Abstract
A triangle is a simplex (see 2.E) in a Euclidean affine plane, or, in other words, three non-collinear points x, y, z; we can write J = {x, y, z}. These three points are the vertices of J; we call sides the segments [y, z], [z, x], [x, y], and also their lengths, which are conventionally written a = yz, b = zx, c = xy. The angles of J are elements of ]0, π[, measured between oriented lines (cf. 8.F), and written \(A = \overline {\overrightarrow {xy} ,\overrightarrow {xz} } , B = \overline {\overrightarrow {yz} ,\overrightarrow {yx} } , C = \overline {\overrightarrow {zx} ,\overrightarrow {zy} } .\). We also have the semi-perimeter p = (a + b + c) /2.
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© 1984 Marcel Berger
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Berger, M., Pansu, P., Berry, JP., Saint-Raymond, X. (1984). Triangles, Spheres, and Circles. In: Problems in Geometry. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1836-2_10
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DOI: https://doi.org/10.1007/978-1-4757-1836-2_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2822-1
Online ISBN: 978-1-4757-1836-2
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