Little explorations with HP calculators (no Prime)
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04-09-2017, 03:40 PM
(This post was last modified: 04-09-2017 03:43 PM by Gerson W. Barbosa.)
Post: #166
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RE: Little explorations with the HP calculators
(04-08-2017 09:17 PM)Gerson W. Barbosa Wrote: Sabc a b c A more compact formula in terms of the relationships between the segments and the sides of the outer triangle is better: Given the triangles ABC and DEF, where BC = a BF = r = a/x CF = a - r AC = b CE = s = b/y AE = b - s AB = c AD = t = c/z BD = c - t Then SΔABC x y z ------ = -------------------------- SΔDEF z + (x y - x - y)(z - 1) Examples: 1) x = 2, y = 3, z = 4 SΔABC/SΔDEF = (2*3*4)/(4 + (2*3 - 2 - 3)*(4 - 1) = 24/7 2) x = 2, y = 3, z = 2 SΔABC/SΔDEF = (2*3*2)/(2 + (2*3 - 2 - 3)*(2 - 1) = 4 |
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