Talk:Napkin ring problem

Band around a sphere[edit]

Band around a sphere isn't very clear. It's usually described as a sphere with a hole drilled through it (I believe). The caption on the first diagram is more lucid than the first two paras. --catslash (talk) 21:44, 25 February 2009 (UTC)[reply]

I'm going to think about how to rephrase this. Michael Hardy (talk) 22:11, 25 February 2009 (UTC)[reply]

what is this talk of the volume not depending on the radius of the sphere and only on height of cylinder? The 'height' of the cylinder depends on the radius of the cylindrical column and the radius of the sphere. —Preceding unsigned comment added by 18.111.35.21 (talk) 22:26, 10 December 2010 (UTC)[reply]

The radius of the sphere, the radius of the cylinder, and the height of the cylinder depend on each other, but any two of them can be fixed independently of each other. In the problem described here, the height is one of the fixed variables and the radius of the cylinder can be calculated from it, rather than vice versa. —David Eppstein (talk) 23:18, 10 December 2010 (UTC)[reply]

kokwan[edit]

kokwan looks like an old historical pronunciation to me. Does anyone know if this pronunciation or just the orthografy or neither was still in fashion at the time? — Preceding unsigned comment added by 82.139.81.0 (talk) 14:39, 19 May 2014 (UTC)[reply]

Japanese 弧間 (pronounced kokan) means literally 'arc space', that is, the space bounded by the peripheral arc. That is the best fit I can find for the given romanji and the meaning attributed. I do not know whether that is what Seki Kōwa used or not. 'kokwan' is nonsense. 'kwan' is a corruption of 'kuan' usually. — Preceding unsigned comment added by 70.68.24.153 (talk) 16:23, 15 August 2017 (UTC)[reply]

Why is Cavalieri's principle necessary?[edit]

Besides the pedagogical value, I don't see why we even need to invoke Cavalieri's principle when we can just find the volume by direct integration in cylindrical coordinates. --D昌양 (Talk) 08:16, 23 August 2017 (UTC)[reply]

If we're going to invoke Cavalieri, I think it's simpler to note that all the napkin rings are formed by sweeping the same semicircle around different circular sweep paths. —David Eppstein (talk) 15:45, 23 August 2017 (UTC)[reply]