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wu :: forums    riddles    medium (Moderators: Grimbal, towr, SMQ, Eigenray, william wu, ThudnBlunder, Icarus)    Orthogonal Views « Previous topic | Next topic » Pages: 1 2  Reply Notify of replies Send Topic Print    Author  Topic: Orthogonal Views  (Read 6999 times) william wu wu::riddles Administrator     Gender: Posts: 1291 Orthogonal Views   orthogonalviews.png « on: May 17th, 2008, 2:44am » Quote Modify See the picture below.   This cute puzzle has the nice properties of   (1) being accessible to anyone (e.g., 4 year olds), and (2) initially appearing to be impossible. So it will drive you crazy until you figure it out « Last Edit: May 17th, 2008, 4:34am by william wu » IP Logged [ wu ] : http://wuriddles.com / http://forums.wuriddles.com towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Orthogonal Views   « Reply #1 on: May 17th, 2008, 4:25am » Quote Modify The only thing I can make of it gives numerous possible solutions, so it doesn't really keep my interest enough to drive me crazy. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: Orthogonal Views   « Reply #2 on: May 17th, 2008, 7:07am » Quote Modify a smooth curve resembling y=-x^2 on [-3,3] with a chord across the bottom IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Orthogonal Views   sideview.zip « Reply #3 on: May 17th, 2008, 9:07am » Quote Modify Similar to what rmsgrey said (zipped to hide answer)   --SMQ IP Logged --SMQ FiBsTeR Senior Riddler     Gender: Posts: 581 Re: Orthogonal Views   Orthogonal_Views.JPG « Reply #4 on: May 17th, 2008, 10:01am » Quote Modify I must be missing something; this is what I first thought of, and it still seems to fit the problem: IP Logged Barukh Uberpuzzler     Gender: Posts: 2276 Re: Orthogonal Views   « Reply #5 on: May 17th, 2008, 10:23am » Quote Modify on May 17th, 2008, 9:07am, SMQ wrote: Similar to what rmsgrey said (zipped to hide answer) Cannot imagine how this solves the problem...   Could you draw a stereometric view?   IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Orthogonal Views   3rdview.gif « Reply #6 on: May 17th, 2008, 3:15pm » Quote Modify Is this what you had in mind? IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Orthogonal Views   stereographic_isometric.png « Reply #7 on: May 17th, 2008, 8:29pm » Quote Modify on May 17th, 2008, 10:23am, Barukh wrote: Could you draw a stereometric view?   Sure, stereometric and isometric both. IP Logged --SMQ Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Orthogonal Views   « Reply #8 on: May 17th, 2008, 10:38pm » Quote Modify Now how about an anaglyph image?   IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Orthogonal Views   isoview.gif « Reply #9 on: May 18th, 2008, 2:38am » Quote Modify Why so complicated? IP Logged rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: Orthogonal Views   « Reply #10 on: May 18th, 2008, 4:19am » Quote Modify on May 17th, 2008, 10:01am, FiBsTeR wrote: I must be missing something; this is what I first thought of, and it still seems to fit the problem: It has extra edges on, which would conventionally be drawn in a projection - as silhouettes, the side view has a lot of possibilities even without poking additional holes through. The curved solutions solve the problem of the missing edges, but Grimbal's solution is even better. IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Orthogonal Views   anaglyph_isometric.png « Reply #11 on: May 18th, 2008, 5:47am » Quote Modify on May 17th, 2008, 10:38pm, Eigenray wrote: Now how about an anaglyph image?   If that's what floats your boat. (left eye is cyan)   --SMQ IP Logged --SMQ Barukh Uberpuzzler     Gender: Posts: 2276 Re: Orthogonal Views   « Reply #12 on: May 18th, 2008, 5:50am » Quote Modify Awesome, SMQ!     What software are you using? IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Orthogonal Views   orthogonal_views.pov.txt « Reply #13 on: May 18th, 2008, 6:09am » Quote Modify on May 18th, 2008, 5:50am, Barukh wrote: What software are you using? Povray for the rendering, and since I'm not on my normal computer with Photoshop at the moment, a quickie BASIC program to combine the anaglyph images and MS Paint for cropping and PNG conversion.   I've attached the Povray source for anyone interested.   --SMQ IP Logged --SMQ Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Orthogonal Views   « Reply #14 on: May 18th, 2008, 9:55am » Quote Modify Awesome.   