Bug on a surface

 

I recently reviewed a problem involving a bug on a cylinder.  We need to find the shortest distance from the bug’s original position, A, to B which is on the opposite side of the cylinder.  The bug can only crawl on the surface, and we’re given the height (8) and circumference (12).  One student wanted the bug to crawl along the lower circumference and then crawl straight up the side.

You can more easily visualize the shortest path by using your imagination to “cut” the cylinder along one side starting at point A, then “flatten” the cylinder into a 12×8 rectangle.  Now the shortest path is easily seen as the hypotenuse of the triangle with legs of 6 and 8.  (A 3-4-5 triangle hiding in plain sight!)

IMG_20180125_135906.jpg

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s