Drawing a Line on a Digital Display

Lines at an angle have to be approximated on a digital display by picking a certain sequence of pixels to turn on. The optimal choice has a structure that depends on issues in number theory. Antialiasing can be done by grouping neighboring pixels and weighing them by the distances from the actual line.

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Rational slopes lead to repeating patterns; square roots and other quadratic irrationals lead to nested patterns.
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Related Curriculum Standards

US Common Core State Standards, Mathematics