How many regions can be obtained by drawing two squares?

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SUMMARY

In the discussion, participants explore the maximum number of regions created by drawing two squares, referencing a previous example with two circles that resulted in three regions. The mathematical representation involves the equations \(|x| + |y| = 1\) and \(|x + y| + |y - x| = \frac{3}{2}\). The use of TikZ for sketching the squares is highlighted, indicating a focus on geometric visualization. Ultimately, the conversation emphasizes the importance of precise drawing tools for mathematical representation.

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  • Basic knowledge of mathematical equations involving absolute values
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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.
 

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