Tag Archives: Golden Ratio

Deliberately Difficult to Watch

I’ve never tried this before: create a rotating polyhedral image which is difficult to watch, using disorienting effects, such as the rotation of the images of spirals on the rotating faces. The spiral is made of golden gnomons (obtuse triangles with … Continue reading

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Sprawling Golden Tiling, in Progress

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The Second of Dave Smith’s “Bowtie” Polyhedral Discoveries, and Related Polyhedra

Dave Smith discovered the polyhedron in the last post here, shown below, with the faces hidden, to reveal how the edges appear on the back side of the figure, as it rotates. (Other views of it may be found here.) … Continue reading

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A Euclidean Construction of a Golden Rectangle in Which All Circles Used Have Radius One or Two

There is more than one way to construct a golden rectangle using the Euclidean rules, but all the ones I have seen before use circles with irrational radii. This construction, which I believe to be new, does not use that shortcut, … Continue reading

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The Golden Ratio: Working from a Definition to Find a Value

I found the image above through the Wikipedia article on the golden ratio. After using what appears above to define the golden ratio, the article then reveals its exact and approximate values. Later, the writers of the article do show … Continue reading

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A Regular Decagon, Decomposed into Golden Triangles and Golden Gnomons

The golden triangles, in yellow, are acute isosceles triangles with a leg:base ratio which is the golden ratio. Golden gnomons, shown in orange, are related, for they are obtuse isosceles triangles where the golden ratio shows up as the base:leg … Continue reading

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A Golden Tessellation

This tessellation can be viewed in at least two ways: it can be seen as being composed of overlapping octagons which are equilateral, but not equiangular — or it can be viewed as a periodically-repeating pattern of golden gnomons, as … Continue reading

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