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Circle Packing
From Daniel WIlson on Bluesky. He writes "This could be an interesting board game design. (11,12). Circle packing along logarithmic spirals with filling of sets of two circles and the void between them. #CreativeCoding #MathArt #MathSky #phyllotaxis #SciArt" Made with Excel and Krita.
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HAPPY PI DAY!!
yes, it is finally that time of year, where 3.14 is put into date form - it is 03.14.2025! (or 14.03.2025 if you’re european like me)
i have had to physically stop myself from telling everybody i know, but on the hellsite i must ramble: a pi fact especially for pi day!
did you know bees use pi to store their honey?
beehives are made of hexagonal cells because hexagons are the most efficient shape for storing honey, while using the least wax.
the Honeycomb Conjecture by Thomas Hales states that a regular hexagonal grid (honeycomb) has the least total perimeter when dividing a plane into regions of equal area.
building using squares or triangles require more wax for the bees, and circles would leave gaps when storing honey.
hexagons naturally fit together perfectly, making the most efficient beehive.
the best way to pack circles together is also in a hexagonal pattern (if you can’t tell, i love mathematical packing problems), called the Kepler Conjecture when in a sphere but this is how it looks in 2D circles as shown below:
look at the gaps! look at how they disappear!
the density of an optimal circle packing is given by pi, as pi is included in the area of a circle - meaning bees naturally evolved to use pi in one of the most efficient engineering applications centuries before we even knew what it was!
it’s days like these that remind me without pi, circles would just be… pointless…
alternative text: Black circle outlines fill a leaf shape on a white background. The leaf shape is a stem running from the bottom right of the frame to the top left. There are smaller leaf shapes from the center to the top left coming off the stem on the bottom side.
Part of the Journey
(source code)
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An abstract piece using circle packing.
alternative text: Black circle outlines fill a leaf shape on a white background. The leaf shape is almost centered in the frame; It's slightly offset to the top right. There is a gap in the top left of the shape that looks like a tear. the stem is coming off in the bottom left of the leaf and gradually curls up.
alternative text: Black circle outlines fill a leaf shape on a white background. The leaf shape is centered with the stem at the top and the leaf part at the bottom.
