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I stayed up in bed last night figuring what the altitude of an equilateral triangle inscribed in a societycircle is in terms of the circle's radius.  This took a frustratingly long time, as first I had to remember what cos π/6 is (I knew that it was either √3/2 or .5, but I couldn't remember which, finally determining the answer through extremely disreputable means), and then I had a very hard time holding the image in my head to keep track of what lines were hypotenuses to what right triangles.  The really dumb part is that the answer is exactly what I guessed it would be before actually embarking on this enterprise, and there was no reason at all I had to do it last night.  (What, you might ask, is the reason I was doing this at all?  I thought such knowledge would be useful if I were ever going to want to drill three holes, corresponding to the apices of such a triangle, in a succession of boards, each board host to a triangle rotated 30 degrees in some constant direction (not that that part matters, actually) with respect to the last.  Though 30 might actually be too extreme; oh well.)

Totally unrelatedly, check this shit out: (15" was calculated as the distance between the holes - 21" - divided by 1.4. Adjust if necessary).  At no point is it explained why 1.4 is the magic number, or what sort of adjustments might be necessary, or, for that matter, why the distance between the holes is the relevant measurement, all useful informations, or so one might think.  (I assume the distance between the holes is measured because the holes have to line up at the top and bottom.  But then one would expect the divisor to have, I dunno, more obvious trigonometric significance? 1.4 is close to √2, I guess.  And actually that makes no sense; the pipes aren't rotated and the holes are drilled at 45-degree intervals, and there are three of them; the holes will never line up.)