Now do Magic Eye! IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Orthogonal Views   sird_isometric.png « Reply #15 on: May 18th, 2008, 12:22pm » Quote Modify You just don't give up, do you?   --SMQ IP Logged --SMQ Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Orthogonal Views   « Reply #16 on: May 18th, 2008, 1:13pm » Quote Modify Impressive!   How about an animated anaglyph/autostereogram of it rotating?   « Last Edit: May 18th, 2008, 1:14pm by Eigenray » IP Logged william wu wu::riddles Administrator     Gender: Posts: 1291 Re: Orthogonal Views   orthogonalviews_solution.gif « Reply #17 on: May 19th, 2008, 1:33am » Quote Modify These answers, while perfectly legit, are a lot more complicated than I expected ... Love the pictures! « Last Edit: May 19th, 2008, 1:37am by william wu » IP Logged [ wu ] : http://wuriddles.com / http://forums.wuriddles.com towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Orthogonal Views   « Reply #18 on: May 19th, 2008, 1:57am » Quote Modify on May 19th, 2008, 1:33am, william wu wrote: These answers, while perfectly legit, are a lot more complicated than I expected ... I don't think your solution works; if you cut a piece out of a cylinder at the height required by the front view (with the right width), you won't get a square as required in the top view.. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB JohanC Senior Riddler     Posts: 460 Re: Orthogonal Views   « Reply #19 on: May 19th, 2008, 2:18am » Quote Modify on May 19th, 2008, 1:57am, towr wrote: I don't think your solution works; if you cut a piece out of a cylinder at the height required by the front view (with the right width), you won't get a square as required in the top view.. Maybe an elliptical cylinder would work? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Orthogonal Views   « Reply #20 on: May 19th, 2008, 2:42am » Quote Modify on May 19th, 2008, 2:18am, JohanC wrote: Maybe an elliptical cylinder would work? Then the top view wouldn't be a square. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB william wu wu::riddles Administrator     Gender: Posts: 1291 Re: Orthogonal Views   orthogonalviews_solution_re.gif « Reply #21 on: May 19th, 2008, 12:30pm » Quote Modify Hmm, fair enough ... but, perhaps we can just slice the cylinder in half, lengthwise, to get the front view. « Last Edit: May 19th, 2008, 12:39pm by william wu » IP Logged [ wu ] : http://wuriddles.com / http://forums.wuriddles.com SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Orthogonal Views   triangle_threeview.png « Reply #22 on: May 19th, 2008, 12:39pm » Quote Modify Sorry, William, still won't work.  If, in the side view, you drew an isosceles triangle from the bottom corners to the top center it would pass exactly through the needed width of the top cut out (see diagram).  So any profile which is the same height, is convex on top, and passes through those same points must have some concave portions somewhere along its length.  No profile without at least one inflection point (on each side) can satisfy all the constraints of the given problem.   --SMQ « Last Edit: May 19th, 2008, 12:54pm by SMQ » IP Logged --SMQ Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: Orthogonal Views   plan_elevation_puzzles1.gif « Reply #23 on: May 20th, 2008, 11:49am » Quote Modify When I went to school woodwork, metal work, and technical drawing lessons were compulsory for boys and I loved these types of puzzle. I used to give them to my students when I first started teaching, but it seems that over the years they've become a lost art. Here are two of my fiendishly hard favourites. Puzzle B is a variation of Williams, so it isn't really a challenge now you've seen his answer. However, puzzle A is still a nice one to have a stab at. IP Logged mathschallenge.net / projecteuler.net SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Orthogonal Views   puzzle_a_threeview.zip « Reply #24 on: May 20th, 2008, 12:29pm » Quote Modify I, too, am glad I had the chance to take technical drawing.  On the other hand, I helped to set up the CAD lab at my high school, so I guess I'm partly responsible for the demise of the art...   Zipped solution to A attached. (And I notice you altered your diagram of B to better fit the "intended" solution. )   --SMQ IP Logged --SMQ Pages: 1 2  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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