Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?]

References	(2 earlier) <roy-DA9493.09383329042014@news.panix.com> <8td53bxud5.ln2@news.ducksburg.com> <ljp9sp$h22$1@ger.gmane.org> <CAPTjJmqya7paQowEkY7-pfsSynybEYTVgC2QTbviX5DWc8VHUg@mail.gmail.com> <5360F72F.2000102@stoneleaf.us>
Date	2014-05-01 00:27 +1000
Subject	Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?]
From	Chris Angelico <rosuav@gmail.com>
Newsgroups	comp.lang.python
Message-ID	<mailman.9612.1398875917.18130.python-list@python.org> (permalink)

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On Wed, Apr 30, 2014 at 11:14 PM, Ethan Furman <ethan@stoneleaf.us> wrote:
>> Any point where the mile east takes you an exact number of times
>> around the globe. So, anywhere exactly one mile north of that, which
>> is a number of circles not far from the south pole.
>
>
> It is my contention, completely unbacked by actual research, that if you
> find such a spot (heading a mile east takes you an integral number of times
> around the pole), that there is not enough Earth left to walk a mile north
> so that you could then turn-around a walk a mile south to get back to such a
> location.

The circle where the distance is exactly one mile will be fairly near
the south pole. There should be plenty of planet a mile to the north
of that.

If the earth were a perfect sphere, the place we're looking for is the
place where cutting across the sphere is 1/π miles. The radius of the
earth is approximately 4000 miles (give or take). So we're looking for
the place where the chord across a radius 4000 circle is 1/π; that
means the triangle formed by a radius of the earth and half of 1/π and
an unknown side (the distance from the centre of the earth to the
point where the chord meets it - a smidge less than 4000, but the
exact distance is immaterial) is a right triangle. Trig functions to
the rescue! We want latitude 90°-(asin 1/8000π). It's practically at
the south pole: 89.9977° south (89°59'52").

Are my calculations correct?

