Altitude, Orthocenter of a Triangle and Triangulation [PDF]
Formalized Mathematics, 2016 Summary 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.
Roland Coghetto
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The arid Andean plateau waterscapes and the lithium triangle: flamingos as flagships for conservation of high-altitude wetlands under pressure from mining development [PDF]
Wetlands Ecology and Management, 2022 AbstractThe high Andean arid plateau extends through Peru, Argentina, Bolivia, and Chile. Within the desert matrix, basins contain wetlands that provide essential resources for human activity, and habitat for biodiversity highly adapted to extreme temperatures, altitudes, and salinity gradients.
P. Marconi, F. Arengo, A. Clark
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Irradiance level and elevation shape the soil microbiome communities of Coffea arabica L. [PDF]
Environmental MicrobiomeBackground The nexus plant-microbe-environment is essential to understand the ecosystem processes shaping plant health and fitness. Within this triangle, soils and associated microflora are among the key ecosystem’s drivers, underpinning plant ...
Inocência da Piedade E. Tapaça +9 more
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The Altitudes of a Triangle [PDF]
The American Mathematical Monthly, 2023 A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a remarkable number of proofs have been put forward; this suggests a search for the most elementary and direct proof.
Mark Mandelkern
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BASIC ELEMENTS OF A TRIANGLE BISECTOR, ALTITUDE, MEDIAN [PDF]
European Journal of Education and Applied PsychologyTarana Gashimova, Narmina Chelyabieva
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On triangles with rational altitudes, angle bisectors or medians [PDF]
Bulletin of the Australian Mathematical Society, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ralph H. Buchholz
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The Triangle Altitudes Theorem in Hyperbolic Plane Geometry
, 2019 15 pages. Keywords: Hyperbolic triangle, triangle altitude, hyperbolic plane.
Nicholas Phat Nguyen
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One group of inequalities with altitudes and medians in triangle
, 2008 In the article we prove some inequalities that contain relations between altitudes and medians in triangle. At least one of these inequalities has not been considered in the literature before and the main theorem has also not been proved elsewhere in that form. Some immediate corollaries have been presented as well.
Zhelev Zhivko
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Equicevian points on the altitudes of a triangle
Elemente der Mathematik, 2012 Mowaffaq Hajja, Sadi Abu-Saymeh
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Research on Type Selection of Diving Tower in 110kV Single and Double Circuit Transmission Line [PDF]
E3S Web of Conferences, 2021 With the continuous development of EHV (UHV) transmission lines，new lines often need to drill through the built lines，so it is urgent to study the type of diving towers.
Yu Xinmin +5 more
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