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Maximal buttonings of trees

100%

Short I.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 2

415-420

A buttoning of a tree that has vertices v1, v2, . . . , vn is a closed walk that starts at v1 and travels along the shortest path in the tree to v2, and then along the shortest path to v3, and so forth, finishing with the shortest path from vn to v1. Inspired by a problem about buttoning a shirt inefficiently, we determine the maximum length of buttonings of trees

Circumcenter, Circumcircle and Centroid of a Triangle

86%

Coghetto R.

Formalized Mathematics

2016

tom 24

nr 1

17-26

We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula of the radius of the Morley’s trisector triangle are formalized [3]. Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the centroid (the common point of the medians [4]) of a triangle.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Formalized Mathematics

1 Coghetto R.

1 Short I.

1 2016

1 2014

Wyniki wyszukiwania

Maximal buttonings of trees

Circumcenter, Circumcircle and Centroid of a Triangle