Viviani’s Theorem

In Geometry, we proved Viviani’s Theorem. Individual groups’ lightbulb moments diffused across the room, ensuring that everybody had a chance to experience that giddy moment of discovery. Collaborative work to share knowledge, individual write-up to assess internal understanding.

I have been giving the students problems that I would find interesting. “Treat them like experts and they will become experts” is an unwritten mantra. Is there any justification for this? Am I prioritizing my intellectual enjoyment over the students’ needs? In any case, there are some outstanding proofs here:


A great idea to use circles, but is it justified?


Excellent attempt at dynamic proof without words:


This student is thinking very precisely, but I have no idea what is going on:


Equilateral triangles within equilateral triangles…


As a starting point, this is ripe for extension. What about other properties of equilateral triangles? What about other triangles? What about other polygons? what about other dimensions?

A South African high-school student stumbled across a different invariant. His name is now immortalized in the Clough Conjecture.¬†Students began this journey the following lesson…



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