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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Angular inclination of an interstate highway
From: Jackson McDonald
Date: 2013 Dec 31, 20:07 +0000
From: Jackson McDonald
Date: 2013 Dec 31, 20:07 +0000
Yep, that's me.
From: FrankReed@HistoricalAtlas.com
To: jacksonmcdonald@hotmail.com
Date: Tue, 31 Dec 2013 11:57:56 -0800
Subject: [NavList] Re: Angular inclination of an interstate highway
From: FrankReed@HistoricalAtlas.com
To: jacksonmcdonald@hotmail.com
Date: Tue, 31 Dec 2013 11:57:56 -0800
Subject: [NavList] Re: Angular inclination of an interstate highway
Jackson McDonald, you wrote:
"I'm neither an engineer nor a math whiz"
In this case, actually, you may be in safer waters BECAUSE you do not have as much math background. This issue of dealing with small angles is one where a certain amount of mathematical background can get a person in trouble. Everyone that I have met who has good competence in trigonometry immediately wants to jump for the trig functions when they encounter a puzzle like this. This works... much as you can break eggs with a sledgehammer. Very effective. But over-kill and... messy! For small angles, we need to remember that angles ARE ratios --expressable as "percentages" as in those road signs or as plain numbers which is when they're often called angles in "radians" (this is true for any angle, but for small angles it's more important in practical terms). And we convert those ratios to minutes arc by multiplying by that magic number, 3438.
And if you can do it in your head, then you can entertain yourself while driving! Whenever I am driving cross-country, when I encounter one of these grade signs giving the inclination in percentage, I work out the angle in my head to keep myself a little busy.
-FER
PS: This must be you: http://en.wikipedia.org/wiki/Jackson_McDonald. Fascinating! ? ???? ?????? ???????? ??-??????.
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: http://fer3.com/arc/m2.aspx?i=126067"I'm neither an engineer nor a math whiz"
In this case, actually, you may be in safer waters BECAUSE you do not have as much math background. This issue of dealing with small angles is one where a certain amount of mathematical background can get a person in trouble. Everyone that I have met who has good competence in trigonometry immediately wants to jump for the trig functions when they encounter a puzzle like this. This works... much as you can break eggs with a sledgehammer. Very effective. But over-kill and... messy! For small angles, we need to remember that angles ARE ratios --expressable as "percentages" as in those road signs or as plain numbers which is when they're often called angles in "radians" (this is true for any angle, but for small angles it's more important in practical terms). And we convert those ratios to minutes arc by multiplying by that magic number, 3438.
And if you can do it in your head, then you can entertain yourself while driving! Whenever I am driving cross-country, when I encounter one of these grade signs giving the inclination in percentage, I work out the angle in my head to keep myself a little busy.
-FER
PS: This must be you: http://en.wikipedia.org/wiki/Jackson_McDonald. Fascinating! ? ???? ?????? ???????? ??-??????.
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