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Radians Or Degrees?

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  Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-21 22:35 +0000
    Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-21 17:55 -0500
      Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-22 01:59 +0200
        Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 01:55 +0000
          Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 19:14 +0000
            Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:48 +0000
              Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 20:16 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 21:04 +0000
                  Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-22 23:39 +0200
                    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 21:47 +0000
                    Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-22 22:57 +0000
                      Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 00:13 +0000
                        Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:49 -0800
                          Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:59 -0800
                            Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 02:42 +0000
                              Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-23 12:28 -0800
                                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:42 +0000
                                  Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-24 12:40 -0800
                                    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 22:52 +0000
                                      Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-24 19:26 -0800
                                        Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-25 06:30 +0000
                                        Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-22 21:58 -0700
                        Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 02:28 +0000
                          Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-23 11:10 +0100
                            Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-14 11:26 +0200
                              Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 17:34 +0000
                                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 19:48 +0000
                                  Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 12:16 +0100
                                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-03-14 20:30 +0000
                                  Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:12 -0700
                                  Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 22:19 +0000
                                    Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:21 -0700
                                      Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:22 -0700
                                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 13:49 +0200
                              Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 11:23 +0100
                                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 14:15 +0200
                                  Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:23 +0000
                                    Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-16 16:59 +0100
                                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 13:59 -0700
                                  Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:13 -0700
                                    Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-16 13:23 -0700
                                  Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 14:16 -0700
                                    Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:26 -0700
                                      Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:30 -0700
                                        Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 15:48 -0700
                                          Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 13:41 -0700
                                            Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 21:49 -0700
                                    Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:16 +0000
                                      Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 19:08 +0200
                                        Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 17:22 +0000
                                          Re: Radians Or Degrees? scott@slp53.sl.home (Scott Lurndal) - 2024-03-16 18:32 +0000
                                          Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 20:49 +0200
                                          Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 16:19 -0700
                                            Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 00:00 +0000
                                              Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 18:38 -0700
                                                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 01:57 +0000
                                                  Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 19:57 -0700
                                                    Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-03-17 13:10 +0100
                                            Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:06 +0200
                                              Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:34 +0200
                                              Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 10:59 +0000
                                                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 14:15 +0200
                                  Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 15:13 -0700
                              Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-18 15:18 -0400
                                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-18 22:19 +0000
                                  Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 09:54 -0400
                                    Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-20 18:21 +0200
                                      Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 12:59 -0400
                                        Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:40 +0000
                                          Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:52 +0100
                                            Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 14:51 +0200
                                              Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-21 16:37 +0000
                                              Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-23 09:11 +0100
                                      Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-03-20 17:02 +0000
                                        Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:47 +0000
                                      Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:33 +0000
                                        Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 00:03 +0200
                                    Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:26 +0000
                                      Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 16:34 -0400
                                    Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:38 +0100
                        Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-23 14:32 +0200
                          Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 20:02 +0000
                            Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 20:38 +0000
                              Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 22:29 +0000
                                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:39 +0000
                                  Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 04:03 +0000
                                    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 04:47 +0000
                                      Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 05:27 +0000
                                        Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 05:48 +0000
                                    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 05:38 +0000
                                      Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 06:13 +0000
                                        Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 17:15 +0000
                                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 23:20 +0000
                              Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:39 +0000
                                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-23 23:16 +0000
                                  Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 23:44 +0000
                                    Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-24 01:15 +0000
                                      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 01:19 +0000
                                        Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-24 01:27 +0000
                                          Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 01:42 +0000
                                            Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-25 00:18 +0000
                                              Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-25 12:57 +0200
                                          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 02:21 +0000
                                            Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 02:49 +0000
                                              Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 03:07 +0000
                                                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 03:12 +0000
                                      Re: Radians Or Degrees? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-02-23 18:49 -0800
                                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-23 23:30 +0000
                                Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-24 02:25 -0500
                                  Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 21:21 +0000
                                    Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-24 17:32 -0500
                                      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 22:50 +0000
                              Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-25 16:19 +0100
                                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-25 18:11 +0000
                    Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-23 11:01 +0100
                  Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 22:09 +0000
                    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 22:30 +0000
                      Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-23 00:56 +0200
                        Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 23:03 +0000
    Re: Radians Or Degrees? fir <fir@grunge.pl> - 2024-02-22 00:15 +0100
      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 01:55 +0000
        Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 09:32 +0100
          Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 09:38 +0000
            Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 11:04 +0100
        Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-22 14:28 +0000
          Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 16:26 +0100
            Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:45 +0000
            Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-22 21:30 +0000
              Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:11 +0100
          GGs [was Radians Or Degrees?] Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-23 13:57 +0000
            Re: GGs [was Radians Or Degrees?] "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-23 11:15 -0800
              Re: GGs [was Radians Or Degrees?] Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-23 19:26 +0000
    Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 07:17 +0000
      Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-22 16:49 +0000
    Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 09:06 +0100
    Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-22 08:27 +0000
      Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 11:09 +0100
        Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 13:48 +0000
        Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-22 15:29 +0000
          Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 20:02 +0100
            Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-23 02:15 +0000
            Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 02:24 +0000
              Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:16 +0100
        Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:39 +0000
          Re: Radians Or Degrees? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2024-02-22 21:25 +0100
            Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 20:58 +0000
              Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:33 +0100
                Re: Radians Or Degrees? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2024-02-23 12:53 +0100
                  Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 20:23 +0000
          Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-25 11:19 +0000
            Re: Radians Or Degrees? Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-25 13:08 +0000
              Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-25 22:21 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-25 22:29 +0000
                  Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:29 +0000
                    Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-26 13:44 -0800
                      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 23:15 +0000
                        Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-26 16:02 -0800
                          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-27 00:55 +0000
                        Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-27 09:53 +0100
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-25 14:43 -0800
                  Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:32 +0000
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-02-25 23:09 +0000
                  Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:32 +0000
                    Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-02-26 23:01 +0000
                      Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-27 09:59 +0100
        Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:44 +0000

