[jakear]

Looks like this is just a debate of the semantics of the word "obvious". Feynman would likely find a great many things "obvious" that I could not hope to understand. This doesn't mean they aren't "obvious", just that I don't have the requisite mental frameworks.

The only frameworks required to reach this conclusion are the Pythagorean theorem (8th grade geometry), the definition of a circle (same), and the ability to generalize the Pythagorean theorem to higher dimensions. I take it this last bit is where you think people would struggle. I don't think so. Looking at the theorem, there are basically 2 ways one might attempt to generalize it, and the incorrect way (a^n + b^n + ... )^(1/n) can be demonstrated to fall on its face pretty easily by considering small values of higher dimensioned components.

I consider these a "basic understanding of arithmetic" as these frameworks have been around for thousands of years and are expected knowledge for the youngest of teenagers. Yes some hand holding may be required to generalize the idea of distance to higher dimensions, but I'd wager not as much as you seem to think.

Testing this is interesting. If a random person at a bar can be given a refresher on the above frameworks and reach the desired conclusion themselves in 5 minutes or less, would you grant the problem is "obvious to people who haven't been trained in college-level mathematical thinking, or people who don't think about higher-dimensional objects using the handlebars of abstraction"?