Wednesday, November 5, 2014

TV around a corner

What is the largest TV that could fit around a corner in your house?

This was the question we answered in my calculus class.

First I showed this applet and had students play with it

Next I asked what do we need to know?

Students asked for the width of the hallways which are 0.8 m and 0.9 m wide.

Next we realized that actually to determine the largest TV we actually need to MINIMIZE the length of the line.  As the smallest line will be the line that can fit around the entire corner.

Calling the, angle between the TV and the 0.8 m wall, theta you get the equation of the TV length at any angle to be

Next taking the derivative, and solving for when it equals 0, gives us

Substituting this back into the equation gives us a TV (or any rigid object) with a length of 2.4 m or 94.45 in across.  

We then did have a discussion around what assumptions are we making?  Some are...
  • The TV has no depth at all
  • The TV will scrap across the wall
  • The TV is out of the box

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