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.

Unit Circlehttp://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 formulahttp://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]

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] 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.

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...

[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.

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.

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.

//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.)

//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.)

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?

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?

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.

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.

[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.