The Erdős-Bacon Number

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What do Carl Sagan, Richard Feynman, and Natalie Portman have in common?

They all have the same Erdős-Bacon number:  six.

Natalie Portman collaborated (as Natalie Hershlag) with Abigail A. Baird, who wrote mathematical papers in a further collaborative path which leads to Joseph Gillis. Gillis, having co-written a paper with Paul Erdős himself, has an Erdős number of one. This gives Portman an Erdös number of five. Bacon and Portman both appear a movie (which one?  See the details in this Wikipedia article: http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Bacon_number), which gives Portman a Bacon number of one.

The Erdős-Bacon number is simply the sum of these two numbers — hence Natalie Portman’s six:  five plus one.

Feynman’s and Sagan’s sixes are more balanced. Richard Feynman’s is the most so, since his Erdős and Bacon numbers are both three.

I haven’t been able to determine who first thought of an Erdős-Bacon number, but . . . wow. It came from the blogosphere (Where else?) — Wikipedia reveals that much.

Some blogger might be obsessive enough, someday, to exhaustively determine exactly how many people even have such numbers. However, that person will not be me.

Ring of Ten Rhombicosidodecahedra

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Ring of Ten Rhombicosidodecahedra

If oriented just right, ten rhombicosidodecahedra can be stuck together to form a regular decagonal ring.

You may try the software I used to make this, as a free trial download, at http://www.software3d.com/stella.php.

An Icosahedral Cluster of Truncated Icosahedra

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An Icosahedral Cluster of Truncated Icosahedra

Software credit: http://www.software3d.com/stella.php

Ring of Seven Snub Cubes

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Augmented Snub Cube

Seven snub cubes almost make a perfect ring. There’s a small region of overlap between two of them which precludes perfection in this case. If you click on the image, it will rotate, and you’ll be able to spot this overlap-region more easily.

Software credit: see http://www.software3d.com/stella.php

Fifth Wheel

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Fifth Wheel

32 Circles

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56 Circles

Tricycle

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tricycle
(Click to enlarge)

Nonagonal Mandala II

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Nonagonal Mandala II

Tessellation Featuring Golden Rectangles

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Tessellation Featuring Golden Rectangles

Nonagonal Mandala

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