On Mon, 24 Jun 2002 16:22:10 Joseph B. Reid wrote: >Ma Be wrote in USMA 20599: > >>I cannot fathom for the love of me why we still haven't dealt with this >>issue yet. If we all agree with a decimal system of units we should also >>all agree that decimalization of angles should be "in the agenda" of >>things to do (just like with time!). Now... Why don't we "change >>slightly" the subject of these discussions to what solution we should >>support? As far as I'm concerned there can only be 4 reasonable options >>here: either go with 100 or 1000 for a unit or 1 or 4 for the entire >>circle. My vote goes to 100 for the entire circle due mainly to its "tie" >>with percentages. > >>Marcus > >Marcus: >How would you write one-third and two-thirds of a right angle? > Well... I knew this was coming... So, here is how I'd tackle this conundrum.
Firstly, it's not because we could be faced with "untractable" fractions for some "important" angles that we should shun from decimalizing angles. Secondly, since we would rarely have math operations involving adding/subtracting/dividing/multiplying angles *directly*, using fractions as "final" values should not be as bad as with other ordinary measurements. Thirdly, since I also think that it's not because we defend decimalization that we should *necessarily* "avoid" fractions I honestly wouldn't mind writing things like: 8 1/3 and 16 2/3. In case this would "look" horrible or "anathema" to some, fine, let's use 8.3 and 16.6 with the dot on top of the 3 and last 6 to denote infinite series as is the normal convention for things like 8.333... and 16.666... True, there could be issues to address when it comes to printing this information due to well-known printing limitations in some applications. (I'm assuming my option for 100 units for the entire circle would "win the contest" here) Fourthly, there would be only 8 of such values to worry about for trigonometry issues (1/3 and 2/3 of every "quadrant" of the circle, or 8.3, 16.6, 33.3, 41.6, 58.3, 66.6, 83.3 and 91.3), hence, not such a big deal (IMHO). Finally, we may elect to create some "symbolism" for such situations to avoid this quagmire, like, 'first third', 'second third', etc, denoted possibly by some 1 with a raised 3, whatever (I'd be open to suggestions here...). A similar notion could be extended for eighths as well, like 'first eighth', etc, in which case it would be the 8 that would be raised. In other words, we could get... "creative" to address the use of fractions *for this particular application*, in a fashion that wouldn't be cumbersome for professionals in areas like aviation, etc. Again, I'm fully aware of the weaknesses associated with decimalizing angles here. However, I honestly think they shouldn't be too strong a deterrent to preclude its decimalization IMHO. Marcus Is your boss reading your email? ....Probably Keep your messages private by using Lycos Mail. Sign up today at http://mail.lycos.com