ChrisA

Thread

Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-28 12:00 -0400
  Re: Significant digits in a float? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-04-29 02:34 +0000
    Re: Significant digits in a float? Ben Finney <ben@benfinney.id.au> - 2014-04-29 13:23 +1000
      Re: Significant digits in a float? Steven D'Aprano <steve@pearwood.info> - 2014-04-29 05:43 +0000
        Re: Significant digits in a float? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-04-29 20:33 -0400
          Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-29 20:42 -0400
            Re: Significant digits in a float? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-04-30 20:02 -0400
              Re: Significant digits in a float? Mark H Harris <harrismh777@gmail.com> - 2014-04-30 22:54 -0500
                Re: Significant digits in a float? Paul Rubin <no.email@nospam.invalid> - 2014-04-30 20:56 -0700
                Re: Significant digits in a float? Mark H Harris <harrismh777@gmail.com> - 2014-04-30 23:16 -0500
                Re: Significant digits in a float? William Ray Wing <wrw@mac.com> - 2014-05-01 11:53 -0400
                Re: Significant digits in a float? Mark H Harris <harrismh777@gmail.com> - 2014-05-06 11:29 -0500
                Re: Significant digits in a float? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-05-01 22:06 -0400
                Re: Significant digits in a float? Mark H Harris <harrismh777@gmail.com> - 2014-05-06 09:51 -0500
                Re: Significant digits in a float? alister <alister.nospam.ware@ntlworld.com> - 2014-05-06 15:18 +0000
                Re: Significant digits in a float? Joel Goldstick <joel.goldstick@gmail.com> - 2014-05-06 12:14 -0400
                Re: Significant digits in a float? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-05-06 19:48 -0400
                Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-05-01 08:56 -0400
                Re: Significant digits in a float? Larry Hudson <orgnut@yahoo.com> - 2014-05-01 12:51 -0700
                Re: Significant digits in a float? Adam Funk <a24061@ducksburg.com> - 2014-05-01 22:05 +0100
                Re: Significant digits in a float? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-05-01 21:47 -0400
                Re: Significant digits in a float? Mark H Harris <harrismh777@gmail.com> - 2014-05-06 09:59 -0500
                [OT] Silde rules [was Re: Significant digits in a float?] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-05-06 16:10 +0000
                Re: [OT] Silde rules Ben Finney <ben@benfinney.id.au> - 2014-05-07 10:01 +1000
              Re: Significant digits in a float? Adam Funk <a24061@ducksburg.com> - 2014-05-01 21:55 +0100
                Re: Significant digits in a float? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-05-01 22:26 -0400
                Re: Significant digits in a float? Adam Funk <a24061@ducksburg.com> - 2014-05-08 20:58 +0100
    Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-29 09:38 -0400
      Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 02:30 +1000
        Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-29 19:53 -0400
          Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 10:13 +1000
          Re: Significant digits in a float? Ben Finney <ben@benfinney.id.au> - 2014-04-30 10:13 +1000
          Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 10:17 +1000
          Re: Significant digits in a float? Ben Finney <ben@benfinney.id.au> - 2014-04-30 10:20 +1000
          Re: Significant digits in a float? Grant Edwards <invalid@invalid.invalid> - 2014-04-30 18:19 +0000
      Re: Significant digits in a float? Ned Batchelder <ned@nedbatchelder.com> - 2014-04-29 12:47 -0400
        Re: Significant digits in a float? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-04-30 09:45 +1200
      Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 02:59 +1000
      Re: Significant digits in a float? Adam Funk <a24061@ducksburg.com> - 2014-04-29 21:16 +0100
        Re: Significant digits in a float? Mark H Harris <harrismh777@gmail.com> - 2014-04-29 15:39 -0500
          Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 07:15 +1000
        Re: Significant digits in a float? Ryan Hiebert <ryan@ryanhiebert.com> - 2014-04-29 15:42 -0500
        Re: Significant digits in a float? emile <emile@fenx.com> - 2014-04-29 15:42 -0700
          Re: Significant digits in a float? alister <alister.nospam.ware@ntlworld.com> - 2014-04-30 09:03 +0000
          Re: Significant digits in a float? Grant Edwards <invalid@invalid.invalid> - 2014-04-30 18:21 +0000
            Re: Significant digits in a float? emile <emile@fenx.com> - 2014-05-01 09:34 -0700
              Re: Significant digits in a float? alister <alister.nospam.ware@ntlworld.com> - 2014-05-01 17:13 +0000
        Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 08:51 +1000
          Re: Significant digits in a float? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-04-30 20:14 +1200
            Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 18:27 +1000
            Re: Significant digits in a float? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-04-30 14:05 +0100
        Re: Significant digits in a float? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-04-30 00:34 +0100
        Re: Significant digits in a float? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-04-29 20:37 -0400
        Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-29 20:45 -0400
        Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 10:45 +1000
          Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-29 20:48 -0400
        Re: Significant digits in a float? Ethan Furman <ethan@stoneleaf.us> - 2014-04-29 19:31 -0700
          Re: Significant digits in a float? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-04-30 02:59 +0000
            Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-29 23:30 -0400
              Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 13:40 +1000
        Re: Significant digits in a float? Chris Angelico <rosuav@gmail.com> - 2014-04-30 13:03 +1000
          Re: Significant digits in a float? Roy Smith <roy@panix.com> - 2014-04-30 08:01 -0400
        Off-topic  circumnavigating the earth in a mile or less  [was Re: Significant digits in a float?] Ethan Furman <ethan@stoneleaf.us> - 2014-04-30 06:14 -0700
        Re: Off-topic  circumnavigating the earth in a mile or less  [was Re: Significant digits in a float?] Ethan Furman <ethan@stoneleaf.us> - 2014-04-30 07:02 -0700
          Re: Off-topic  circumnavigating the earth in a mile or less Adam Funk <a24061@ducksburg.com> - 2014-05-01 21:52 +0100
        Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?] Chris Angelico <rosuav@gmail.com> - 2014-05-01 00:27 +1000
        Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?] Chris Angelico <rosuav@gmail.com> - 2014-05-01 05:10 +1000
        Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?] Ryan Hiebert <ryan@ryanhiebert.com> - 2014-04-30 10:24 -0500
        Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?] Ian Kelly <ian.g.kelly@gmail.com> - 2014-04-30 17:46 -0600
        Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?] Terry Reedy <tjreedy@udel.edu> - 2014-04-30 22:20 -0400
          Re: Off-topic circumnavigating the earth in a mile or less [was Re:   Significant digits in a float?] Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-05-01 18:16 +1200
          Re: Off-topic circumnavigating the earth in a mile or less Adam Funk <a24061@ducksburg.com> - 2014-05-01 21:57 +0100
            Re: Off-topic circumnavigating the earth in a mile or less Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-05-01 22:49 +0100
            Re: Off-topic circumnavigating the earth in a mile or less alister <alister.nospam.ware@ntlworld.com> - 2014-05-02 08:49 +0000
        Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?] Chris Angelico <rosuav@gmail.com> - 2014-05-01 11:57 +1000
        Re: Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?] Vlastimil Brom <vlastimil.brom@gmail.com> - 2014-05-01 09:49 +0200
      Re: Significant digits in a float? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-04-30 02:50 +0000
      Re: Significant digits in a float? Grant Edwards <invalid@invalid.invalid> - 2014-04-30 18:18 +0000

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