Sunday, January 8, 2017

Some Reverses in Gamma (Euclidea series)

I found several of the puzzles in Gamma pack to be cute, even though they aren't necessarily hard. In especially liked the "reverse" constructions, finding the triangle given the orthocenter (3.2) or given the circumcenter (3.3).

Note: toward the latter half of this pack, I was getting anxious to see what Delta pack had in store, so I bashed through constructions for 3.5-3.8 without always finding the minimal moves solutions. Among those four challenges, I still have 5 missing stars.

Triangle from orthocenter (3.2)
Obtaining the E star gave me trouble on this one. I didn't originally get one, but figured I would try harder for these notes.

Triangle from intersection of perpendicular bisectors (3.3)

Three equal distances (3.4)
When going back to write up these notes, I didn't remember how this construction worked and was concerned I'd have trouble working through a tricky challenge. Fortunately, ....

Those V stars


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  2. Ha, ha. I know that this is just spam, but I appreciate the idea that India is so special that it has multiple orthocenters and one is somehow "best."

  3. Tho I still can’t prove the 5E solution to myself given the answer :-/

    1. It has been a long time since I worked on these. Could you remind me what the construction is for 3.5 and I'll try to give some guidance on the E solution.

    2. 3.5 is: Construct a circle through the point A that is tangent to the given line at the point B (A is not on the given line). To get the E star, you need to use 6 elementary construction steps. Is that the one you are working on?