Dividing the Perimeter of a Triangle into Unequal Proportions
We fully describe the envelope of all line segments that divide the perimeter of a triangle into the ratio α:1−α as α varies from 0 to 1/2. If α is larger than the ratio of the longest side length to the perimeter, then the envelope is a 12-sided closed curve consisting of six line segments and six...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/2751666 |
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| _version_ | 1832565510111232000 |
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| author | Nawinda Amadtohed Thitipon Chaidee Phonthakorn Racha-in Thunwa Theerakarn |
| author_facet | Nawinda Amadtohed Thitipon Chaidee Phonthakorn Racha-in Thunwa Theerakarn |
| author_sort | Nawinda Amadtohed |
| collection | DOAJ |
| description | We fully describe the envelope of all line segments that divide the perimeter of a triangle into the ratio α:1−α as α varies from 0 to 1/2. If α is larger than the ratio of the longest side length to the perimeter, then the envelope is a 12-sided closed curve consisting of six line segments and six parabolic arcs. For other values of α, the envelope is the union of one to three parabolic arcs and possibly a 5- or 9-sided nonclosed curve consisting of line segments and parabolic arcs. |
| format | Article |
| id | doaj-art-5ebb44c98c3844aa93f520d2d119a580 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5ebb44c98c3844aa93f520d2d119a5802025-02-03T01:07:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/2751666Dividing the Perimeter of a Triangle into Unequal ProportionsNawinda Amadtohed0Thitipon Chaidee1Phonthakorn Racha-in2Thunwa Theerakarn3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsWe fully describe the envelope of all line segments that divide the perimeter of a triangle into the ratio α:1−α as α varies from 0 to 1/2. If α is larger than the ratio of the longest side length to the perimeter, then the envelope is a 12-sided closed curve consisting of six line segments and six parabolic arcs. For other values of α, the envelope is the union of one to three parabolic arcs and possibly a 5- or 9-sided nonclosed curve consisting of line segments and parabolic arcs.http://dx.doi.org/10.1155/2022/2751666 |
| spellingShingle | Nawinda Amadtohed Thitipon Chaidee Phonthakorn Racha-in Thunwa Theerakarn Dividing the Perimeter of a Triangle into Unequal Proportions International Journal of Mathematics and Mathematical Sciences |
| title | Dividing the Perimeter of a Triangle into Unequal Proportions |
| title_full | Dividing the Perimeter of a Triangle into Unequal Proportions |
| title_fullStr | Dividing the Perimeter of a Triangle into Unequal Proportions |
| title_full_unstemmed | Dividing the Perimeter of a Triangle into Unequal Proportions |
| title_short | Dividing the Perimeter of a Triangle into Unequal Proportions |
| title_sort | dividing the perimeter of a triangle into unequal proportions |
| url | http://dx.doi.org/10.1155/2022/2751666 |
| work_keys_str_mv | AT nawindaamadtohed dividingtheperimeterofatriangleintounequalproportions AT thitiponchaidee dividingtheperimeterofatriangleintounequalproportions AT phonthakornrachain dividingtheperimeterofatriangleintounequalproportions AT thunwatheerakarn dividingtheperimeterofatriangleintounequalproportions |