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wu :: forums    riddles    easy (Moderators: SMQ, ThudnBlunder, Grimbal, Eigenray, towr, Icarus, william wu)    Angles in GP « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Angles in GP  (Read 772 times) Ronno Junior Member     Gender: Posts: 140 Angles in GP   « on: Mar 2nd, 2009, 7:21pm » Quote Modify All points on a plane are colored with three colors. Prove that there exist an infinite number of triangles on the plane with all vertices the same color, that are either isosceles or have their angles in geometric progression.   Prove the statement when geometric progression is replaced by arithmetic progression and degenerate triangles are allowed. IP Logged Sarchasm: The gulf between the author of sarcastic wit and the person who doesn't get it.. Ronno Junior Member     Gender: Posts: 140 Re: Angles in GP   « Reply #1 on: Mar 8th, 2009, 11:59pm » Quote Modify No takers?   The problems are variations of one given in this year's Indian Math Olympiad. IP Logged Sarchasm: The gulf between the author of sarcastic wit and the person who doesn't get it.. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Angles in GP   « Reply #2 on: Mar 9th, 2009, 4:03am » Quote Modify Here's a thread that deal with two-colored plane. In that case it applies to any triangle. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Angles in GP   « Reply #3 on: Mar 9th, 2009, 8:45am » Quote Modify We can use the idea used at this site.   It may be interesting to do it without using Van der Waerden's Theorem, using the given properties, but I haven't any ideas. « Last Edit: Mar 9th, 2009, 8:46am by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Ronno Junior Member     Gender: Posts: 140 Re: Angles in GP   « Reply #4 on: Mar 9th, 2009, 9:58am » Quote Modify Yeah, the problems are similar. Both of these can be solved with 7 points in very symmetric configurations. IP Logged Sarchasm: The gulf between the author of sarcastic wit and the person who doesn't get it.. Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------=> easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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