Thursday, June 16, 2016

The Euler Line in Computational Architecture

There are many connections between circles and trigonometry so when I found a great example of this in a new book I got I wanted to try it for myself in Dynamo/REVIT. The theorem, named after the Swiss mathematician Leonhard Euler, can be constructed several different ways but in essence describes a line created by the following three points derived from a triangle inscribed in a circle:

  1. The center point of the circle;
  2. the intersection of each side’s midline bisectors and;
  3. the orthocenter created by each side’s altitude line when each side is split into two right angle triangles. 
If it’s hard to explain, it was even harder to code for a novice programmer like myself. This geometric proof holds for any 3 points on a circle. I can’t image how long one would have stare at a triangle to uncover a relationship like this but it does indeed hold when experimenting with the code as shown in the images accompanying this post.

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