A puzzle about "someone"

Question

Which symbol is missing? Explain your reasoning.

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Answer 1

The missing symbol is:

the number 1.

If we look at the letters in the corners of the squares...

...these form an anagram of GEOMETRIC. If we order the squares so as to spell this out (disambiguating the two Es by judging what makes the most sense), we see the following:



In other words:

$(\frac{1}{2})^n, n ∈ N$

This is the summand of a famous geometric series related to Zeno's paradoxes.

The terms of this series are $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$, $\frac{1}{16}$, and so on, with the more terms you add taking the total sum a little bit closer towards 1, so that over time we would say that this infinite series 'converges towards 1'. Convergence is represented by an arrow in mathematics, so in the diagram here we are being asked what this infinite geometric series will converge to - and that answer is our missing symbol: 1.

This can be seen and understood a little more clearly through the use of a diagram. Here, adding rectangles with areas equivalent to the terms in this series means that the more terms in the sequence, and the more rectangles you add, the closer you get to a complete unit square of area 1:


^{Source: Wikipedia (link above)}

As for the title:

While you might suggest that Zeno is the "someone" referred to in the title, since his paradoxes - like 'Achilles and the tortoise' - play on this mechanism, the OP points out in comments that it's actually a pun: someone just sounds like sum one!