# Pillar Wrapping Problem

This is a fun problem from the 1949 Eureka magazine.

“The following problems were set at the Archimedeans’ 1949 Problems Drive. Competitors were allowed five minutes for each question.  [This is problem #9.]

A pillar is in the form of a truncated right circular cone. The diameter at the top is 1 ft., at the bottom it is 2 ft. The slant height is 15 ft. A streamer is wound exactly five times round the pillar starting at the top and ending at the bottom. What is the shortest length the streamer can have?”

See the Pillar Wrapping Problem for solution.

# Bugles, Trumpets, and Beltrami

This essay began as an effort to prove Tanya Khovanova’s statement in her article “The Annoyance of Hyperbolic Surfaces” that her crocheted hyperbolic surface had constant (negative) curvature. I discussed Khovanova’s article in my previous essay “Exponential Yarn”. What I thought would be a fairly straight-forward exercise turned into a more concerted effort as I concluded that her crocheted surface did not have constant curvature. However, I found additional references that supported her statement, so I was becoming quite confused. I looked at other, similar surfaces to try to understand the whole curvature situation. This involved a lot of tedious computations (with my usual plethora of mistakes) that proved most challenging. But then I realized where I had gone astray. To cover my ignorance I claimed my error stemmed from a subtle misunderstanding. Herewith is a presentation of what I found. See Bugles, Trumpets, and Beltrami.