Problem 1459. Triangular 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/Triangular_tiling\"><w:r><w:t>Triangular 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).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Assume that a Triangular 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/Bravais_lattice\"><w:r><w:t>2D Hexagonal Bravais lattice</w:t></w:r></w:hyperlink><w:r><w:t> with |</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>a1</w:t></w:r><w:r><w:t> | = |</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>a2</w:t></w:r><w:r><w:t> | = 1 and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>φ</w:t></w:r><w:r><w:t> = 120°.</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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56 Solutions
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Last Solution submitted on Jan 30, 2021

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1 Comment

Rafael S.T. Vieira on 23 Jun 2020

This problem set has so many problems about dots that I'm starting to see spots in my vision.

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geometry grid hexagon

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Problem 1459. Triangular Tiling Dots in a Circle

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Problem 1459. Triangular Tiling Dots in a Circle

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Last 200 Solutions

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Problem Recent Solvers25

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