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| This problem was solved by ] in 1995 for 2 dimensions, with a 26-sided room with a dark spot. This was a borderline case, however, since a finite number of dark ''points'' (rather than regions) that are unilluminable from any given position of the point source. A more rigorous solution was put forward by D.Castro in 1997, with a 24-sided room that | This problem was solved by ] in 1995 for 2 dimensions, with a 26-sided room with a dark spot. This was a borderline case, however, since a finite number of dark ''points'' (rather than regions) that are unilluminable from any given position of the point source. A more rigorous solution was put forward by D.Castro in 1997, with a 24-sided room that | ||
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| The '''illumination problem''' is a resolved mathematical problem first posed by ]. There are several equivalent statements of the problem: | |||
| *If a room has walls that are all mirrors, is there any point at which a ] will not illuminate another point in the room, allowing for repeated reflections. | |||
| *If a ] can be constructed in any required shape, is there a point where it is impossible to pot the ] from another point, assuming the ball continues infinitely rather than being subject to ]. | |||
| This problem was solved by ] in 1995 for 2 dimensions, with a 26-sided room with a "dark spot" which is not illuminated from another point in the room, even allowing for repeated reflections.<ref>{{Cite journal | |||
| | last = Tokarsky | |||
| | first = George | |||
| | authorlink = George Tokarsky | |||
| | title = Polygonal Rooms Not Illuminable from Every Point | |||
| | journal = American Mathematical Monthly | |||
| | volume = 102 | |||
| | issue = 10 | |||
| | pages = 867-879 | |||
| | publisher = Mathematical Association of America | |||
| | location = University of Alberta, Edmonton, Alberta, Canada | |||
| | date = December 1995 | |||
| | url = http://www.jstor.org/stable/2975263 | |||
| | accessdate = 19 December 2010}}</ref> This was a borderline case, however, since a finite number of dark ''points'' (rather than regions) that are unilluminable from any given position of the point source. A more rigorous solution was put forward by D.Castro in 1997, with a 24-sided room. | |||
| ] | ] | ||
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This article was last edited by Larryisgood (talk | contribs) 14 years ago. (Update timer) |
The illumination problem is a resolved mathematical problem first posed by Ernst Straus. There are several equivalent statements of the problem:
- If a room has walls that are all mirrors, is there any point at which a point light source will not illuminate another point in the room, allowing for repeated reflections.
- If a snooker table can be constructed in any required shape, is there a point where it is impossible to pot the billiard ball from another point, assuming the ball continues infinitely rather than being subject to friction.
This problem was solved by George Tokarsky in 1995 for 2 dimensions, with a 26-sided room with a dark spot. This was a borderline case, however, since a finite number of dark points (rather than regions) that are unilluminable from any given position of the point source. A more rigorous solution was put forward by D.Castro in 1997, with a 24-sided room that
| This article or section is in a state of significant expansion or restructuring. You are welcome to assist in its construction by editing it as well. If this article or section has not been edited in several days, please remove this template. If you are the editor who added this template and you are actively editing, please be sure to replace this template with {{in use}} during the active editing session. Click on the link for template parameters to use.
This article was last edited by Larryisgood (talk | contribs) 14 years ago. (Update timer) |
The illumination problem is a resolved mathematical problem first posed by Ernst Straus. There are several equivalent statements of the problem:
- If a room has walls that are all mirrors, is there any point at which a point light source will not illuminate another point in the room, allowing for repeated reflections.
- If a snooker table can be constructed in any required shape, is there a point where it is impossible to pot the billiard ball from another point, assuming the ball continues infinitely rather than being subject to friction.
This problem was solved by George Tokarsky in 1995 for 2 dimensions, with a 26-sided room with a "dark spot" which is not illuminated from another point in the room, even allowing for repeated reflections. This was a borderline case, however, since a finite number of dark points (rather than regions) that are unilluminable from any given position of the point source. A more rigorous solution was put forward by D.Castro in 1997, with a 24-sided room.
- Tokarsky, George (December 1995). "Polygonal Rooms Not Illuminable from Every Point". American Mathematical Monthly. 102 (10). University of Alberta, Edmonton, Alberta, Canada: Mathematical Association of America: 867–879. Retrieved 19 December 2010.