Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > sci.crypt > #50059

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

Show all headers | View raw

"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.

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?

Phil
-- 
We are no longer hunters and nomads. No longer awed and frightened, as we have
gained some understanding of the world in which we live. As such, we can cast
aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

Back to sci.crypt | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

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

csiph-web