This is important now as schools are working to figure out how to place desks so that each student is 6 feet apart from their peers.
Circle Packing
11–20 of 32 posts
Re: Circle Packing
#12I recently saw pictures of social distancing circles drawn on the grass in parks [1]. They were drawn in a square grid. It would be more space-efficient to draw them in a hexagonal packing arrangement.
[1] example: https://images.foxtv.com/static.ktvu.com/www.ktvu.com/conten...
Re: Circle Packing
#13Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and Groups -- which summarizes the subject concisely. A recent (2017) break through, was the proof that the Leech Lattice [2] yields the optimal sp…
Our of curiosity and as a noob to coding theory, what makes a Binary Golay code more useful than say a RS Code or something else more common?
The linked wiki article said that given 12 bits, the BG code can encode them as 24 bits with the ability to correct up to 3 bit errors and detect up to 7. If I'm understanding RS codes correctly, an RS code with 12 data and 12 parity bits would be able to correct up to 6 bit errors and detect up to 12. So what is the advantage of a BG code in that case?
Re: Circle Packing
#14I recently saw pictures of social distancing circles drawn on the grass in parks [1]. They were drawn in a square grid. It would be more space-efficient to draw them in a hexagonal packing arrangement. [1] example: https://images.foxtv.com/static.ktvu.com/www.ktvu.com/conten...
I don't think space efficiency is a goal
Re: Circle Packing
#15I was surprised to see the Wikipedia page didn’t mention any best-effort algorithms but I guess they can’t list everything. I like the natural noise you get from Poisson Disc Sampling [1] [1] https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3
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Re: Circle Packing
#16Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and Groups -- which summarizes the subject concisely. A recent (2017) break through, was the proof that the Leech Lattice [2] yields the optimal sp…
I didn't realize he died from COVID complications. That just makes it all the worse.
He was 82.
Re: Circle Packing
#17Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and Groups -- which summarizes the subject concisely. A recent (2017) break through, was the proof that the Leech Lattice [2] yields the optimal sp…
Can you suggest some books to learn interesting math topics for someone with just high school understanding of math?
Re: Circle Packing
#18Saw a beautiful example of this in action the other day in the Observable "cherry logo" notebook: https://observablehq.com/@observablehq/cheery-logo
Re: Circle Packing
#19I recently saw pictures of social distancing circles drawn on the grass in parks [1]. They were drawn in a square grid. It would be more space-efficient to draw them in a hexagonal packing arrangement. [1] example: https://images.foxtv.com/static.ktvu.com/www.ktvu.com/conten...
There's a picture from a Belgian school using hexagons.
https://www.theguardian.com/world/gallery/2020/may/30/how-we...
Re: Circle Packing
#20Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and Groups -- which summarizes the subject concisely. A recent (2017) break through, was the proof that the Leech Lattice [2] yields the optimal sp…
There is a great Numerphile video that links sphere packing to mathematics.
https://youtu.be/CROeIGfr3gs