By karen newman on Tuesday, April 23, 2002 - 08:31 pm:
Is it possible to construct a pyramid using scalene triangles?
By Emma McCaughan on Wednesday, April 24, 2002 - 05:21 pm:
Yes. I don't know which of the following
will be most helpful.
Imagine a cuboid with all three lengths different. Now imagine
slicing it through the diagonal of the base up to one of the top
corners not above that diagonal.
I'm afraid I can't draw on this computer - I've got a net in front
of me. Try following this description:
For the base, draw a right-angled triangle with the perpendicular
sides length 3 and 4. Then imagine that the vertex is 2 units above
the right-angle. The next two triangles are right-angled triangles
with perpendicular sides 4/2 and 3/2. The last triangle will need
to be constructed with compasses:it will not be right-angled, and
the side-lengths will need to match the three hypotenuses.
Sorry if that's rather garbled. If you can't follow either
description, post again, and maybe someone will provide a
diagram.
This, of course, is just one example. I suspect constructing one
with fewer right-angles will be harder.
By Emma Mccaughan on Thursday, April 25, 2002 - 04:36 pm:
Here's a picture. The green triangle is
what I described as the base. The fourth triangle will go on the
third side of the green triangle, and would need constructing with
compasses.
By Karen Newman on Wednesday, May 08, 2002 - 03:26 pm:
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