Can Two Rectangles Form a Disjoint Union of Six?

  • Thread starter Thread starter AxiomOfChoice
  • Start date Start date
  • Tags Tags
    Plane
AI Thread Summary
The discussion revolves around the claim that the union of any two rectangles in the x-y plane can form a disjoint union of at most six rectangles. The original poster has been unable to find an example that necessitates six rectangles, consistently arriving at five. Participants are encouraged to provide an example of two rectangles that result in a disjoint union of six. There is also a query regarding the nature of the rectangles, whether they are closed or open. The conversation seeks clarity on the conditions under which this claim holds true.
AxiomOfChoice
Messages
531
Reaction score
1
Consider any two rectangles in the x-y plane. I have a book that asserts that the union of any two such rectangles is the DISJOINT union of AT MOST SIX rectangles. I've been sketching rectangles and simply can't come up with an example that demands SIX rectangles in the disjoint union. The most I can find is FIVE. Can someone come up with an example of two rectangles whose union is a disjoint union of six rectangles? Thanks!
 
Mathematics news on Phys.org
Is there no more information? Are the rectangles closed, open, etc?

What is your 5-rect solution?
 

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 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Similar threads

I Two basic results from measure theory -- on volumes of rectangles
Replies
2
Views
2K
MHB How can I calculate the union of two rotated rectangles using an algorithm?
Replies
8
Views
5K
I Collection of finite unions of half-open intervals form an algebra
Replies
3
Views
3K
I The Basic Area Problem (introduction to the topic of integrals)
Replies
24
Views
3K
Geometry of perspective: apparent projected distance
Replies
1
Views
2K
Open Sets of R^n: Countable Union of Open Rectangles/Balls?
Replies
4
Views
4K
What Does Mathematical Sameness Mean?
Replies
7
Views
3K
Making equations with six six-sided dice
Replies
2
Views
2K
MHB Union of Disjoint Sets with at Most k Sets - Algorithm
Replies
2
Views
2K
How Can We Quantify the Concept of 'Sameness' in Mathematics?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top