In my 7 years of math study I never came across this, so I settled down for some analysis of the problem. I set up some equations and the thing fell out at the first step. I then had to find something else to do that afternoon !

Here is a suggestion:
Show how the medians of a triangle meet at a point by starting with an equilateral triangle and doing a shear parallel to one of the sides.

in x, y, z
cylinder x=cos(theta), y=sin(theta) z=anything
cutting plane x+z=0 , y=anything
solution z=-cos(theta) (plot z against theta)
done, or “it fell out”

In my 7 years of math study I never came across this, so I settled down for some analysis of the problem. I set up some equations and the thing fell out at the first step. I then had to find something else to do that afternoon !

Here is a suggestion:

Show how the medians of a triangle meet at a point by starting with an equilateral triangle and doing a shear parallel to one of the sides.

What do you mean by ‘the thing fell out’? The strip of paper?

in x, y, z

cylinder x=cos(theta), y=sin(theta) z=anything

cutting plane x+z=0 , y=anything

solution z=-cos(theta) (plot z against theta)

done, or “it fell out”