521
/www/nrich/html/content/97/07/six6/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">
<p>It is possible to dissect any square into smaller squares. For
example a 3 by 3 square can be dissected into either 9 smaller
squares or 6 squares:</p>
<mdo:image src="pic4.gif" border="0" alt=""></mdo:image> <br></br>
<br></br>
<br></br>
<ul type="DISC">
<li>What is the minimum number of squares a 13 by 13 square can be
dissected into?<br></br>
<br></br></li>
<li>What is the smallest size square which can be dissected into
squares which are all different sizes?<br></br>
<br></br></li>
</ul>
</mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><p>The minimum number of squares a 13 by 13 square can be dissected into is 11:<br></br>
<mdo:image src="dissect.png"></mdo:image></p>
<p>There is one trivial solution to the size of the smallest square which can be dissected into squares which are all different sizes: the unit square! The smallest non-unit square which can be dissected into squares which are all different sizes has sides of length 175 units.</p>
<p>For further information on this and other similar problems see Chapter 11, Mrs. Perkins Quilt and Other Square-Packing Problems in Mathematical Carnival by Martin Gardner, published by Pelican books.</p></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
It is certainly worthwhile looking at gradually increasing the size
of the squares. With younger pupils it would be good to allow them
to discuss the situation for even sided squares and those with a
side that is a multiple of 3. For older/more able pupils its a good
idea to go at least as far as a 43 by 43 square! When a large
number have been tried I would suggest that pupils try to examine
their "system" for getting the least number of squares.<br></br></mdoxml>
2
4
0
0
1
0
0
Dissect
It is possible to dissect any square into smaller squares. What is
the minimum number of squares a 13 by 13 square can be dissected
into?
Measures and Mensuration
Area
Sequences, Functions and Graphs
Maximise/minimise/optimise
Using, Applying and Reasoning about Mathematics
Visualising
2D Geometry, Shape and Space
Squares