Page 8 of 9 — ← Prev page 1 2 3 4 5 6 7 [8] 9  Next page →

#382930

David Brown wrote:

> On 22/02/2024 16:29, Blue-Maned_Hawk wrote:
>> David Brown wrote:
>> 
>>> On 22/02/2024 09:27, Blue-Maned_Hawk wrote:
>>>>
>>>> Radians is the only angle unit which is not arbitrary.
>>>>
>>>>
>>>>
>>> No, it is not.  "Turns" are also not arbitrary, and are also
>>> mathematically fundamental.
>> 
>> That is a good point that i had not thought about.  Thank you.
>> 
>>> And while degrees were created by people, rather than something
>>> fundamental in the mathematics, the number of divisions was picked
>>> carefully for particular properties (lots of divisors).  And since
>>> degrees are a well-established and commonly known angle unit, using
>>> them is not arbitrary.  Even gradians were defined that way for good
>>> reasons.
>>>    So these units are not arbitrary - even though they were defined by
>>> humans and not mathematics.
>> 
>> I do not see how this is not still completely arbitrary.
>> 
>> 
> "Arbitrary" means that you picked something without any particular
> reason, and could just as well have picked something else.  We use base
> ten - that is not arbitrary, it is based on the number of fingers we
> have.  The Babylonians and Sumerians liked 5, 12 and 60 - also not
> arbitrary, but picked as numbers with a lot of convenient factors.  The
> French revolutionists picked 400 for gradians, because 100 parts in a
> right angle fit well with their new metric system, which fit well with
> our standard number base.  And one gradian of arc on a map corresponds
> almost exactly to 100 km in distance - also very intentional, and not
> arbitrary.
> 
>  From a purely mathematical viewpoint, these units are arbitrary - but
> from a human and historical viewpoint, they are not.

Then in that case, it sounds like they are either irrationally natural-
human-centric or irrationally steeped in tradition.



-- 
Blue-Maned_Hawk│shortens to 
Hawk│/
blu.mɛin.dÊ°ak/
│he/him/his/himself/Mr.
blue-maned_hawk.srht.site
Tradition is the reason for doing something there's no longer any good 
reason for doing.

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#382931

On Thu, 22 Feb 2024 20:02:30 +0100, David Brown wrote:

> The French revolutionists picked 400 for gradians, because 100 parts in
> a right angle fit well with their new metric system, which fit well with 
> our standard number base.

I wondered where they came from. But that reinforces my point, that 
supporting even little-known units like these are very easy with my 
scheme, requiring only the definition of a single conversion factor.

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#382935

On 23/02/2024 03:24, Lawrence D'Oliveiro wrote:
> On Thu, 22 Feb 2024 20:02:30 +0100, David Brown wrote:
> 
>> The French revolutionists picked 400 for gradians, because 100 parts in
>> a right angle fit well with their new metric system, which fit well with
>> our standard number base.
> 
> I wondered where they came from. But that reinforces my point, that
> supporting even little-known units like these are very easy with my
> scheme, requiring only the definition of a single conversion factor.

