Dear Mom,
Toady in my MATH 3500 class we learned how to cut
different cross sections out of a given unit cube. A unit cube is
a cube with all edges equal to one unit in length. A cube has six
faces, which are the flat sides. Each face has an area of one square
unit. The cube also has eight vertices. A vertex is a corner
of the cube. Finally a cube has twelve edges, which are connecting
lines between vertices. In our observations in class we wanted to
see what kind of cross section of a cube would result in certain planner
figures. The figures that we were trying to create were a square;
a shape with four edges all of the same length, and four vertices, that
are all ninety degrees in measure. We also wanted to try and create
a rectangle, which is almost exactly like a square, except one pair of
parallel edges is not the same length as the other. We also wanted
to try and create an isosceles triangle, which is a shape with three edges,
and three vertices, where the two top edges are equal in length, and the
two bottom vertices are equal in measure. We also were trying to
create an equilateral triangle, which is a triangle with all three edges
equal in length, and all three vertices equal to sixty degrees. The
last planner shape that we were trying to create from the cube was an isosceles
trapezoid. This is shape with only one pair of parallel edges, and
the other pair of edges are equal in length, but not parallel. The
vertices of an isosceles trapezoid have two pair that are equal, the top
two of vertices are equal to each other in measure, and the bottom pair
are different measures from the top pair, but equal in measure to each
other. Next we wanted to find the largest possible area of three
of the faces, the rectangular cross section, the square cross section,
and the equilateral triangle cross section. So if you go to my web
page you will be able to see how we made all of these cuts, and what the
shapes look like. So look at those, and if you have any questions
just let me know, and I will be home in a few days to do laundry.
Love your son,
Erik
Click here to see the script for the cube.
Click here to see the original cube.
Click here to see the square cut.
Click here to see the rectangle cut.
Click here to see the isosceles triangle cut.
Click here to see the equilateral triangle cut.
Click here to see the isosceles trapeziod cut.