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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-0425 |