Quoted passage from Time's Eye

"I don't get," said Casey.  "It's just a sphere.  If you know the radius you can work out the rest from all those formulae.  The surface area is, what, four times pi times the radius squared..."

"You can work that out if you make the assumption that this sphere is like every other sphere you've encountered before." Abdi said mildly.  "But here it is floating in the air, like nothing I've ever seen.  I didn't want to make any assumptions about it; I wanted to check everything I could."

Bisesa nodded.  "And you found-"

"For a start, it is a perfect sphere."  He glanced up again.  "And I mean [i]perfect[/i], within the tolerances even of my laser measurements, in every axis I tried.  Even in 2037 we couldn't shape any material to such a fantastic degree of precision."

De Morgan nodded soberly.  "An almost arrogant display of geometrical perfection."

"Yes.  But that's just the start."  Abdikadir held up his watch so Bisesa could see its tiny screen.  "Your high school geometry, Casey.  The ratio of a circle's circumference to it's diameter is...?"

"Pi," rumbled Casey.  "Even a jock Christian knows that much."

"Well, not in this case.  The ratio for the Eye is [i]three[/i].  Not about three, or a bit more than three—three, to laser precision.  My error bars are so small it's quite impossible that the ratio is actually pi, as it ought to be.  Your formulae don't work after all, you see, Casey.  I get the same number for 'pi' from the volume.  Although of course my reliability is way down; you can't compare a laser with a bucket of dusty water..."

Bisesa stood and walked around the Eye, peering up at it.  She continued to have an uneasy sense about it.  "That's impossible.  Pi is pi.  The number is embedded in the structure of our universe."

"[i]Our[/i] universe, yes," Abdikadir said.