102.13 Distance from the incentre of the tangential triangle of an obtuse triangle to the Euler line

2018 ◽  
Vol 102 (553) ◽  
pp. 133-135
Author(s):  
Sava Grozdev ◽  
Hiroshi Okumura ◽  
Deko Dekov
Keyword(s):  
Euler Line

scholarly journals Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining

Pythagoras ◽  
2008 ◽  
Vol 0 (68) ◽  
Author(s):  
Michael De Villiers
Keyword(s):  
History Of Mathematics ◽  
Genetic Approach ◽  
Mathematical Content ◽  
Euler Line ◽  
History Of ◽  
Mathematics For Teaching ◽  
The Creation ◽  
Reasoning By Analogy

This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. It then uses constructive defining to generate a new generalization of the Nagel line of a triangle to polygons circumscribed around a circle, based on an analogy between the Nagel line and the Euler line of a triangle.

Euler and triangle geometry

2007 ◽  
Vol 91 (522) ◽  
pp. 436-452 ◽  
Author(s):  
Gerry Leversha ◽  
G. C. Smith
Keyword(s):  
Scale Factor ◽  
Triangle Geometry ◽  
Euler Line

There is a very easy way to produce the Euler line, using transformational arguments. Given a triangle ABC, let AʹBʹ'C be the medial triangle, whose vertices are the midpoints of the sides. These two triangles are homothetic: they are similar and corresponding sides are parallel, and the centroid, G, is their centre of similitude. Alternatively, we say that AʹBʹC can be mapped to ABC by means of an enlargement, centre G, with scale factor –2.

Incenters and Excenters Viewed from the Euler Line

1985 ◽  
Vol 58 (2) ◽  
pp. 89-92 ◽  
Author(s):  
Andrew P. Guinand
Keyword(s):  
Euler Line

The Euler Line: A Vector Approach

1982 ◽  
Vol 13 (5) ◽  
pp. 329
Author(s):  
Norman Schaumberger
Keyword(s):  
Euler Line ◽  
Vector Approach

Orthocenters in real normed spaces and the Euler line

2004 ◽  
Vol 67 (1-2) ◽  
pp. 180-187 ◽  
Author(s):  
Claudi Alsina ◽  
Maria Santos Tomás
Keyword(s):  
Normed Spaces ◽  
Euler Line

scholarly journals Hyperspherical variables analysis of lattice QCD three-quark potentials: skewed Y-string as the mechanism of confinement?

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
James Leech ◽  
Milovan Šuvakov ◽  
V. Dmitrašinović
Keyword(s):  
Lattice Qcd ◽  
Flux Density ◽  
Equilateral Triangle ◽  
Qualitative Agreement ◽  
Shape Space ◽  
Data Sets ◽  
Smooth Curves ◽  
Euler Line ◽  
Elastic Strings ◽  
The Right

AbstractWe have re-analysed the lattice QCD calculations of the 3-quark potentials by: (i) Sakumichi and Suganuma (Phys Rev D 92(3), 034511, 2015); and (ii) Koma and Koma (Phys Rev D 95(9), 094513, 2017) using hyperspherical variables. We find that: (1) the two sets of lattice results have only two common sets of 3-quark geometries: (a) the isosceles, and (b) the right-angled triangles; (2) both sets of results are subject to unaccounted for deviations from smooth curves that are largest near the equilateral triangle geometry and are function of the hyperradius – the deviations being much larger and extending further in the triangle shape space in Sakumichi and Suganuma’s than in Koma and Koma’s data; (3) the variation of Sakumichi and Suganuma’s results brackets, from above and below, the Koma and Koma’s ones; the latter will be used as the benchmark; (4) this benchmark result generally passes between the Y- and the $$\Delta $$ Δ -string predictions, thus excluding both; (5) three pieces of elastic strings joined at a skewed junction, which lies on the Euler line, reproduce such a potential, within the region where the data sets agree, in qualitative agreement with the calculations of colour flux density by Bissey et al. (Phys Rev D 76, 114512, 2007).

A theorem on concurrent Euler lines

2006 ◽  
Vol 90 (519) ◽  
pp. 412-416 ◽  
Author(s):  
C. J. Bradley
Keyword(s):  
Euler Line

In the configuration, illustrated in Figure 1, ABC is a triangle with I1; I2, I3 the excentres opposite A, B, C respectively. The triangles I1BC, I2CA, I3AB are denoted by T1, T2, T3 respectively. Ok, Hk, are the circumcentre, orthocentre respectively of triangle Tk, k = 1, 2, 3. Lk is the Euler line of Tk, k = 1, 2, 3. Define the point Ek (t) on Lk by the equation

A Counterpart for the Euler Line

2008 ◽  
pp. 1-2
Author(s):  
O. Bottema ◽  
Reinie Erne
Keyword(s):  
Euler Line
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