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A Matter of Degree.

Divide the circle into 384 degrees.
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Suppose your spaceship crashes onto a habitable planet. Everyone is OK but everything else is destroyed. There is no chance of being rescued. You have to rebuild modern technology from scratch. You will have to calculate angles, but you have no computer or calculator. You'll have to make a trig table yourself. You know that the cosine of 60 is 0.5. Using the formula for finding the cosine for half the angle whose cosine is known and the formula for the cosine of added angles of known cosines, you could easily make a table of trig functions for each 15/16 of a degree. To calculate the functions of whole number degrees would take years. So why not designate 15/16 of a degree as one degree with 96 degrees to a right angle. you could use the same formulae to get half, quarter, eighth etc. degrees between each integer. In fact you could change to an octal or hexadecimal number system to further simplify matters for when you eventualy redevelop digital electronics.
tonybe, Apr 26 2010

Unit Circle http://en.wikipedia.org/wiki/Unit_circle
Trig values come from ratios within a circle. These ratios are linked to the fundamental ratio of diameter & perimeter of all circles - Pi. The 'degrees' system is pretty arbitrary. [Jinbish, Apr 27 2010]

pi formula http://www.math.hmc...files/20010.5.shtml
It is interesting that the discussion here mentions circles divided by powers-of-2, and that pi itself has a close connection with Base 16. [Vernon, Apr 27 2010]

[link]






       Rad idea.   

       If you know your trig, there is no problem. Keep terms as fractions, use radians, keep surds (rather than irrational decimals).   

       {Edit: Thanks [px]. That was horrible.}
Jinbish, Apr 26 2010
  

       "If you know you're trig..."
How do I know if I'm trig?
phoenix, Apr 26 2010
  

       //How do I know if I'm trig?//   

       Eugh! How did that happen?! I'm not trig, I'm appalled.
Jinbish, Apr 26 2010
  

       If you're Appalled, then who's Spartacus ?
8th of 7, Apr 26 2010
  

       One of the Pauls.
Ian Tindale, Apr 26 2010
  

       tonybe, - you lost me after the word “calculate”, after which I traversed through a sustained experience much resembling the sensory evidence of being fairly close-up to a collection of pigeons, seagulls and parakeets, all put together in a cage that’s evidently too small and uncomfortable, resulting in constant flapping and reorientation and squawking — a sensation combining the audible, visual and you could almost feel the noise.
Ian Tindale, Apr 26 2010
  

       [Ian Tindale] Jargon, noun "unintelligible talk, gibberish," from Old French jargon "a chattering" (of birds).
mouseposture, Apr 26 2010
  

       [Ian Tindale] can I quote you as an example of the widespread social phenomenon whereby it is amusing to be confused by mathematics?   

       Also, for the record, I am pretty sure that it wouldn't be that difficult to calculate trig tables for regular degrees - somebody did it once, I remember. And, for the CD, I suspect that [Jinbish] speaks wisely.
MaxwellBuchanan, Apr 26 2010
  

       would it be easier to do this and then convert back to the normal cosign results?
Voice, Apr 27 2010
  

       No.   

       The trig identities are only simple ratios that describe an angle within a circle. It's the fraction of the circle you are concerned with. So it really doesn't matter so much when you use radian measures (i.e. Fractions of Pi are useful because 2*pi = 360•).   

       Now, anyone heard of Pythagoras? He and his Greek chums did a lot of work with circles and triangles and stuff - and they didn't gave a calculator...
Jinbish, Apr 27 2010
  

       [Max] not only amusing, but I have seen in others a certain pride in having no knowledge of mathematics, from people who would be ashamed if they had no knowledge of English literature, or philosophy.
hippo, Apr 27 2010
  

       Is there a commonality in nature for dividing circles? Orange or tangerine segments? Lemons, limes and grapefruits? Frangipani flowers, other flowers, cauliflowers? Starfish?   

