Finding a loose cover of a triangle with circles whose total area is minimal
Consider an arrangement of circles covering the total area of an equilateral
triangle. Assume that the length of the sides of the triangle is 1
and that each of the three circles centred at the corners of the
triangle all have the same radius. Which arrangement has the minimal
total area? Observe that the arrangement is completely determined by
R .
Before looking at the solution try to
solve the problem on your own. Simple trigonometry should allow you to
determine the length of the line segment from the centre of the
triangle to the midpoint of a side. Once you have this, the rest of
the geometry is quite simple.
Instructor
Juris Steprans
email address: steprans@mathstat.yorku.ca
Department of Mathematics and Statistics.
Ross 624 South, ext. 33952
York University
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