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:
“... But all the feelings that evoke in us the joy or the misfortune of a real person are only produced in us through the intermediary of an image of that joy or that misfortune; the ingeniousness of the first novelist was in understanding that, in the apparatus of our emotions, since the image is the only essential element, the simplification which consists of purely and simply suppressing the factual characters is a definitive improvement.”
—Marcel Proust (1871–1922)
“In time the scouring of wind and rain will wear down the ranges and plane off the region until it has the drab monotony of the older deserts. In the meantime—a two-million-year meantime—travelers may enjoy the cruel beauties of a desert in its youth,....”
—For the State of California, U.S. public relief program (1935-1943)