Tag Archives: Viviani Theorem

Polygon Altitude Problems II

James Tanton has provided further elaborations on the polygons and the sum of perpendicular distances from interior points. Again I approached the solutions with a mix of areas and vectors. It is rather impressive to see the number of variations that can be rung on the Viviani Theorem theme. See Polygon Altitude Problems II

Polygon Altitude Problems I

I found this collection of related problems by James Tanton on Twitter. Even though all these problems do not involve perpendiculars, they have a common solution approach – a sort of theme and variations idea. In a later tweet Tanton refers to a Viviani Theorem associated with these types of problems. I did not recall that theorem explicitly or by name. I also have not looked it up yet, in order to solve these problems on my own. I am guessing there is a more classical Euclidean geometry proof, but I like my vector approach for its clarity. I also throw in a bit a calculus at the end for fun. See Polygon Altitude Problems I