Problem 1459. Triangular Tiling Dots in a Circle

Created by Yaroslav

Solve Later

{"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>"}]}

Solve

Solution Stats

61 Solutions
29 Solvers

Last Solution submitted on May 16, 2023

Last 200 Solutions

Problem Comments

1 Comment

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.

Solution Comments

Show comments

Problem Recent Solvers29

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 1459. Triangular Tiling Dots in a Circle

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers29

Suggested Problems

More from this Author18

Problem Tags

Community Treasure Hunt

Problem 1459. Triangular Tiling Dots in a Circle

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers29

Suggested Problems

More from this Author18

Problem Tags

Community Treasure Hunt

Players