Time for MATH MINUTE! (provide your favorite theme music
here).
Get out
your paper & pencil, because I have a new puzzle for you!!
PUZZLE #86 Squares inside squares
This
puzzle is based on an idea from the Math Forum.
A. In the
picture below there is a 12x12 square ABCD with another square EFGH inside it
which is formed by connecting the midpoints of the sides of ABCD. Repeating
this operation we get a 3rd square IJKL inside the smaller square
EFGH.
What
is the size of the smallest square IJKL?
If
you measure it with a ruler you can get an approximate size, but can you find
the exact size? (This requires a mathematical argument.)
B. If we
repeat the above construction to get a smaller square QRST inside a square MNOP
inside square IJKL, what is the size of this square?
Is
there a pattern here?
If
we were to repeat the process again, what size square would we get? Can you make
a mathematically educated guess?
Have
fun!
Send
your comments, ideas and solutions before Monday to the email below, and
in the subject line be sure to put
MM in the subject line
Visit
us here online at:
http://www2.potsdam.edu/parksjm/MM1.1.htm
to see the results every Friday.
See you next time on MATH MINUTE! (theme music fades out here).