Circling the Square

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circling the square

Snowflake Mandala

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Snowflake Mandala

Dodecagon with Diagonals

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dodecagon

Euclidean Construction of the Regular Triacontagon

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Euclidean Construction of the Regular Triacontagon

Another Construction of the Golden Rectangle

As if one were needed:

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Mandala for the Number 8

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Mandala for the Number 8

Cuboctahedron Constructed from Rhombic Triacontahedra

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Cuboctahedron Constructed from Rhombic Triacontahedra

The software used to produce this image may be tried as a free trial download at http://www.software3d.com/Stella.php.

Count the Dots!

I’ll be nice, and not name names, but there was a time, when I taught at another school, when I had in-school suspension for half a day, every school day, for an entire semester. It sucked.

There was a senior in this high-school version of, well, jail, who was working on Geometry homework. I was trying to help him — and to get him to think for himself. (I’m always trying crazy stuff like that.)

To do the problem he was working on, he had to know what three times eight equals. He was 18, or perhaps 19, and a senior. I was not willing to simply tell him the product of three and eight, because . . . that’s just ridiculous.

I told him to draw a row of eight dots on his paper. He did. I told him to draw another such row beside the first row. He did. I told him, finally, to add a third row. He did, and gave me an utterly blank look.

I said, “Now count the dots.” He did.

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Even though he got the correct answer, he was still furious at me for, well, possibly the rest of his life, which may or may not still be going on. We haven’t kept in touch.

Mandala Based On 45

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Mandala Based On 45

Rotating Zonish Polyhedron

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Rotating Zonish Polyhedron

Creating zonish polyhedra (related to zonohedra) and creating rotating polyhedral .gifs are two features newly added to Stella, the program used to make this, which may be tried for free at http://www.software3d.com/stella.php