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

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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.
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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...
 
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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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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