Dear Frank, Can I help the POTUS? No. Can I answer your question? Maybe but I am not used to working in imperial units.
Consider a horizontal cross section of the gnomon at any height above the dial plate. The shape of the section would be an ellipse with minor axis equal to 0.5" aligned East-West. The major axis would be equal to 0.5"/sin 30 = 1" aligned North-South. At noon, each section of the gnomon will cast a shadow as wide as its minor axis, thus 0.5" wide. At 6 am or pm, each section will cast a shadow as wide as its major axis, thus 1" wide. Best wishes, Geoff On 17 January 2018 at 18:04, Frank King <f...@cl.cam.ac.uk> wrote: > Dear All, > > I gather from the UK media that > the recent medical check-up > undertaken by the U.S. President > involved some "cognitive tests" > and he scored 30 out of 30. > > One of these tests requires the > subject to mark in the hands of > a clock at a specified time. > > It is, of course, reassuring to > know that he is familiar with > analog(ue) time measuring > instruments so I would like to > propose a test which is just a > whisker more ambitious for next > year... > > I would present the subject > with a mock-up horizontal > sundial equipped with a rod > gnomon which has a circular > cross-section and is about > 0.5" in diameter. > > The dial would be properly > set up for a latitude of > 30 deg N. so the gnomon would > slope at a 30 deg angle to the > horizontal. > > I would then ask the subject to > draw the shadow of the gnomon as > it would be at 6am and 12 noon. > > Since the mock up would include > a full set of labelled hour lines > this should not be too much of a > challenge BUT... > > Part of the required answer is > that the shadow at 6am should be > wider than the shadow at 12 noon. > > I would then ask by how much the > shadow is wider at 6am than at > 12 noon and to explain why. > > Can you help the President? > > Frank > > Frank H. King > Cambridge, U.K. > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > >
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