* Shark Attack*

By:  Allison K. Kootsikas

Guppy, Tadpole, and Goldfish beach surround Equilateral Sea. Why do you think Equilateral Sea is named that way?

Tiger shark and his family swim together in the Equilateral Sea. When the family gets hungry, Tiger makes sure they stay in one place (so he doesn't lose them), and then finds food at each of the beaches. Tiger gets food at one beach at a time because he can only hold so much food in his mouth at one time. So he gets food at one beach, comes back to share the food (red square), and then repeats the process at the other beaches.

Where should Tiger place his family in the Equilateral Sea in order to swim the least distance for his three hunting trips? Explain your reasoning.

The first step in this is to construct an equilateral triangle using GSP.  To do this, construct a circle and its radius.  Then construct a circle from the radius and point.  Connect the intersection and center points and an equilateral triangle is formed.

The next step is to hide the circles, leaving an equilateral triangle.  All three sides are the same distance.

The first thing I tried to do was to just put points on the triangle and move them until the distance was small.  Here are the steps I went through to find that method.

The next step is to construct a point on each side of the triangle. Also construct a point inside of the triangle and make segments from the inner point to the sides.

The next step is to measure the lengths of the segments and add them up.  By moving the center point around, you will find the shortest distance.

Click here for my GSP sketch

After investigating what would occur if I entered random points, I decided to find out what happened if I found the intersection of the angle bisectors (incenter) and the intersection of the midpoints (centroid).

Click here to see my GSP sketch.

I found that it did not matter if the centroid, the incenter, or random points were used to determine the shortest distance the shark would have to travel to bring food to his babies.