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What is the shape of a rocket? My English teacher has challenged me with that question and I am not sure of the answer. My friends suggest 'polygon' but I believe the answer is a little more complicated.

While rockets come in a variety of shapes and sizes, they have a similar job to do, and so the general shape of a rocket is highly recognizable even in cartoon forms or kids' drawings. They are tall, skinny, and pointed at one end.

Is there some way to express this shape in mathematical terminology? It's not exactly a cone (although some experimental vehicles and early designs have looked mostly conical), but can the general form of a rocket, stemming from its function, be described using mathematical terms?

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    $\begingroup$ Hm. This would count as a homework question, so please review our policies about that. For starters, polygons are flat shapes that can have any number of sides, so that is super wrong, and you can find that out immediately by googling it. And i'm not sure i understand you - a rocket is a compound shape, it can't be described with one word. Also, this is about geometry, not space exploration. $\endgroup$ – kim holder Apr 15 '18 at 3:10
  • $\begingroup$ @kimholder you seem qualified to answer our meta question then; Does this site have anything like a homework policy? Since Stack Overflow is about computer programming and is one of the more rough-and-tumble sites, it may not be an ideal source for policies here. Would you consider distilling that SO meta answer to something you think would work here and posting as answer in SX meta? $\endgroup$ – uhoh Apr 15 '18 at 4:15
  • $\begingroup$ I think this question is profound, and that reaching for the insta-close button was premature. I've made an edit to clarify this. I've then cast the last close vote so that it can be reopened. I believe there is a potentially good answer to this question which relates to aerodynamic considerations in rocket design, and hope there's an opportunity for it to be posed once the question is reopened. $\endgroup$ – uhoh Apr 15 '18 at 5:29
  • $\begingroup$ Most rockets could be described as variable diameter cylinders with a conical cap, but this description wouldn't apply well to the Soviet/Russian R7 family of rockets, prior to launch, with the four booster rockets attached. As for the mathematics of the shape, maybe someone familiar with topology could assist. $\endgroup$ – Fred Apr 15 '18 at 12:20
  • $\begingroup$ How about moving this to the Mathematics or English Language Learning site? We need cross-site tagging. As for the actual question, i suggest restriction to a particular rocket family. $\endgroup$ – Everyday Astronaut Apr 15 '18 at 17:33
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Here is an attempt at answering this question without recourse to mathematical topology, i.e. using terminology that can be digested by a good physics sophomore. I am describing the outer shape of rockets, not the shape of the various internals (tanks, ducts, wires, combustion chambers...); also, I am consciously simplifying by assuming that apart from the nozzle no part of an engine protrudes from e.g. its fairing.

Most, if not all, rockets can be described as a cluster of three-dimensional bodies of which each one intersects with at least one and at most two other ones. The bodies are always: cylinders, sections of cones, (partial) bodies of revolution of cone sections (paraboloids, hyperboloids, ellipsoids, spheres), or bodies of revolution of some curve of dimension 2 (think of certain fairings). Some, but not all rockets, have fins that can ideally be described by polygons (of dimension 2), although of course in practice fins have a non-zero measure in dimension 3 and can hence be approached by trapezoidal prisms, scalene or not.

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