(41C) Area of Triangle (SSS)

12042019, 03:03 PM
Post: #13




RE: (41C) Area of Triangle (SSS)
(11162018 03:33 AM)Albert Chan Wrote: Trivia: Area Δ = √((aby)*y), max(y/(ab)) = 1/4 Simpler proof, using Law of Cosine: c² = (ab)² + 4ab sin(C/2)² Angle A ≥ B ≥ C → max(C) = 60° → y/(ab) = sin(C/2)² ≤ ¼ (11122018 08:28 PM)Dieter Wrote: Both the formula and the program look good. This is Kahan's formula: Area Δ = ¼ √((a+(b+c)) (c(ab)) (c+(ab)) (a+(bc)) Note that 4y = (c(ab)) (c+(ab)) = middle 2 terms inside Kahan's √ All is needed is to show 4(aby) also as accurate as (a+(b+c)) (a+(bc)) With 0 < y/(ab) ≤ ¼, (aby) terms are too far apart to hit by catastrophic cancellation. 

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Messages In This Thread 
(41C) Area of Triangle (SSS)  Gamo  11102018, 12:20 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11102018, 03:22 PM
RE: (41C) Area of Triangle (SSS)  Dieter  11102018, 08:53 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11122018, 02:55 PM
RE: (41C) Area of Triangle (SSS)  Dieter  11122018, 08:28 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11122018, 10:33 PM
RE: (41C) Area of Triangle (SSS)  Gamo  11112018, 05:04 AM
RE: (41C) Area of Triangle (SSS)  Dieter  11112018, 07:53 AM
RE: (41C) Area of Triangle (SSS)  Gamo  11112018, 12:23 PM
RE: (41C) Area of Triangle (SSS)  Dieter  11112018, 04:25 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11122018, 01:32 AM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11162018, 03:33 AM
RE: (41C) Area of Triangle (SSS)  Albert Chan  12042019 03:03 PM

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