Monday, March 19, 2012

[aggcqjtd] Nice rectangles

Given an number x, find the smallest rectangle with integer side lengths whose area exceeds x, but whose dimensions do not exceed a certain ratio, say 2:1.

Also, what is the sequence of integers which may be written as the product of two integers whose ratio does not exceed, say, 2:1?  What is an algorithm for listing them in order?  I suspect lazy lists might be useful.

Writing text into a rectangular area with minimal padding.

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