Results 11 to 20 of about 46,285 (150)
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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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 Triangle Altitudes Theorem in Hyperbolic Plane Geometry [PDF]
, 2019 15 pages. Keywords: Hyperbolic triangle, triangle altitude, hyperbolic plane.
Nicholas Phat Nguyen
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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 +2 more
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One group of inequalities with altitudes and medians in triangle [PDF]
, 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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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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Equicevian points on the altitudes of a triangle
Elemente der Mathematik, 2012 Let \(ABC\) be a triangle. Consider a point \(P\neq B\) a point in the plane containing \(ABC\) such that \(BP\) is not parallel to \(AC\). We denote (it it exists) by \(BB_P\) the cevian from \(B\) through \(P\). In the same way, if \(P\neq C\) and \(CP\) is not parallel to \(AB\), we could define \(CC_P\).
Sadi Abu-Saymeh, Mowaffaq Hajja
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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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, 2021 The aim of this research is to examine the efforts of 7th grade students to draw altitude in parallelograms and triangles. Moreover, it is to reveal the difficulties students experience in drawing altitude. For this purpose, a case study from qualitative research methods was managed.
Kazım Çağlar Şengün, Süha Yılmaz
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