Nice find, HH. http://chesswanks.com/txt/BatterseaPowerStationPuzzle.pdf It is hard to imagine how Messrs Salomon, Armstrong & Sylvester could have managed to convince themselves about the conic shown in the final figure of Singmaster's document: for instance, their point o = 0 coincides with the origin tower, from where the other angles cannot possibly be equal. [Unless of course BPS has transmogrified into a square floorplan since last I set eyes on it, which would require shifting an awful lot of bricks in addition to the roof.] But it's comforting to know how many other people this wicked problem has tied into knots. Incidentally in Hess' case where angle v = pi/14 , I find the (nontrivial) locus of viewpoint V = (x,y) for variable distance o to be the cubic curve 4*x^3 - 4*x*y^2 - 3*x^2 + y^2 = 0 , which (ummm) also meets the origin! Wait, wait --- at the origin c_0 c_2 - c_1^2 = 3 > 0 indicating an acnode (isolated point), see https://en.wikipedia.org/wiki/Singular_point_of_a_curve Phew --- so everything is alright? Probably; though ACW's telescope may undergo extensive structural modification at this point ... I suppose some of this is going to have be included in my screed. WFL On 7/18/18, Hans Havermann <gladhobo@bell.net> wrote:
gosper.org/battersea_run.txt gosper.org/battersea.pdf
For reference, I have a slightly edited version of David Singmaster's original posing of the problem (of unknown date) wherein I've added a photo at the bottom of page 3 and an addendum page 4, both taken from an alternate (but presumably subsequent) version of the pdf. I've left out the photo of Elton John.
http://chesswanks.com/txt/BatterseaPowerStationPuzzle.pdf
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