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I, repeatedly, find this expression used in many places, especially when talking about probabilities. I am interested in understanding the meaning of the expression in a $2$-dimensional and $3$-dimensional spaces.

Let's say we have a set $S$ of $N$ objects that have the same shape.

  1. What does it mean to evenly distribute the set of objects $S$ on an rectangular area $A$ ?
  2. The same question but $A$ is now $3$-dimensional space.
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    "uniformly distributed". Uniformly must be understood with respect to a defined criteria. Your example seems quite strange... do you have a reference for it ? – Mauro ALLEGRANZA Nov 05 '18 at 10:35
  • There is some question below but it does not have to do with geometry. In geometrical sense, I guess it would mean the center of the objects are placed with the same distance from one another. https://math.stackexchange.com/questions/1462382/what-is-the-chance-that-the-balls-are-evenly-distributed-in-the-box – NoChance Nov 05 '18 at 10:56

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