Partition of a rectangle into squares problem: Difference between revisions
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==Problem statement== | ==Problem statement== | ||
Show that a rectangle can be partitioned into finitely many squares if and only if the ratio of its sides is rational | Show that a rectangle can be partitioned into finitely many squares if and only if the ratio of its sides is rational | ||
==Proof via Dirichlet's simultaneous [[rational approximation]] theorem== | ==Proof via Dirichlet's simultaneous [[rational approximation]] theorem== | ||
We can choose an integer <math>q</math> such that the product of every coordinate of any vertex of | We can choose an integer <math>q</math> such that the product of every coordinate of any vertex of | ||
Revision as of 21:42, 24 June 2006
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Problem statement
Show that a rectangle can be partitioned into finitely many squares if and only if the ratio of its sides is rational
Proof via Dirichlet's simultaneous rational approximation theorem
We can choose an integer 
such that the product of every coordinate of any vertex of
