Largest sphere in the space between dense packed spheres

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Discussion Overview

The discussion revolves around determining the radius of the largest sphere that can fit in the space between four densely packed spheres arranged in a tetrahedron configuration. The inquiry touches on geometric considerations and the relevance of visual representations in solving the problem.

Discussion Character

  • Homework-related
  • Exploratory

Main Points Raised

  • One participant poses a question about the radius of the largest sphere fitting between four unit radius spheres arranged in a tetrahedron.
  • Another participant suggests that the inquiry is typical of homework questions and prompts the original poster to consider their prior efforts in solving it.
  • A participant expresses uncertainty about the relevance of drawing a tetrahedron and using 2D circles in their approach.
  • Another participant encourages the original poster to pursue any better ideas they might have.
  • A moderator closes the thread, indicating that the question qualifies as a homework-type inquiry and emphasizes the importance of providing prior efforts in such discussions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solution to the original question, and the discussion remains unresolved due to the thread being closed for homework classification.

Contextual Notes

The discussion lacks specific mathematical steps or assumptions that could clarify the problem further. The closure of the thread limits the exploration of potential solutions or methodologies.

iantresman
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If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?
FCC_closed_packing_tetrahedron_(4).jpg
 

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Well, since this is PF, the inevitable reply is: what did you do so far to find it ?
Did you alredy draw the tetrahedron in the usual manner (lines) ?
 
I didn't know where to start, whether drawing a tetrahedron and 2D circles is relevant.
 
If you have a better idea, follow that !
 
Thread closed, as it is a homework type question.

A reminder: To qualify as homework merely the problem itself is taken into account, not its real life origin, which we cannot know anything about. So if a problem is of numerical nature or involves an otherwise special example, then it's likely homework. We request our users of the homework section to use and fill out the template, which will automatically be inserted there, esp. part 3, which covers own efforts. It helps us a lot in order to solve the obstacles the user might have.

Thank you.
 

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