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The altitudes of a triangle [PDF]
Amer. Math. Monthly 131 (2024), 162-163, 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.
arxiv +3 more sources
The Triangle Altitudes Theorem in Hyperbolic Plane Geometry [PDF]
arXiv, 2019 We provide a new formulation and proof of the triangle altitudes theorem in hyperbolic plane geometry, together with an easily computed discriminant to distinguish between different basic configurations of the altitudes of such a triangle.
arxiv +3 more sources
One group of inequalities with altitudes and medians in triangle [PDF]
arXiv, 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.
arxiv +3 more sources
A strong triangle inequality in hyperbolic geometry [PDF]
arXiv, 2015 For a triangle in the hyperbolic plane, let $\alpha,\beta,\gamma$ denote the angles opposite the sides $a,b,c$, respectively. Also, let $h$ be the height of the altitude to side $c$. Under the assumption that $\alpha,\beta, \gamma$ can be chosen uniformly in the interval $(0,\pi)$ and it is given that $\alpha+\beta+\gamma<\pi$, we show that the strong ...
Biró, Csaba, Powers, Robert C.
arxiv +4 more sources
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
doaj +2 more sources
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
doaj +1 more source
Applied Sciences, 2023 Compared to maximum state parameters, such as maximum altitude and Mach, the number of hovers and S turns can be used as process parameters representing the complexity of military aircraft maneuvers when classifying big flight mission data to compile ...
Moli Chen +3 more
doaj +1 more source
Can geographical factors determine the choices of farmers in the Ethiopian Highlands to trade in livestock markets? [PDF]
PLoS ONE, 2012 Proximity and affiliation to the local market appear to be two of the most relevant factors to explain farmer's choices to select a particular trading point. Physical barriers may limit the options , especially in developing countries.
Angel Ortiz-Pelaez +3 more
doaj +1 more source
Journal of Glaciology, 2021 The current paper studies the dynamics and age of the Triangle du Tacul (TDT) ice apron, a massive ice volume lying on a steep high-mountain rock wall in the French side of the Mont-Blanc massif at an altitude close to 3640 m a.s.l.
Grégoire Guillet +4 more
doaj +1 more source
Robust Low-Sidelobe Transmit Beamforming under Peak-to-Average-Power Ratio Constraint
Sensors, 2023 Transmit beamforming (TBF) provides the capability of focusing illuminating power in the desired directions while reducing the emitting power in undesired directions.
Lingping Cai +4 more
doaj +1 more source