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Russian Impact Crater Found in Frozen Lake By Fishermen

Russian Impact Crater Found in Frozen Lake By Fishermen

Can you imagine what it would be like to encounter such a thing as this crater?

Can you imagine what it is like to have every window in your whole region suddenly turned into a shower of broken glass, with the temperature at -15 degrees Celsius, as many thousands did?

Thus far, no deaths are known to have happened from this February 15 airburst, nor the 1908 Tunguska Event, the largest in recorded history. In that sense, the Russians lucked out. Twice.

[image source: screenshot posted to Wikipedia]

Zome Icosahedron Encasing a Rhombic Enneacontahedron

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Zome Icosahedron Encasing a Rhombic Enneacontahedron

Zome is a three-dimensional ball-and-stick geometrical modeling system based on the Golden Ratio. I have a large collection, and have used it for years, both as a teaching tool, and for my own investigations. Zome is available for sale at www.zometool.com.

Here is a close-up shot, so you can better see the interior of this figure:

Rotating Icosidodecahedral Shell

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Rotating Icosidodecahedral Shell

Website where you can try the software used to create this image: http://www.software3d.com/stella.php

I bought this program, Stella 4d, years ago, and have never regretted it. It is one of the most powerful tools available for doing work at the intersection of art and mathematics.

Imp

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Imp

16″ x 20″
acrylic on canvas
2004

Op Art Pentagrams

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Op Art Pentagrams

Icosidodecahedral Nulloid

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Icosidodecahedral Nulloid

Like all nulloids, this has zero volume. It may be seen as six intersecting, regular decagons. Some consider nulloids a subset of polyhedra; others do not.

I made this using Stella 4d, which you can find at http://www.software3d.com/stella.php.

Cuboctahedral Nulloid

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Cuboctahedral Nulloid

Like all nulloids, this has zero volume. It may be seen as four intersecting, regular hexagons. Some consider nulloids a subset of polyhedra; others do not.

I made this using Stella 4d, which you can find at http://www.software3d.com/stella.php.

Faceted Icosidodecahedron

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Faceted Icosidodecahedron

Check out http://www.software3d.com/stella.php to try the software used to make this image.

Triangles, and the Circles for Which Their Sides Are Diameters

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As you can see, these circles intersect on the sides of the triangles. I did not expect that, nor have I proven it. I have moved the triangle around to check to see if this remained true, and it did pass this test. If I can figure out a proof for this, I’ll post it; if one exists already, please post a comment letting me know where to find it.

Later edit: I found out that these points of intersection are the altitude feet. Here’s a diagram showing the lines containing the altitudes, meeting at the orthocenter. These blue lines also contain the angle bisectors of the brown triangle defined by the altitude feet.