I agree with your approach - with the proviso that implementations that 
are specialised for a particular angle measurement might be more 
efficient, more accurate, or have greater range than simply scaling the 
argument to radians and using radian-based trig functions.  Numerical 
floating point calculations on finite systems do not quite follow the 
simple rules of real number mathematics, unfortunately.

But your approach (which is what most people use if they want trig in 
degrees) gives a lot of flexibility for very little cost.

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#382911

On Thu, 22 Feb 2024 11:09:50 +0100, David Brown wrote:

> And while degrees were created by people, rather than something
> fundamental in the mathematics, the number of divisions was picked
> carefully for particular properties (lots of divisors).

I know base-360 is supposed to have come from the Babylonians. But 
consider: you get exactly the same range of exact divisors (2, 3, 5, and 
powers and products thereof) with base-30.

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#382916

On 22.02.2024 20:39, Lawrence D'Oliveiro wrote:
> On Thu, 22 Feb 2024 11:09:50 +0100, David Brown wrote:
> 
>> And while degrees were created by people, rather than something
>> fundamental in the mathematics, the number of divisions was picked
>> carefully for particular properties (lots of divisors).
> 
> I know base-360 is supposed to have come from the Babylonians. But 
> consider: you get exactly the same range of exact divisors (2, 3, 5, and 
> powers and products thereof) with base-30.

Not the range of the unique divisors alone might be relevant but also
the number of duplicate divisors. As integer 30 is not dividable by 4
(which is a very common partition!), for example, but 360 is...

$ factor 360 30
360: 2 2 2 3 3 5   => 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ...
30: 2 3 5          => 2, 3, 5, 6, 10, 15

Mind that David wrote about "particular properties (lots of divisors)";
and 4 is (while not a prime) yet a [in practice very common] divisor.

Janis

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#382917

On Thu, 22 Feb 2024 21:25:28 +0100, Janis Papanagnou wrote:

> Not the range of the unique divisors alone might be relevant but also
> the number of duplicate divisors. As integer 30 is not dividable by 4
> (which is a very common partition!), for example, but 360 is...

Doesn’t matter, because a fraction with a divisor that is any power of 2 
is exactly representable in base-30.

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#382936

On 22/02/2024 21:58, Lawrence D'Oliveiro wrote:
> On Thu, 22 Feb 2024 21:25:28 +0100, Janis Papanagnou wrote:
> 
>> Not the range of the unique divisors alone might be relevant but also
>> the number of duplicate divisors. As integer 30 is not dividable by 4
>> (which is a very common partition!), for example, but 360 is...
> 
> Doesn’t matter, because a fraction with a divisor that is any power of 2
> is exactly representable in base-30.

That's true, but the Sumerians and Babylonians did not have decimal (or 
rather trigesimal for base 30 - or sexagesimal for base 60) points.  I 
don't think they made much use of fractions at all, but moved on to 
smaller units (dividing a degree into 60 minutes, and minutes into 60 
seconds).  That kept everything in integers.

It's not just the Babylonians that prefer integers - so does everyone 
else.  Would you rather that right-angled isosceles triangles had 45° 
angles, or 3.75° angles?

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#382939

On 23.02.2024 09:33, David Brown wrote:
> On 22/02/2024 21:58, Lawrence D'Oliveiro wrote:
>> On Thu, 22 Feb 2024 21:25:28 +0100, Janis Papanagnou wrote:
>>
>>> Not the range of the unique divisors alone might be relevant but also
>>> the number of duplicate divisors. As integer 30 is not dividable by 4
>>> (which is a very common partition!), for example, but 360 is...
>>
>> Doesn’t matter, because a fraction with a divisor that is any power of 2
>> is exactly representable in base-30.

I don't understand what you mean by "exactly representable", where
the analogon of the numeric e.g. "7.5" is concerned. (I thought we
were talking about the origins, how the choice of 360 came about.)

