- January-February 1998 - Triangle Area and Perimeter
I was looking at a common right triangle the other day, and noticed
that when I computed its perimeter, I got the same number as when I
computed its area (though of course the units were different, being
centimeters for perimeter and square centimeters for area). What right
triangle might it have been?...
- March-April 1998 - The Euler Line
Triangle exercises: defining terms; finding triangles given vertices;
creating your own...
- September 1998 - Building a Mobile
Build a three-dimensional object that, when looked at from different angles,
looks like the two-dimensional pictures shown.
- October 1998 - Drawing Segments on a Grid
If you connect (0,0) to (5,3) with a line segment, it goes through seven
unit squares. If you connect (0,0) to (p,q) where p and q are positive whole
numbers, how many squares do you go through?
- November 1998 - Find the Angle Sum of Star Polygons
First, looking at the two "star polygons" in the picture, find the sum of
the angles formed at the tips of each star. Second, find a formula for the
sum of the angle measures at the tips of an n-pointed star.
- December 1998 - Inscribing Nice Boxes in Nice Spheres
Given a box inscribed in a sphere: for all spheres up to 15 units in
diameter, find the dimensions of all the boxes with integer edges that
can be inscribed in a sphere with a diameter that is also an integer.
- January 1999 - A Coloring Exercise
In the picture shown, a square is split into 8 equal parts. How many
different ways can you color in exactly half of the blocks? There's a small
catch - two colorings are considered the same if they could be rotated or
flipped to match up...
- February 1999 - A Counting Exercise
Take a 1x1 square. Count how many squares there are total. Now take a 2x2
square. Count the total number of squares (including the larger one that is
formed by the outside of the whole thing). Take a 3x3 square and find the total.
How many squares would there be in a 10x10 square? How about an NxN square?
Now do the same thing with triangles...