We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.
@article{bwmeta1.element.doi-10_1515_forma-2016-0003,
author = {Roland Coghetto},
title = {Altitude, Orthocenter of a Triangle and Triangulation},
journal = {Formalized Mathematics},
volume = {24},
year = {2016},
pages = {27-36},
zbl = {1343.51009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0003}
}
Roland Coghetto. Altitude, Orthocenter of a Triangle and Triangulation. Formalized Mathematics, Tome 24 (2016) pp. 27-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0003/
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