> 
> That's true, but the Sumerians and Babylonians did not have decimal (or
> rather trigesimal for base 30 - or sexagesimal for base 60) points.  I
> don't think they made much use of fractions at all, but moved on to
> smaller units (dividing a degree into 60 minutes, and minutes into 60
> seconds).  That kept everything in integers.
> 
> It's not just the Babylonians that prefer integers - so does everyone
> else.  Would you rather that right-angled isosceles triangles had 45°
> angles, or 3.75° angles?
> 

The old Greeks certainly didn't have a concept of fractional numbers;
fractions appeared as geometrical partitions (cf. e.g. the problem
of angle trisections); they handled mathematical and physical problems
by geometry (and by integral counting for the more mundane things).

Janis

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#382945

On Fri, 23 Feb 2024 12:53:49 +0100, Janis Papanagnou wrote:

> On 22/02/2024 21:58, Lawrence D'Oliveiro wrote:
>
>> On Thu, 22 Feb 2024 21:25:28 +0100, Janis Papanagnou wrote:
>>
>>> Not the range of the unique divisors alone might be relevant but also
>>> the number of duplicate divisors. As integer 30 is not dividable by 4
>>> (which is a very common partition!), for example, but 360 is...
>>
>> Doesn’t matter, because a fraction with a divisor that is any power of
>> 2 is exactly representable in base-30.
> 
> I don't understand what you mean by "exactly representable", where the
> analogon of the numeric e.g. "7.5" is concerned.

E.g. using “a” .. “t” to represent the digits with (decimal) values 10 .. 
29 in base-30:

    1 / 2  = 0.f
    1 / 2² = 0.7f
    1 / 2³ = 0.3mf
    1 / 3  = 0.a
    1 / 3² = 0.3a
    1 / 3³ = 0.13a
    1 / 5  = 0.6
    1 / 6  = 0.5

All those fractions are exact.

(And all worked out in my head, for better or for worse.)

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#383003

On 22/02/2024 19:39, Lawrence D'Oliveiro wrote:
> On Thu, 22 Feb 2024 11:09:50 +0100, David Brown wrote:
> 
>> And while degrees were created by people, rather than something
>> fundamental in the mathematics, the number of divisions was picked
>> carefully for particular properties (lots of divisors).
> 
> I know base-360 is supposed to have come from the Babylonians. But
> consider: you get exactly the same range of exact divisors (2, 3, 5, and
> powers and products thereof) with base-30.

A year has 365 days, and that influenced the idea that there should be 
360 degrees in a circle. But the Babylonians knew that it was 365 or 
close and not 360. So did they think that having 360 degrees was a 
fundamental, inherent, mathematical property of a circle, or did they not?
-- 
Check out Basic Algorithms and my other books:
https://www.lulu.com/spotlight/bgy1mm

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#383005

On 25/02/2024 11:19, Malcolm McLean wrote:
> On 22/02/2024 19:39, Lawrence D'Oliveiro wrote:
>> On Thu, 22 Feb 2024 11:09:50 +0100, David Brown wrote:
>>
>>> And while degrees were created by people, rather than something
>>> fundamental in the mathematics, the number of divisions was picked
>>> carefully for particular properties (lots of divisors).
>>
>> I know base-360 is supposed to have come from the Babylonians. But
>> consider: you get exactly the same range of exact divisors (2, 3, 5, and
>> powers and products thereof) with base-30.
> 
> A year has 365 days, and that influenced the idea that there should be 
> 360 degrees in a circle. But the Babylonians knew that it was 365 or 
> close and not 360. So did they think that having 360 degrees was a 
> fundamental, inherent, mathematical property of a circle, or did they not?

I don't think that's true.

It's 360 because it divides by {lots}, nothing to do with days in a year.

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#383017

On Sun, 25 Feb 2024 13:08:53 +0000, Richard Harnden wrote:

> It's 360 because it divides by {lots}, nothing to do with days in a year.

And you can get all those same divisors with 30.

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#383018

Lawrence D'Oliveiro <ldo@nz.invalid> writes:

> On Sun, 25 Feb 2024 13:08:53 +0000, Richard Harnden wrote:
>
>> It's 360 because it divides by {lots}, nothing to do with days in a year.
>
> And you can get all those same divisors with 30.

You are confusing unique prime factors with divisors.  Well, that's what
you appear to be doing but I suspect another motive altogether.

-- 
Ben.

