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Re: Comic relief... The trisector...

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On 9/20/2021 6:58 AM, Phil Carmody wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>> On 9/18/2021 7:31 AM, Max wrote:
>>> On 18.09.21 00:16, Chris M. Thomasson wrote:
>>>> https://i.ibb.co/nn83q6g/ct-tri-shit-lol.png
> 
>>> Good job! You found a pretty approximation there. ;-)
> 
>> Its radically simple and seems to approximate kind of "decent'ish" for
>> angles [0...pi/2]. Here is one for .5 radians:
>>
>> https://i.ibb.co/JxM8M0k/ct-tri-shit-lol-p1.png
>>
>> It seems to do a much better job for small angles... ;^)
>>
>> Shit hits the fan for larger angles. Here is 2.5 radians:
>>
>> https://i.ibb.co/xs6gpjK/ct-tri-shit-lol-p2.png
> 
> Of course, this means that with just a single iterative step it can be
> incredibly accurate. First, by eyeballing or any technique, construct
> any angle that is a goodish approximation to theta/3, say a_0. Now
> 3.a_0 ~= theta, and therefore delta_0 = |3.a_0 - theta| is small.
> Trisect delta_0 using your technique. Add or subtract this new sliver
> from your original a_0 approximation to get a_1, a better approximation.

Sounds good. I should have more time tonight or tomorrow to give it a go.


> If this is too complicated, there's an even simpler hack - you never
> need to trisect obtuse angles, as you can just trisect their complement
> (this is just a special case of the above where you chose a_0 = pi/3).
> And it's no great leap to retrict yourself to only having to consider
> angles in [0..pi/4].
> 
> I'd be willing to bet this converges very quickly, as I said at the
> start, probably just one iteration is enough for government work.
> Maybe you'd like to code it up and plot a few images?

I will. Also, I was thinking of a way to get a loose approximation using 
only a compass. It involves drawing at a constant speed for three units 
of time. Say, seconds. So, place the compass, and start slowly rotating 
it as you count to three. Now, we have an angle. Then, repeat the 
process using the same speed. At one, put a mark using the compasses 
nib. At two put another mark. The angle is trisected at a certain 
approximation... Sound kosher? lol.

To do this for any given angle, try to rotate the compass at a speed 
such that it goes from start to end in 3 seconds. That should give an 
approximation.

;^)

Start at the beginning. This is zero time. Start rotating. At one second 
place a mark. At two seconds place a mark. At the third second, mark and 
stop.

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Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-17 15:16 -0700
  Re: Comic relief... The trisector... Max <maxturv26@gmx.net> - 2021-09-18 16:31 +0200
    Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 13:32 -0700
      Re: Comic relief... The trisector... Max <maxturv26@gmx.net> - 2021-09-19 22:42 +0200
        Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 20:07 -0700
          Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 20:10 -0700
      Re: Comic relief... The trisector... Phil Carmody <pc+usenet@asdf.org> - 2021-09-20 16:58 +0300
        Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-22 12:31 -0700
  Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 20:13 -0700
  Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 23:56 -0700
    Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-22 21:53 -0700

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