By Bloch S. (ed.)
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Extra resources for Algebraic Geometry - Bowdoin 1985, Part 1
141) where O is the triangle circumcenter. 128), p. 36, and mk , PSfrag replacements May 25, 2010 13:33 WSPC/Book Trim Size for 9in x 6in ws-book9x6 41 Euclidean Barycentric Coordinates A3 a12 = −A1 + A2 , a12 = a12 a13 = −A1 + A3 , a13 = a13 a23 = −A2 + A3 , a23 = a23 α3 a13 a2 3 P2 O P1 α2 α1 A1 a12 γ12 = γa12 = γa12 γ13 = γa13 = γa13 γ23 = γa23 = γa23 A2 P3 R = − A1 + O = − A 2 + O = − A 2 + O Fig. 10 The Circumcenter O and Circumradius R of a triangle A1 A2 A3 in a Euclidean space Rn . 136), p.
Then, in the standard triangle notation, Figs. 120) Proof. 119). 120) are obtained from the first by vertex cyclic permutations. 77), p. 24, to calculate the distance r between the point A3 and the line LA1 A2 that contains the points A1 and A2 , Fig. 14 (The Triangle Inradius). Let A1 A2 A3 be a triangle in a Euclidean space Rn . Then, in the standard triangle notation, Fig. 14 it is appropriate to present the well-known Heron’s formula [Coxeter (1961)]. 15 (Heron’s Formula). Let A1 A2 A3 be a triangle in a Euclidean space Rn .
26) of barycentric representations. 33) of P . 26) of barycentric representations. (4) Follows from (3) immediately. (5) Follows from (4) straightforwardly, noting that the contribution of pairs (i, j) vanishes when i = j. (6) Follows from (5) by interchanging the labels i and j of the two summation indexes in the argument of the second Σ on the numerator of (5). (7) Follows from (6) immediately. (8) The passage from (7) to (8) is merely a matter of notation that we introduce here for its importance in the book.
Algebraic Geometry - Bowdoin 1985, Part 1 by Bloch S. (ed.)