Hi Andrew, A closer and somewhat easier method would be to continue dividing the string in half til it had been divided into 16 equal parts. Measure out 15 of those parts and then at a right angle go 4 parts. As I mentioned to Steve LeLievre this approximates the tangent of 15 degrees with better than 1/2 percent accuracy. [ tan(15) roughly is equal to 0.267949 and 4/15 is about equal to 0.266667, arctan(4/15) is about 14.93 degrees ]. Of course any object marked out in equal divisions would do as well to mark out the 15 and 4. It just so happens that my fist is right at 4 inches wide and the length measured from my elbow to the end of my fist is right at 15 inches, so, I'm lucky, I carry this measure about with me!
How many of the rest of you are so lucky? How many find your fist width to elbow-fist length ratio to be even closer to the tangent of 15 degrees? Are there even better measurements taken from our self dimensions? Edley. You wrote: > Steve Lelievre suggested using arc tan 1/4 to find 15 degrees "in > emergency". > > A slightly better approximation is to go via > sin(15) = 0.2588 and arcsin(0.25) = 14.4775 deg > cf. tan(15) = 0.2679 and arctan(0.25) = 14.0362 degrees > > So, take your string and find a quarter of its length as before by two > halvings. Start from the centre point and mark a point on a first line at > the string's length away. From that point draw an arc (or mark a few > points to indicate it) using the quarter string as radius. Go back to the > centre and take the tangent to that arc as the second line. > > The angle subtended is arcsin 0.25 or about 14 degrees 29 minutes, close > enough for practical purposes I would think. > > If you want to get still closer, then do it both ways and add the > difference between them to the larger of the two angles to get 14 degrees > 55 minutes. (And if you dislike estimating the addition to make rather > than constructing it, then take two of the sine angles one after the other > i.e. added together and go back one of the tan angles to subtract it.) > > Or of course you could just use the same process, with half the string > length instead of a quarter, to go via arcsin 1/2 and obtain 30 degrees, > then take the string and mark two points equidistant from the origin on > the two lines 30 degrees apart, and use doubling the string to find the > point midway between those two - hence bisecting the angle into two angles > of exactly 15 degrees with no error at all. But we're getting close to > terrestrial origami I fear ...
