How many regions can be obtained by drawing two squares?

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  • Thread starter Thread starter Sadia Ali
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Discussion Overview

The discussion revolves around the problem of determining the maximum number of regions that can be created by drawing two squares. Participants explore this concept through various sketches and mathematical expressions, seeking clarification and insights into the geometric implications.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Mike initially references a scenario involving two circles that create three regions, prompting a question about the analogous situation with two squares.
  • Some participants share sketches using TikZ to illustrate their interpretations of the problem, though the clarity of these sketches is noted to be informal.
  • There is a mention of mathematical expressions related to geometry, though their direct relevance to the main question is not fully articulated.
  • Humorous remarks about drawing tools and the quality of sketches are exchanged, indicating a light-hearted approach to the discussion.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the maximum number of regions created by two squares, and multiple interpretations and approaches are presented without resolution.

Contextual Notes

Some participants express uncertainty regarding the clarity of their sketches and the mathematical expressions shared, indicating potential limitations in understanding the problem fully.

Sadia Ali
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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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