I don’t usually post the work of others here, but, since I am now using this as my blog’s header-image (in slightly altered form), it seemed appropriate to make an exception for this cartoon, in its original format. I didn’t know that the cartoonists at Cyanide and Happiness monitored my life, but, clearly, that guy in the blue shirt is me!
Because I did not start this blog until mid-2012, I sometimes encounter things I made before then, but have not yet posted here. I made this image in 2011, after reading that the ancient Greeks discovered how to combine the Euclidean constructions of the regular pentagon and the equilateral triangle, in order to create a construction for the regular pentadecagon. Having read this, I felt compelled to try this for myself, without researching further how the Greeks did it — and, as evidenced by the image above, I successfully figured it out, using the Euclidean tools embedded in a computer program I often use, Geometer’s Sketchpad.
What I did not do at that time was show the pentagon’s sides (so it is rather hard to find in the image above, but its vertices are there), nor record step-by-step instructions for the construction. For those who wish to try this themselves, I do have some advice: construct the pentagon before you construct the triangle, and not the other way around, and you are likely to find this puzzle easier to solve than it would be, if this polygon-order I recommend were reversed.
I also have two more hints to offer: 108º – 60º = 48º, and half of 48º is 24º. Noticing this was, as I recall, the key to cracking the puzzle.
Media used: acrylic on canvas.
Although I have not yet seen it in person, this painting is based on images I have seen of Delicate Arch, in Utah’s Arches National Park.
Media used: acrylic on canvas.
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