Problem 1489. Hexagonal Tiling Dots in a Circle

Created by Yaroslav

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Return how many</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Hexagonal_grid\"><w:r><w:t>Hexagonal Tiling</w:t></w:r></w:hyperlink><w:r><w:t> grid points there are inside a circle of radius</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>r</w:t></w:r><w:r><w:t> centred at (0,0) (including points on the edge). Assume that a Hexagonal Tiling grid is a</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Regular_tiling\"><w:r><w:t>2D Regular Hexagonal Tessellation</w:t></w:r></w:hyperlink><w:r><w:t> with equal edges of size</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>e</w:t></w:r><w:r><w:t>=1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For symmetry purposes, assume that (0,0) point is a</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>vacancy</w:t></w:r><w:r><w:t>; i.e., there</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>are</w:t></w:r><w:r><w:t> points at (±1,0), (±1/2,±√3/2), etcetera.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Neither</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>string operations</w:t></w:r><w:r><w:t> nor</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>interpolations</w:t></w:r><w:r><w:t> are allowed!</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

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Last Solution submitted on Jul 22, 2020

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James on 10 Mar 2017

This problem is looking for the number of vertices on the hexagonal grid inside the circle of radius r. The center of the hexagon is not counted as a point for this problem, and this is true for every hexagon inside the circle.

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geometry grid hexagon

Problem 1489. Hexagonal Tiling Dots in a Circle

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Problem 1489. Hexagonal Tiling Dots in a Circle

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