Warm-Up 3, Due Monday, February 1, noon.

Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try and state why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.

Your Name:

Question 1

What is the "golden ratio"? What is a "golden rectangle"?

Question 2

What do you think: For which of the paintings or buildings shown does the golden rectangle appear by purpose of the artist, not just by accident?

Question 3

Assume you have an art gallery, and somebody started to draw inside edges to triangulate it, but didn't finsih this yet. Can you always finish this into a complete triangulation of the art gallery?
Now assume you have a complete triangulation of an art gallery, and somebody started to color some of the vertices red, green, blue in such a way that no triangle contains a color twice. Of course, since not all triangles have been colored yet, some triangles will only contain one colored vertex or two, or even none. Can you always extend this coloring into a complete coloring---all vertices are colored---such that all triangles contain all three colors exactly once?