CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION
Fix an n ≥ 3. Consider the following two operations: given a line with a specified point on the line we can construct a new line through the point which forms an angle with the new line which is a multiple of π/n (folding); and given two lines we can construct the point where they cross (intersectio...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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World Scientific Pub Co Pte Lt
2019
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| Online Access: | https://hdl.handle.net/1721.1/121356 |
| _version_ | 1826197407655788544 |
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| author | Butler, Steven Kay Demaine, Erik D Graham, Ron Tachi, Tomohiro |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Butler, Steven Kay Demaine, Erik D Graham, Ron Tachi, Tomohiro |
| author_sort | Butler, Steven Kay |
| collection | MIT |
| description | Fix an n ≥ 3. Consider the following two operations: given a line with a specified point on the line we can construct a new line through the point which forms an angle with the new line which is a multiple of π/n (folding); and given two lines we can construct the point where they cross (intersection). Starting with the line y = 0 and the points (0,0) and (1,0) we determine which points in the plane can be constructed using only these two operations for n = 3,4,5,6,8,10,12,24 and also consider the problem of the minimum number of steps it takes to construct such a point. |
| first_indexed | 2024-09-23T10:47:14Z |
| format | Article |
| id | mit-1721.1/121356 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:47:14Z |
| publishDate | 2019 |
| publisher | World Scientific Pub Co Pte Lt |
| record_format | dspace |
| spelling | mit-1721.1/1213562022-09-30T23:01:42Z CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION Butler, Steven Kay Demaine, Erik D Graham, Ron Tachi, Tomohiro Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Fix an n ≥ 3. Consider the following two operations: given a line with a specified point on the line we can construct a new line through the point which forms an angle with the new line which is a multiple of π/n (folding); and given two lines we can construct the point where they cross (intersection). Starting with the line y = 0 and the points (0,0) and (1,0) we determine which points in the plane can be constructed using only these two operations for n = 3,4,5,6,8,10,12,24 and also consider the problem of the minimum number of steps it takes to construct such a point. 2019-06-19T14:43:28Z 2019-06-19T14:43:28Z 2013 2013-03 2019-06-18T19:10:16Z Article http://purl.org/eprint/type/JournalArticle 0218-1959 https://hdl.handle.net/1721.1/121356 Butler, Steve, Erik Demaine, Ron Graham and Tomohiro Tachi. "Constructing points through folding and intersection." International Journal of Computational Geometry & Applications, Vol. 23 (01) 2016: 49-64. en 10.1142/S0218195913500039 International Journal of Computational Geometry & Applications Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf World Scientific Pub Co Pte Lt other univ website |
| spellingShingle | Butler, Steven Kay Demaine, Erik D Graham, Ron Tachi, Tomohiro CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION |
| title | CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION |
| title_full | CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION |
| title_fullStr | CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION |
| title_full_unstemmed | CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION |
| title_short | CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION |
| title_sort | constructing points through folding and intersection |
| url | https://hdl.handle.net/1721.1/121356 |
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