| Title |
Trikampio egzistavimas, kai žinomi trys jo elementai / |
| Translation of Title |
The existence of a triangle when its three elements are known. |
| Authors |
Mazėtis, Edmundas ; Melničenko, Grigorijus |
| DOI |
10.15388/LMR.2022.29758 |
| Full Text |
|
| Is Part of |
Lietuvos matematikos rinkinys. Ser. B.. Vilnius : Vilniaus universiteto leidykla. 2022, t. 63, p. 54-61.. ISSN 0132-2818. eISSN 2335-898X |
| Keywords [eng] |
triangle ; solution of triangles ; lexicographic order ; height ; median ; bisector ; radii of the circumscribed and inscribed circles ; perimeter |
| Abstract [eng] |
The problem of the existence of a triangle with respect to three given elements in some cases can be very difficult. For example, Brokard's problem about the existence of a triangle, given its three bisectors [1], has a long history [3] and solved only in 1994 [10]. We include in the number of elements: three sides, three angles, three heights, three medians, three bisectors, radii of the circumscribed and inscribed circles, and perimeter. In total, there are 186 different problems of the existence of a triangle with three given elements and for 116 problems are given sufficient conditions (for some sufficient and necessary conditions of existence) when a triangle can be construct by a compass and a ruler, and the remaining 70 problems when it is impossible to construct a triangle by a compass and a ruler. The authors list these 70 problems and indicate for which of them the necessary and sufficient conditions for the uniqueness of the existence of a triangle with three prescribed elements have found. |
| Published |
Vilnius : Vilniaus universiteto leidykla |
| Type |
Journal article |
| Language |
Lithuanian |
| Publication date |
2022 |
| CC license |
|