       I was just thinking only the other day how kind nature is for making segments in tangerines. Thoughtful and convenient. But the tangerine was so small that once I peeled it I ate it whole. That felt wrong, as though I had denied a gift.
Ian Tindale, Apr 27 2010
  

       Quite a lot of things - the arrangement of the branches in a pine cone, the arrangement of branches around the stem of a plant, etc. seem to be based on mathematical relationships like Phi (the "Golden Ratio"), or 2.61803399 (also known as the ratio between successive numbers in the Fibonacci series) - maths is everywhere.
hippo, Apr 27 2010
  

       If you're rebuilding modern technology from scratch, why not just ditch degrees entirely and go with radians from the ground up?
Wrongfellow, Apr 27 2010
  

       [hippo] "Intellectuals, particularly literary intellectuals, are natural Luddites" (CP Snow)
mouseposture, Apr 27 2010
  

       //maths is everywhere//
sp. "math is everywhere", or "maths are everywhere", shirley?
coprocephalous, Apr 27 2010
  

       //sp.// Don't think so; not according to Chambers.
Maths: singular noun, British colloq mathematics. N Amer equivalent math
  

       On saying that, my copy of the concise OED leaves the door open to either.
maths n. Brit. colloq. mathematics [abbreviation]
mathematics n.pl. (usually treated as sing.)
Jinbish, Apr 27 2010
  

       There were five things I absolutely hated at school: maths; physics; PE and french. The rest is history.
Ian Tindale, Apr 27 2010
  

       But we know that Mr. [Tindale] likes Morden Studies...
Jinbish, Apr 27 2010
  

       To be honest, I’ve never been that far. Never been to Morden. It’s outside zone four, isn’t it?
Ian Tindale, Apr 27 2010
  

       You mean it's in ... The Twilight Zone ...?   

       <dramatic chords>   

       DAH Da DAAAAAA .....   

       </dramatic chords>   

       Or should that be The Outer Limits ?   

       // The rest is history //   

       Or if you're John Cage, The Rest Is Silence.
8th of 7, Apr 27 2010
  

       //I have seen in others a certain pride in having no knowledge of mathematics, from people who would be ashamed if they had no knowledge of English literature, or philosophy.//   

       I, conversely, am woefully ignorant of English literature, and am indeed ashamed of this shortcoming. (I'm also ignorant of philosophy, but that doesn't worry me. If they ever find something out after nthousand years of trying, then they can let me know and I'll catch up with it.)
MaxwellBuchanan, Apr 27 2010
  

       And while we're on the subject (which we weren't), wouldn't it make more sense to divide the circle into 2^n degrees - either 256 or 512? Or even 1024 to get a rough alignment with a base-10 system?
MaxwellBuchanan, Apr 27 2010
  

       Not if you're a Sumerian or Babylonian.
hippo, Apr 27 2010
  

       But I'm not.
MaxwellBuchanan, Apr 27 2010
  

       Well, you could be - sitting somewhere in Sumeria 5000 years ago, looking at stuff on the Halfbakery through a freak wormhole in the space-time continuum... - but more seriously, does 60 have more unique factors than 2^n, for any n?
hippo, Apr 27 2010
  

       60 has 10 factors (not including 1 and itself);
512, or 2^n, where n=9, has 10 factors.
  

       However, 2^n does not divide by 3 or 5 at any point.
Jinbish, Apr 27 2010
  

       All true, all true. But, the original problem was calculating trig functions and, since it's supposedly easy to calculate functions for half an angle, a power of 2 would make life easier. Maybe.
MaxwellBuchanan, Apr 27 2010
  

       Ah - but the trig functions are based on a right-angle triangle. You start getting square roots all over the shop: it all goes to hell in a hand-basket, thanks to Pythagoras.
Jinbish, Apr 27 2010
  

       No problem. We start with a bigger circle.
MaxwellBuchanan, Apr 27 2010
  

       [Maxwell B], I thought of making a right angle 64 degrees, but that would make 1/6 and 1/12 of a circle fractional degrees. I found it pettier to make 64 the new 60.
tonybe, Apr 28 2010
  
      
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