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The Nine-Point Center
X(5) in Kimberling's Encyclopedia of Triangle Centers, is the center of the nine-point circle, which is the unique circle passing through the midpoints of the sides of the triangle. The radius of the nine-point circle is one-half the circumradius.
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Excellent! With just the points, this is one of my favourite animations to be projected at the start/end of a class -- the brain can't help but fill in lots of patterns as the angles start increasing.
ReplyDeleteThanks, Jon!
ReplyDeleteI agree...I got the idea for this kind of animation a couple of years ago from an American Mathematical Monthly article. I will need to find it and link it here.