Never used the word circle in my definition of pi. If planes curve in another geometry then no. I think these would called surfaces rather than planes. You coul

Never used the word circle in my definition of pi. If planes curve in another geometry then no. I think these would called surfaces rather than planes. You could define a plane as simply the set of points sharing a common normal vector not intersected more than once by lines oriented in directions that have a non-zero normal component (i.e. parallel planes are unique).