems to converge slowly to a value close (?) to e.

B) Let's consider the limit of the n*(n+1)*(n-1)/6-th root of the product of all binomial coefficients (n choose i) raised at the i-th power.

(see second formula image)

It seems to converge slowly to another value greater than 4.

In each case the idea is to count the number of factors incorporating the variable n in the product and then applying the corresponding inverse power.

The correct offset for the polynomials involved in the exponentials might be different from the one I suggest for best results.

**e**.A) Let's consider the limit of the n*(n-1)/2 -th root of the product of all binomial coefficients of order n.

(see first formula image)

It seems to converge slowly to a value close (?) to e.

B) Let's consider the limit of the n*(n+1)*(n-1)/6-th root of the product of all binomial coefficients (n choose i) raised at the i-th power.

(see second formula image)

It seems to converge slowly to another value greater than 4.

In each case the idea is to count the number of factors incorporating the variable n in the product and then applying the corresponding inverse power.

The correct offset for the polynomials involved in the exponentials might be different from the one I suggest for best results.

2013-09-07

2 Photos - View album

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**Black and White Geometric Animations**

h/t to Does it Float

**Animations géométriques en noir et blanc**

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**Aaron Swartz, JStor "disseminator", creator of DemandProgress, dies at 26**

He was also instrumental in pushing what is now RSS.

http://boingboing.net/2013/01/12/rip-aaron-swartz.html

http://www.aaronsw.com/weblog/dalio

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**Salt Labyrinths**

Motoi Yamamoto is a japanese artist constructing large structures with cristallized salt. Among other themes, labyrinths of white salt on dark background, as illustrated here.

More on the artist's web site www.motoi.biz

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**The Geometry of plant seeds**

Splendid illustrations (warning: most colors are arbitrary)

http://blogs.smithsonianmag.com/artscience/2012/11/amazing-close-ups-of-seeds/

h/t to "But does it float".

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Transportation and restoration of a 1949 programmable computer at Bletchley Park. This one was used up to 1973.

See also http://news.bbc.co.uk/2/hi/technology/8234428.stm

I am interested to see it actually working. At the time of the BBC report, the project members say they have not run tests on it yet.

See also http://news.bbc.co.uk/2/hi/technology/8234428.stm

I am interested to see it actually working. At the time of the BBC report, the project members say they have not run tests on it yet.

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Simple but fascinating, visual factorization of integers, in an animated film.

n dots are grouped according to its divisors, one dot added at a time, the previous dots reorganizing.

by Stephen Von Worley at Data Pointed

n dots are grouped according to its divisors, one dot added at a time, the previous dots reorganizing.

by Stephen Von Worley at Data Pointed

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Nice interactive visualization of colors by preference, perceived gender, saturation.

by Stephen Von Worley

by Stephen Von Worley

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**Polygonal forms taken by viscous fluids**

By John Bush and the fluids lab at MIT.

Both experimental and theoretical, stationary figures of flows under controlled conditions, enlarging what was known possible.

Here, as an example, a pentagonal jump boundary.

With short explanations and reference to research papers, starting at this home page http://www-math.mit.edu/~bush/fish.htm.

h/t to +Paul Bourke

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