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wu :: forums    riddles    putnam exam (pure math) (Moderators: Grimbal, Icarus, william wu, towr, SMQ, Eigenray)    Semi-circle in a Square « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Semi-circle in a Square  (Read 1309 times) ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Semi-circle in a Square   « on: Dec 15th, 2006, 6:28pm » Quote Modify What is the largest semi-circle you can fit inside a unit square?   « Last Edit: Dec 15th, 2006, 7:28pm by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. flamingdragon Uberpuzzler     Gender: Posts: 671 Re: Semi-circle in a Square   « Reply #1 on: Dec 15th, 2006, 10:07pm » Quote Modify A semi-circle the size of a unit square.   IP Logged "The fool doth think he is wise, yet the wise man knoweth himself to be a fool" "He who commands the past, commands the future. He who commands the future, commands the past." Barukh Uberpuzzler     Gender: Posts: 2276 Re: Semi-circle in a Square   « Reply #2 on: Dec 16th, 2006, 5:14am » Quote Modify 0.58? IP Logged Whiskey Tango Foxtrot Uberpuzzler Sorry Goose, it's time to buzz a tower.     Gender: Posts: 1672 Re: Semi-circle in a Square   « Reply #3 on: Dec 16th, 2006, 10:14am » Quote Modify Are you talking about 1.414/2 Barukh? IP Logged "I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Semi-circle in a Square   « Reply #4 on: Dec 16th, 2006, 10:36am » Quote Modify looks more like 2-sqrt(2), as a radius IP Logged Whiskey Tango Foxtrot Uberpuzzler Sorry Goose, it's time to buzz a tower.     Gender: Posts: 1672 Re: Semi-circle in a Square   « Reply #5 on: Dec 16th, 2006, 10:54am » Quote Modify Of course.  Thanks G-man. IP Logged "I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei flamingdragon Uberpuzzler     Gender: Posts: 671 Re: Semi-circle in a Square   « Reply #6 on: Dec 16th, 2006, 10:58am » Quote Modify I take it then that I was wrong? IP Logged "The fool doth think he is wise, yet the wise man knoweth himself to be a fool" "He who commands the past, commands the future. He who commands the future, commands the past." Ken_Wiley Newbie     Gender: Posts: 22 Re: Semi-circle in a Square   « Reply #7 on: Dec 16th, 2006, 11:32am » Quote Modify Does seem like would be bigger than just half of a circle in it. « Last Edit: Dec 16th, 2006, 11:32am by Ken_Wiley » IP Logged Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Semi-circle in a Square   « Reply #8 on: Dec 16th, 2006, 1:47pm » Quote Modify on Dec 16th, 2006, 10:36am, Grimbal wrote: as a radius Ahhh, I had gotten .539, and thought, "well, that's less than Barukh's answer, so I must be missing something..." IP Logged Barukh Uberpuzzler     Gender: Posts: 2276 Re: Semi-circle in a Square   « Reply #9 on: Dec 17th, 2006, 12:39am » Quote Modify A follow up: what is the largest circular sector with central angle that can be fit in a unit square? IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Semi-circle in a Square   « Reply #10 on: Dec 17th, 2006, 6:21am » Quote Modify Is alpha given?   Then I'd say you have to consider 3 cases IP Logged Barukh Uberpuzzler     Gender: Posts: 2276 Re: Semi-circle in a Square   « Reply #11 on: Dec 18th, 2006, 11:27pm » Quote Modify on Dec 17th, 2006, 6:21am, Grimbal wrote: Is alpha given? Yes, of course.   Quote: Then I'd say you have to consider 3 cases Why 3? IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Semi-circle in a Square   « Reply #12 on: Dec 19th, 2006, 1:32am » Quote Modify There would be one formula for alpha<1/2·pi, one formula from 1/2·pi/2  to 3/2·pi and a third for alfa>3/2·pi   I am just a little lazy to figure out the formulas.  I think the last one is the constant 1/2 if the radius is what is asked. IP Logged 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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