Renkonti is a transitive verb. For speaking about the act or the event of meeting, it would be shorter to use Renkonto instead of Renkontiĝo. Why is the word second more common?
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Have you got any figures on how frequent the words are in a corpus of texts? – Oliver Mason Oct 31 '16 at 17:25
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@OliverMason I have tried both on tekstaro, but both had more than 100 results, so I don't have precise metrics. On Google "Esperanta renkonto" has 564 results while "Esperanta renkontiĝo" has 4 290 results. – Vanege Oct 31 '16 at 18:31
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In the Tekstaro: 473 for renkontiĝo and 123 for renkonto. – Tomaso Alexander Nov 1 '16 at 12:15
Simply put, we can say multaj personoj renkontiĝas - and that is a renkontiĝo.
Of course renkonto is a valid word with a similar meaning, but it doesn't have this same feeling as the act done by people who renkontiĝas.
In English, you can write We met in London as a complete sentence. In Esperanto, however, the verb renkonti is transitive, so Ni renkontis ("We met...") feels incomplete on its own: it is more complete as Ni renkontis nin or Ni renkontis unu la alian.
Otherwise, we can make the verb intransitive: renkontiĝi ("to be met, to meet (each other), to encounter"). Then the sentence is complete in the form Ni renkontiĝis en Londono.
Looking at the nouns, renkonto is a single encounter between two people or two groups, while renkontiĝo is vaguer, possibly referring to many people or sets of people in a process. That is why the latter is much more often used for the names of Esperanto events.