Dividing the Perimeter of a Triangle into Unequal Proportions

Nawinda Amadtohed, Thitipon Chaidee, Phonthakorn Racha-in, Thunwa Theerakarn and Vladimir Mityushev

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-8

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:2751666

DOI: 10.1155/2022/2751666

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