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The Geometry of Packing Circle Sectors

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Tags: geometrytiling

This video is about circular sectors (https://en.wikipedia.org/wiki/Circular_sector), specifically their packing density. I determined a lower bound for the packing density of this shape that I haven't seen discussed anywhere. This video serves to document the method and talk about packing mathematics in general. It starts with the very basics of packing and works up to a derivation for this new packing density method. The math is all at a high school level; the most complex equations used are the Law of Sines and Law of Cosines, and a single instance of the floor function.

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7 Overall score*

24 Rank

11 Votes

5 Comments

Comments

8.6

Very cool video. Very good animation/editing, very nice explanation, prefect length and good background music. It’s basicly perfect. The only things that I could think of that could be better, are the voice audio quality (The skipping between different recordings) and I’m pretty sure that some body has looked into this tiling of sectors. So maybe a bit of background info/literature research could be helpful. But generally very very good. Keep it going.

6.5

The motivation for this video is cute, and it is very standard for recreational mathematics to start with such a simple curiosity. The final derivation is complex and glossed over, but the rest of the video is quite well paced and is done extremely well.

8.5

Amazing video !

8.3

This is the one sentence that describes this work: Really shows well the creative process (thinking outside the box), and then mathematical refinement for rigour used in problem solving for interesting geometry problems.

Congratulations on the chosen topic, the execution, and the animations. I watched the entire video with pleasure. It could be useful for high-school students who are strengthening their mathematics skills, but unfortunately the students who struggle the most are left out (perhaps already because of the choice of topic), and this somewhat falls outside the aim of SoME4.