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#383064

On Sun, 25 Feb 2024 22:29:41 +0000, Ben Bacarisse wrote:

> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> 
>> On Sun, 25 Feb 2024 13:08:53 +0000, Richard Harnden wrote:
>>
>>> It's 360 because it divides by {lots}, nothing to do with days in a
>>> year.
>>
>> And you can get all those same divisors with 30.
> 
> You are confusing unique prime factors with divisors.

No, I’m not. Once you have one occurrence of a prime factor, you get the 
ability to exactly represent fractions involving all powers of that 
factor, and all products of that factor with other factors.

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#383069

Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> On Sun, 25 Feb 2024 22:29:41 +0000, Ben Bacarisse wrote:
>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>>> On Sun, 25 Feb 2024 13:08:53 +0000, Richard Harnden wrote:
>>>> It's 360 because it divides by {lots}, nothing to do with days in a
>>>> year.
>>>
>>> And you can get all those same divisors with 30.
>> 
>> You are confusing unique prime factors with divisors.
>
> No, I’m not. Once you have one occurrence of a prime factor, you get the 
> ability to exactly represent fractions involving all powers of that 
> factor, and all products of that factor with other factors.

It would have saved some time if you had said that in the first place,
rather than claiming that "you can get all those same divisors with 30".

I suppose that you meant that 1/N where N is a divisor of 360 can be
represented in base 30 without repeating.  But the obvious meaning of
what you wrote was that all divisors of 360 are divisors of 30, and I'm
not the only one who thought so.

Either way, I'm not sure why you thought it was a point worth making.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */

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#383074

On Mon, 26 Feb 2024 13:44:45 -0800, Keith Thompson wrote:

> It would have saved some time if you had said that in the first place,
> rather than claiming that "you can get all those same divisors with 30".

Why, what else could you possibly have thought I meant? Dividing by things 
is precisely what fractions are all about.

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#383078

Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> On Mon, 26 Feb 2024 13:44:45 -0800, Keith Thompson wrote:
>> It would have saved some time if you had said that in the first place,
>> rather than claiming that "you can get all those same divisors with 30".
>
> Why, what else could you possibly have thought I meant? Dividing by things 
> is precisely what fractions are all about.

I took your statement that "you can get all those same divisors with 30"
to mean that you thought that 30 has all the same divisors that 360 has.
It's obvious that, for example, 180 is a divisor of 360 and not of 30,
but I thought you might have thought that all the divisors of 360 up to
30 are also divisors of 30, which is also wrong but not quite as
obviously so.

You've now clarified that that's not what you meant, but I'm just one of
several people who interpreted your original statement the same way I
did.  Given that, consider the possibility that your statement was not
as clear as you thought it was.

Since it wasn't an important or relevant point in the first place, I'm
going to drop it, and I suggest you do the same.  Nobody is going to
start using base 30 anyway.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */

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#383079

On Mon, 26 Feb 2024 16:02:17 -0800, Keith Thompson wrote:

> Since it wasn't an important or relevant point in the first place, I'm
> going to drop it, and I suggest you do the same.

You seem to do that a lot.

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#383088

On 27/02/2024 00:15, Lawrence D'Oliveiro wrote:
> On Mon, 26 Feb 2024 13:44:45 -0800, Keith Thompson wrote:
> 
>> It would have saved some time if you had said that in the first place,
>> rather than claiming that "you can get all those same divisors with 30".
> 
> Why, what else could you possibly have thought I meant? Dividing by things
> is precisely what fractions are all about.

I, for one, thought you were mistaken and confused.  It seemed to be the 
more logical explanation (and less unkind than assuming you are trolling 
or intentionally trying to cause confusion), since everyone else was 
clearly talking about divisors as the term is used in mathematics.  The 
"divisors" of an integer "N" are integers that divide wholly into N.  4 
is a divisor of 360, but it is not a divisor of 30.  It is /that/ simple.

No one is particularly interested in decimals here, much less interested 
in some kind of base 30 decimal (which is what you need to make your 
claims correct).  And the context was historical - why the Babylonians 
and Sumerians had 360 degrees in a circle.  They did not have radix 
points of any kind.

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#383019

Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> On Sun, 25 Feb 2024 13:08:53 +0000, Richard Harnden wrote:
>
>> It's 360 because it divides by {lots}, nothing to do with days in a year.
>
> And you can get all those same divisors with 30.

All except 4, 8, 9, 12, 18, 20, 24, 36, 40, 45, 60, 72, 90, 120, 180,
and 360.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */

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