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:
“The spring is here, young and beautiful as ever, and absolutely shocking in its display of reckless maternity; but the Judas tree will bloom for you on the Bosphorus if you get there in time. No one ever loved the dog-wood and Judas tree as I have done, and it is my one crown of life to be sure that I am going to take them with me to heaven to enjoy real happiness with the Virgin and them.”
—Henry Brooks Adams (1838–1918)
“At the moment when a man openly makes known his difference of opinion from a well-known party leader, the whole world thinks that he must be angry with the latter. Sometimes, however, he is just on the point of ceasing to be angry with him. He ventures to put himself on the same plane as his opponent, and is free from the tortures of suppressed envy.”
—Friedrich Nietzsche (1844–1900)