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:
“It can be demonstrated that the child’s contact with the real world is strengthened by his periodic excursions into fantasy. It becomes easier to tolerate the frustrations of the real world and to accede to the demands of reality if one can restore himself at intervals in a world where the deepest wishes can achieve imaginary gratification.”
—Selma H. Fraiberg (20th century)
“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)