Little explorations with HP calculators (no Prime)
04-09-2017, 03:40 PM (This post was last modified: 04-09-2017 03:43 PM by Gerson W. Barbosa.)
Post: #166
 Gerson W. Barbosa Senior Member Posts: 1,116 Joined: Dec 2013
RE: Little explorations with the HP calculators
(04-08-2017 09:17 PM)Gerson W. Barbosa Wrote:    Sabc                   a b c
------ = -----------------------------------
Sdef    a(b - r)(c - s) + t(c r + b(s - c))

Making r = b/2, s = c/3 and t = a/4 per the original problem, the expression easily evaluates to 24/7. Perhaps r should be associated with side a, s to side b, t to side c and the expression rewritten accordingly for mnemonic purposes.

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
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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Barbosa - 04-10-2017, 04:49 PM RE: Little explorations with the HP calculators - pier4r - 04-10-2017, 09:20 PM RE: Little explorations with the HP calculators - pier4r - 04-14-2017, 08:30 PM RE: Little explorations with the HP calculators - pier4r - 04-15-2017, 06:59 AM RE: Little explorations with the HP calculators - pier4r - 04-18-2017, 04:15 PM RE: Little explorations with the HP calculators - Gerson W. 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DavidM - 03-10-2018, 05:14 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-11-2018, 12:07 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 03-11-2018, 06:25 PM RE: Little explorations with HP calculators (no Prime) - Neve - 03-11-2018, 06:47 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-11-2018, 07:30 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-12-2018, 09:03 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-16-2018, 07:48 PM RE: Little explorations with HP calculators (no Prime) - Thomas Okken - 03-16-2018, 08:24 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-16-2018, 09:10 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-17-2018, 12:27 PM RE: Little explorations with HP calculators (no Prime) - Csaba Tizedes - 03-17-2018, 01:22 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 03-17-2018, 08:00 PM RE: Little explorations with HP calculators (no Prime) - grsbanks - 03-17-2018, 02:37 PM RE: Little explorations with HP calculators (no Prime) - Dieter - 03-16-2018, 08:29 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-17-2018, 08:55 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-18-2018, 12:14 PM RE: Little explorations with HP calculators (no Prime) - grsbanks - 03-18-2018, 12:27 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 04-02-2018, 08:55 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-18-2018, 09:54 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-18-2018, 12:50 PM RE: Little explorations with Casio 9750/9860 calculators - brickviking - 03-20-2018, 11:59 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-21-2018, 10:45 AM RE: Little explorations with Casio 9750/9860 calculators - brickviking - 03-22-2018, 02:16 AM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-22-2018, 11:32 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-21-2018, 11:23 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-21-2018, 08:37 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-21-2018, 11:27 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-22-2018, 11:15 AM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-23-2018, 02:02 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-23-2018, 08:20 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 04-02-2018, 09:29 AM RE: Little explorations with HP calculators (no Prime) - rprosperi - 04-02-2018, 01:50 PM RE: Little explorations with HP calculators (no Prime) - Zaphod - 04-02-2018, 02:24 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 04-02-2018, 05:34 PM RE: Little explorations with HP calculators (no Prime) - Zaphod - 04-02-2018, 06:17 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 04-02-2018, 08:53 PM RE: Little explorations with HP calculators (no Prime) - Zaphod - 04-02-2018, 09:16 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-25-2018, 05:01 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-25-2018, 07:34 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-25-2018, 08:00 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-25-2018, 08:45 PM RE: Little explorations with HP calculators (no Prime) - Dave Frederickson - 03-25-2018, 09:40 PM RE: Little explorations with HP calculators (no Prime) - Dave Frederickson - 03-25-2018, 09:43 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 04-02-2018, 01:53 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 04-02-2018, 09:11 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 05-05-2018, 02:22 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 05-21-2018, 12:53 PM RE: Little explorations with HP calculators (no Prime) - grsbanks - 05-21-2018, 01:04 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 05-21-2018, 06:02 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-26-2018, 09:34 PM RE: Little explorations with HP calculators (no Prime) - ijabbott - 12-26-2018, 11:41 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 03:22 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 04:59 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-31-2018, 07:59 PM RE: Little explorations with HP calculators (no Prime) - brickviking - 12-28-2018, 09:42 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-28-2018, 09:53 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 12-28-2018, 11:21 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-29-2018, 12:10 AM RE: Little explorations with HP calculators (no Prime) - 3298 - 12-29-2018, 02:05 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-27-2018, 06:52 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 08:31 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-27-2018, 08:47 PM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 12-27-2018, 10:20 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 11:58 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-28-2018, 01:38 AM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 12-28-2018, 04:04 AM RE: Little explorations with HP calculators (no Prime) - ijabbott - 12-28-2018, 09:06 AM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-28-2018, 02:00 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-28-2018, 03:41 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-29-2018, 04:06 PM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 12-29-2018, 07:35 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-29-2018, 10:02 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-30-2018, 01:26 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-31-2018, 04:30 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-31-2018, 08:20 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-31-2018, 08:36 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-13-2019, 10:48 AM RE: Little explorations with HP calculators (no Prime) - DavidM - 01-13-2019, 05:05 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 01-13-2019, 08:27 PM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 01-13-2019, 01:44 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 01-13-2019, 01:48 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-13-2019, 07:00 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-28-2019, 01:38 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-31-2019, 04:07 PM

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