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Estimation quiz!
08-08-2020, 05:01 PM
Post: #57
RE: Estimation quiz!
(08-08-2020 07:35 AM)EdS2 Wrote:  Albert:
> → L = pi*R / cos(22.5°) = pi*R * 2/√(2+√2) ≈ 20000 km * 1.0824 = 21648 km

Nice! But, I wonder, what mental arithmetic might you do to estimate that result?

Pythogrean triples a,b,c = 5,12,13 had ∠A ≈ 22.6°

L = pi*R * sec(22.5°) ≈ 20000*13/12 = 20000+10000/6 ≈ 21667 km

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This is equivalent to assuming √2 = 238/13² ≈ 1.4083

sec(22.5°) = 2/√(2+√2) ≈ 2/√(2+238/13²) = 2*13/√576 = 13/12

A better estimate for √2 is 239/13² ≈ 1.4142 (this is actually √2 rational convergent, after 99/70)

sec(22.5°) ≈ 2*13/√577 = 13/12 / √(1+1/576) ≈ 13/12 * √(1-1/576) ≈ 13/12 * (1-1/1152) ≈ 1.0824
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Messages In This Thread
Estimation quiz! - EdS2 - 07-30-2020, 10:54 AM
RE: Estimation quiz! - Paul Dale - 07-30-2020, 11:27 AM
RE: Estimation quiz! - cruff - 07-30-2020, 01:00 PM
RE: Estimation quiz! - Paul Dale - 07-30-2020, 01:04 PM
RE: Estimation quiz! - cruff - 07-31-2020, 12:01 AM
RE: Estimation quiz! - KeithB - 07-30-2020, 01:56 PM
RE: Estimation quiz! - Paul Dale - 07-30-2020, 10:25 PM
RE: Estimation quiz! - Albert Chan - 07-30-2020, 02:13 PM
RE: Estimation quiz! - Werner - 07-30-2020, 02:24 PM
RE: Estimation quiz! - Massimo Gnerucci - 07-30-2020, 02:34 PM
RE: Estimation quiz! - Albert Chan - 07-30-2020, 03:10 PM
RE: Estimation quiz! - rprosperi - 07-30-2020, 04:20 PM
RE: Estimation quiz! - Werner - 07-30-2020, 05:37 PM
RE: Estimation quiz! - Albert Chan - 07-30-2020, 06:10 PM
RE: Estimation quiz! - rprosperi - 07-30-2020, 08:03 PM
RE: Estimation quiz! - EdS2 - 07-31-2020, 01:26 PM
RE: Estimation quiz! - Paul Dale - 07-31-2020, 01:40 PM
RE: Estimation quiz! - Valentin Albillo - 07-31-2020, 02:33 PM
RE: Estimation quiz! - Paul Dale - 08-01-2020, 01:09 AM
RE: Estimation quiz! - EdS2 - 08-01-2020, 06:48 AM
RE: Estimation quiz! - Thomas Okken - 08-01-2020, 07:30 AM
RE: Estimation quiz! - Massimo Gnerucci - 08-01-2020, 10:09 AM
RE: Estimation quiz! - Valentin Albillo - 08-01-2020, 11:16 PM
RE: Estimation quiz! - ijabbott - 08-01-2020, 05:24 PM
RE: Estimation quiz! - johanw - 08-01-2020, 08:41 PM
RE: Estimation quiz! - J-F Garnier - 08-02-2020, 07:56 AM
RE: Estimation quiz! - SlideRule - 08-02-2020, 12:23 PM
RE: Estimation quiz! - Paul Dale - 08-02-2020, 01:10 PM
RE: Estimation quiz! - EdS2 - 08-02-2020, 03:13 PM
RE: Estimation quiz! - Valentin Albillo - 08-02-2020, 04:02 PM
RE: Estimation quiz! - Maximilian Hohmann - 08-02-2020, 05:04 PM
RE: Estimation quiz! - Valentin Albillo - 08-02-2020, 05:54 PM
RE: Estimation quiz! - Maximilian Hohmann - 08-02-2020, 09:01 PM
RE: Estimation quiz! - Albert Chan - 08-02-2020, 11:36 PM
RE: Estimation quiz! - SlideRule - 08-02-2020, 11:04 PM
RE: Estimation quiz! - Albert Chan - 08-02-2020, 05:41 PM
RE: Estimation quiz! - EdS2 - 08-03-2020, 07:56 AM
RE: Estimation quiz! - Albert Chan - 08-03-2020, 11:00 AM
RE: Estimation quiz! - pinkman - 08-03-2020, 03:08 PM
RE: Estimation quiz! - SlideRule - 08-03-2020, 11:57 AM
RE: Estimation quiz! - Valentin Albillo - 08-03-2020, 03:10 PM
RE: Estimation quiz! - KeithB - 08-03-2020, 01:54 PM
RE: Estimation quiz! - EdS2 - 08-03-2020, 03:22 PM
RE: Estimation quiz! - SlideRule - 08-03-2020, 03:49 PM
RE: Estimation quiz! - EdS2 - 08-04-2020, 10:17 AM
RE: Estimation quiz! - Thomas Okken - 08-04-2020, 12:33 PM
RE: Estimation quiz! - EdS2 - 08-07-2020, 06:57 AM
RE: Estimation quiz! - Thomas Okken - 08-07-2020, 09:03 AM
RE: Estimation quiz! - Albert Chan - 08-07-2020, 12:56 PM
RE: Estimation quiz! - EdS2 - 08-08-2020, 07:35 AM
RE: Estimation quiz! - Albert Chan - 08-08-2020 05:01 PM
RE: Estimation quiz! - Csaba Tizedes - 08-04-2020, 11:25 AM
RE: Estimation quiz! - Csaba Tizedes - 08-07-2020, 02:06 PM
RE: Estimation quiz! - Albert Chan - 08-05-2020, 02:29 PM
RE: Estimation quiz! - KeithB - 08-05-2020, 03:38 PM
RE: Estimation quiz! - Albert Chan - 08-05-2020, 04:22 PM
RE: Estimation quiz! - StephenG1CMZ - 08-05-2020, 06:12 PM
RE: Estimation quiz! - EdS2 - 08-08-2020, 05:25 PM
RE: Estimation quiz! - KeithB - 08-13-2020, 01:41 PM
RE: Estimation quiz! - Albert Chan - 08-16-2020, 11:24 AM



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