Triangles and Circles

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Triangles and Circles

Mostly Empty Space

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Mostly Empty Space

Ask any chemist or physicist, and they’ll verify that ordinary matter is mostly empty space. (The physicist may then go on to confuse you by explaining how that “empty” space isn’t really empty,  if inspected closely enough, but that’s not my subject here.)

This image, geometrically created, is also mostly empty space. To make it, I started with the polyhedron seen in the last post — itself created by stellation of the post before it — and continued stellating, many more times. By doing so, I stumbled across a polyhedron with these “X” shapes included, plus some other stuff. To finish making this, I simply rendered everything except the “X” shapes invisible, then changed the coloring scheme of the result.

Stella 4d was used to create this image, and you may try it for free at http://www.software3d.com/stella.php.

Concentric Pentagons, Pentagrams, and Circles

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Concentric Pentagons, Pentagrams, and Circles

Star 46

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Star 46

I started a personal tradition 43 years ago, on the day I turned three years old, of associating stars with my birthday. On that day, I looked up in the sky, and saw the three stars of Orion’s Belt: Alnitak, Alnilam, and Mintaka. Given that these three stars were bright, and formed a fairly straight line, and given that I was turning three that day, it seemed perfectly obvious that those three stars had been placed there, in the sky, specifically for me — and so, that day, I claimed them as my personal property. (No one has ever accused me of lacking ego, nor self-confidence.)

As a young child, the science that most fascinated me was astronomy. In more recent years, my interest in stars has become more focused on the geometrical figures called stars, or star polygons — and so, now, rather than looking for my birthday stars in the sky, I always use geometry to construct some star, or starlike pattern, based on the number of years I have survived, to date. This is the one for the number 46, my age as of today.

Five

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Five

Twice Seven Is Fourteen

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Twice Seven Is Fourteen

Twice Five Is Ten

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Twice Five Is Ten

Twice Six Is Twelve

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Twice Six Is Twelve

Twenty-five

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Twenty-five

Truncated Octahedron Carousel

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Truncated Octahedron Carousel

The image on each face of this truncated octahedron is the one found in a previous post here, named Ten Circles, and was created with the use of two programs, Geometer’s Sketchpad and MS-Paint. As you’ll notice if you view other posts made today, though, the color scheme has been altered for this polyhedron.

Placing this image on each face of this polyhedron, as well as creating this rotating .gif file, required use of a third program, Stella 4d. This program may tried and/or purchased at http://www.software3d.com/stella.php. Unlike in the previous post, the images were “told” to stay upright while the polyhedron its rotates, creating a rotational effect in the yellow hexagonal faces, but a different effect in the red square faces. As far as I can tell, this is due to their different orientation in space, relative to the axis of rotation.