Math CentralQuandaries & Queries


Subject: advanced geometry
Name: cassie
Who are you: Student

I am a student in 9th grade advanced geometry class. This problem is due january 2
and I can't solve it. Please try to solve this problem and get back to me as soon as possible.
Thank you.

Iago the Insect lives on the surface of a regular tetrahedron with edges of length 4 inches.
He wants to travel on the surface from the midpoint of one edge to the midpoint of the opposite edge. What is the
length of the shortest possible trip for Iago to do this? Two edges in a tetrahedron are opposite if they do
not share a common endpoint!

If you are able to solve this, please provide work to back up your answer!

The simplest way to approach this problem is to lay out a pattern for the tetrahedron:


Now take the midpoint of two opposite sides of the pattern - and draw a straight line between them (red above).

You probably have the information to figure out the length of this line (look at parallel lines of the same length in this picture).

Walter Whiteley
York University

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