Curvature of a plane given a circumference I was skimming through a certain book when I came to an interesting passage.

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.

On a flat plane, 10π≠30, so what radius of a globe would you need to have so that a diameter of 10 creates a circumference of 30?
 A: You have to understand that there is an implied numerical error when the figures are given.  So the diameter could be anything between 9.5 and 10.5, and the circumference between 29.5 and 30.5.  This gives $2.81 \le \pi \le 3.21$.  Remember, the document isn't trying to define $\pi$ - rather it is recording distances.
A: Take $\alpha$ to be the (half) angle of a cone with apex at the center of the globe, and intersects the globe with a circle.
The relation between the diameter $d$ (arc distance) across this circle, the globe radius $r$, and $\alpha$ is $2 \alpha r = d.$
The relation describing the circumference of the circle is $2 \pi r \sin \alpha = 3d.$
Ten cubits is, let's say, $4.572$ meters (according to Google). So
$$r \alpha = 2.286 m; r \sin \alpha = 2.18296m.$$
The value of $\alpha$ that allows these equations to be consistent is around $0.5236$ radians, which means that the radius of the globe would need to be about $4.36 m$.
So, this gives strong evidence that $\pi \approx 3$ was used, rather than careful non-Euclidean geometry.
