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

  • Thread starter Thread starter julien
  • Start date Start date
  • Tags Tags
    Square Unit
AI Thread Summary
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
Messages
1
Reaction score
0
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/" .
 
Last edited by a moderator:
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?
 

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB Induction: Each square can be covered by L-stones
Replies
5
Views
2K
MHB Minimum area of an odd number-sided, equilateral polygon with side lengths of 1 unit.
Replies
2
Views
2K
What Does Mathematical Sameness Mean?
Replies
7
Views
3K
MHB What is the maximum distance between two points in a square of side length 1?
Replies
1
Views
2K
Trig Help: Measuring Length & Coordinates on a Unit Square Grid
Replies
2
Views
2K
Reduced chi square test in physics
Replies
7
Views
7K
Can Dyadic Squares Approximate the Area of a Unit Disc with Minimal Overlap?
Replies
2
Views
4K
How Can You Optimize a Binary Ruler for Efficient Distance Measurement?
Replies
2
Views
2K
I Einstein brother-in-law elevator
Replies
11
Views
2K
MHB Can 101 Discs of Radius 1/2 Cover a Rectangle That 25 Discs of Radius 1 Can?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top