MHB How many regions can be obtained by drawing two squares?

  • Thread starter Thread starter Sadia Ali
  • Start date Start date
  • Tags Tags
    Squares
Click For Summary
The discussion centers on determining the maximum number of regions created by drawing two squares, inspired by Mike's previous experience with circles that produced three regions. Participants express curiosity about the geometric implications of overlapping squares and seek clarification on the mathematical principles involved. Mike shares a sketch using TikZ to illustrate his attempts, despite acknowledging the need for improvement in his drawing skills. There is a light-hearted exchange about the tools available for drawing, including a ruler that Mike has misplaced. The conversation highlights the intersection of geometry and creativity in visualizing mathematical concepts.
Sadia Ali
Messages
1
Reaction score
0
by drawing two circles, Mike obtained a figure, which consists of three regions . at most how many regions could he obtain by drawing two squares? please can someone can explain...
 
Mathematics news on Phys.org
Sadia Ali said:
by drawing two circles, Mike obtained a figure, which consists of three regions . at most how many regions could he obtain by drawing two squares? please can someone can explain...

excuse the finger drawn sketch ...
 
[DESMOS=-3.8620726393622147,4.696963370347444,-5.427839754072847,3.1311962556368065]\left|x\right|\ +\ \left|y\right|\ =\ 1;\left|x\ +\ y\right|\ +\ \left|y\ -\ x\right|\ =\ \frac{3}{2};[/DESMOS]

:p
 
\begin{tikzpicture}[ultra thick]
\draw (-1,-1) rectangle (1,1);
\draw[rotate=45] (-1,-1) rectangle (1,1);
\end{tikzpicture}
[latexs]
\begin{tikzpicture}[ultra thick]
\draw (-1,-1) rectangle (1,1);
\draw[rotate=45] (-1,-1) rectangle (1,1);
\end{tikzpicture}
[/latexs]
:p:p
 
skeeter said:
excuse the finger drawn sketch ...
Mike, don't you have a 6in. little plastic ruler in your
Helix-Oxford Set of Mathematical Instruments?
 
Wilmer said:
Mike, don't you have a 6in. little plastic ruler in your
Helix-Oxford Set of Mathematical Instruments?

My dog buried it somewhere ... just need to practice with the TikZ sketches some more.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
View full post »

Similar threads

MHB Union of 2 Squares: How Many Regions Can Mike Get?
  • · Replies 3 ·
Replies
3
Views
4K
MHB How Can You Calculate the Area of Shaded Regions in Complex Geometric Figures?
  • · Replies 2 ·
Replies
2
Views
2K
I A formula for the number of structures composed of n squares
  • · Replies 3 ·
Replies
3
Views
1K
B How to draw a plane intersecting a cylinder at a "compound angle"
  • · Replies 8 ·
Replies
8
Views
3K
MHB Find the exact shaded area of the region in 4 overlapping circles
  • · Replies 1 ·
Replies
1
Views
3K
MHB How many ways can you draw 3 of one suit and 2 of another suit?
  • · Replies 2 ·
Replies
2
Views
3K
Regions; "Each point of the set is the center of a circle "
  • · Replies 5 ·
Replies
5
Views
2K
MHB Square metric not satisfying the SAS postulate
  • · Replies 3 ·
Replies
3
Views
4K
B Invariant under rotation: Banal, obvious, or noteworthy?
  • · Replies 2 ·
Replies
2
Views
2K
I Is the proof of the KRK endgame theorem rigorous and original?
  • · Replies 13 ·
Replies
13
Views
2K