Arjen Dijksman is a Dutch Physicist whose blogs often tease out relations between physics and geometry,but his recent post is on the "Lost theorem about angular proportions"
The property applies to any triangle in which one interior angle is twice another. Some beautiful extensions of chords in a unit circle produce a proof, but the part I liked was that if the sides and angles are labeled as shown :
Then a2= c2+bc
addendum, I noticed a couple of days after I posted this, that if you draw a segment call it d, cutting the angle formed by c and a so that c and d form the legs of an isosceles triangle, then the other triangle is also isosceles. One triangle with base angles of 2 theta, and the other with base angles of theta.
1 comment:
Thanks for the mention:-)
I remember another of your posts on a near to Pythagoras relation, not long ago. Such relations challenge geometric creativity. Have you published a list of other almost Pythagorean, or do you konw if they are referenced somewhere? It could be interesting to have a wiki about them.
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