Two branches of humanity meet after 300,000 years without contact. At one point, comparison is made between their different modes of existence via explicit calculations of spherical surface area and volume.

Appeared in ISAAC ASIMOV'S SCIENCE FICTION MAGAZINE (Jan 1979) reprinted in Terry Carr (ed) BEST SF NOVELLAS OF THE YEAR #2.

the story and the math are very good!

It's been a long time, but I recall the story very fondly and a little fuzzily. In fact, I'm going to look for the compilation containing it, and buy it. As I recall, some of the math applied to calculating the living space of a planet-sized sphere divided into shells, like the stories of a building. The protagonist's job was to check incoming ships, which may contain any combination of technology and occupant(s), for threat potential. For this he wore a Q-suit, guaranteed invulnerable to any known weapon. He also carried an X-blaster, Y-blaster, and Z-blaster (of increasing force). The Z-blaster could disintegrate any known material. He says, "No, I have never tried firing the Z-blaster at the Q-suit."

This is, in fact, one of my favourite SF short stories. It tells the story of Cotter Oren who is a control pilot on the planet Randar 13. His job is to check incoming space ships and to transfer the ships' data to update the knowledge about the worlds they come from. That's the official story. The hidden aspect is to gain control of the ships' weapon systems in order to prevent attacks.

One day, a small probe arrives and causes considerable confusion in the planetarian control HQ. The probe contains a message that announces the arrival of a 300.000 year old space ship with a diameter of 6.000 Km and Cotter Oren is dispatched to gain control of the ship ...

I can't consider math to be a "main theme", but it is used for some important points. (Most notably, convincing the protagonist that he's got it backward: the inhabitants of the ship can't possibly join his society because there are far too many of them, but his society could easily fit in aboard the ship.)

Note: I just remembered that there's a bit of logic involved as well. The protagonist witnesses a ship's inhabitant pass through a barrier designed to protect the inhabitants from people outside and vice versa, by using (obviously spurious) logic to convince its computer guardian that he is in fact already on the opposite side of the barrier and thus there is no reason to hinder his passage. The protagonist attempts to do the same to get his armor and weapons past the barrier, but he couldn't follow the dizzying arguments used, so his efforts are soundly rejected, with the AI adding a small insult to the effect that it had never heard a less logical argument.

Just finished this intriguing short story. In addition to the math about surface area of planets, livable space and the like there is also math about gravity, distance, space, and speed.

This small planet is bigger than it seems. “Stars and violence in one day!” Basho teaches a lesson in empathy and perspective. Ker-plop (((o)))