How many regions can be obtained by drawing two squares?

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In summary, Mike obtained a figure consisting of three regions by drawing two circles. It is possible to obtain up to three regions by drawing two squares. However, it may be difficult to draw accurate sketches without proper mathematical instruments.
  • #1
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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  • #2
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 ...
 
  • #3
[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
 
  • #4
\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
 
  • #5
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?
 
  • #6
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.
 

FAQ: How many regions can be obtained by drawing two squares?

1. What are regions of two squares?

Regions of two squares refer to the overlapping areas when two squares are placed side by side or on top of each other. These regions can vary in shape and size depending on the orientation of the squares.

2. How many regions can be formed from two squares?

There can be up to nine regions formed from two squares, including the two original squares and the seven overlapping regions. However, the exact number of regions will depend on the size and positioning of the squares.

3. What is the formula for finding the total number of regions from two squares?

The formula for finding the total number of regions from two squares is n^2 + 2n + 1, where n is the number of overlapping regions. In the case of two squares, n = 7, so the total number of regions would be (7)^2 + 2(7) + 1 = 49 + 14 + 1 = 64 regions.

4. How are the regions of two squares useful in geometry and mathematics?

The regions of two squares can be used to demonstrate concepts such as symmetry, area, and perimeter. They can also be used in problem-solving and geometric proofs.

5. Are there any real-world applications for regions of two squares?

Yes, regions of two squares can be applied to real-world scenarios such as tiling patterns, architectural design, and computer graphics. They can also be used in game design and puzzle-solving.

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