In The Real Plane
In a Cartesian coordinate system with coordinates (x, y) the unit square is defined as the square consisting of the points where both x and y lie in a closed unit interval from 0 to 1 on their respective axes.
That is, the unit square is the Cartesian product I × I, where I denotes the closed unit interval.
It is not known whether any point in the plane is a rational distance from all four vertices of the unit square. However, no such point is on an edge of the square.
Read more about this topic: Unit Square
Famous quotes containing the words real and/or plane:
“O.J. Berman: Well, answer the question now. Is she or isn’t she?
Paul: Is she or isn’t she what?
O.J. Berman: A phony.
Paul. I don’t know. I don’t think so.
O.J. Berman: You don’t think so, huh? Well, you’re wrong. She is. But on the other hand, you’re right. Because she’s a real phony.”
—George Axelrod (b. 1922)
“As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the plane at the base of a mountain, instead of climbing steadily to its top.”
—Henry David Thoreau (1817–1862)