What is the geometrical definition of a plane?

Answer 1

A two dimensional surface defined by a point and a straight line.

Answer 2

Over 2000 years ago, Euclid gave the following definitions:

1. A surface is that which has length and breadth only.

2. The edges of a surface are lines.

3. A plane surface is a surface which lies evenly with the straight lines on itself.

I would humbly add that a plane is a perfectly flat surface of zero thickness, which is what I think he was saying in the 3rd sentence.

Answer 3

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors.