Can a Unit Square be Covered with Six Squares of Side Length Less than 1/2?

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The discussion centers on the mathematical challenge of covering a unit square with six squares, each with a side length of less than 1/2. It is established that while seven squares can successfully cover the unit square, the feasibility of doing so with only six remains in question. Participants are encouraged to explore proofs or ideas that demonstrate the impossibility of such a covering with six squares. The original problem references a source from Newman, which outlines the impossibility of covering with five squares. The conversation invites further mathematical exploration and proofs related to this geometric problem.
julien
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Hello,

A problem from Newman, which I posted at
http://www.mymathforum.com/POW/POW1.pdf , asks to show that it is
impossible to cover a unit square with 5 squares whose sides have
lengths <1/2.


It is possible to realize such a covering with 7 squares.


What if we allow us only 6 squares ?


JS,
http://www.mymathforum.com
 
Mathematics news on Phys.org
It's possible with 7 squares, as shown http://www.stetson.edu/~efriedma/squcosqu/" .
 
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julien said:
A problem from Newman, which I posted at
http://www.mymathforum.com/POW/POW1.pdf , asks to show that it is impossible to cover a unit square with 5 squares whose sides have
lengths <1/2.
how can we prove that? any ideas?
 

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