At the end of the first book,
And on far-off Earth, Dr. Carlisle Perera had as yet told no one how he had wakened from a restless sleep with the message from his subconscious still echoing in his brain: The Ramans do everything in threes.
This may be an obvious question. I haven't read the two books written by Gentry Lee and only vaguely remember the original series. Please tell me the appropriate book in case it is mentioned.
I don't believe that there is an explanation for why the Ramans do everything in threes. Arthur C. Clarke wrote, in the afterword to Rama II, that the words you quote from the end of the first book "were a last minute afterthought when I was doing the final revision". If you do a Google book search for "three" or "threes" in the Rama books, you'll find some few mentions of the humans observing instances of this ternary priciple in the work of the Ramans during the four novels, but no explanations are given in the text surrounding those search results. Just as we never see the Ramans themselves, this principle of threes and what Nicole "understands" in her moment of death at the end of the last volume, remain unsolved mysteries. From my experience with Clarke, I would assume that these are intentional mysteries with no real solution, that serve as a storytelling device the function of which is to create a sense of spiritual truth beyond human understanding: the religion in science fiction.
The impression I got from the first book was that Raman engineering (as ours) required important systems to be fault-tolerant. The fact that triple modular redundancy was routine, I think, was meant to inspire awe as the kind of resources they could command, and the reliability of their constructions.
I don't recall a obsession for threes besides engineering. More so, Dr. Perera's quote went unfulfilled, as there were only two visits with the same purpose and trajectory. The third one had a different purpose and trajectory.
So they don't always do everything in threes, they just routinely do triple redundancy.
If I remember correctly, the scout droids had three legs and later on, in Rama they found a suit that seemed to be fitted for three hands. To me it seemed that their physiology had triple redundancy. Just like ours seems to have double redundancy: two arms, two legs, two eyes, and so on. This carries some side effects/abilities when properly combines such as 3-D vision and sound localization and so on.
Anyhow, it maybe that the triple redundancy and triple everything in many of Rama's constructions and biodroids reflected the biology of the Ramans.
It could mean that due to this triple redundancy, a second and third Raman ship should be expected unless it already has gone through undetected. In other words, there maybe other chances for the Ramans to meet the human race.
The literary reference is to systems with a periodicity of 3, which are very special in the Chaos theory admired by the author. Clark made a documentary about fractals and other chaotic phenomena called The Color of Infinity in 1995.
Probably as fail safe? Probably they figured 3 virtually ensures the task is succeeded without leaving stuff to chances.
In an unrelated note, It's what we do with databases replication to ensure high availability
