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:
“I did not go to Boston, for with regard to that place I sympathize with one of my neighbors, an old man, who has not been there since the last war, when he was compelled to go. No, I have a real genius for staying at home.”
—Henry David Thoreau (1817–1862)
“Have you ever been up in your plane at night, alone, somewhere, 20,000 feet above the ocean?... Did you ever hear music up there?... It’s the music a man’s spirit sings to his heart, when the earth’s far away and there isn’t any more fear. It’s the high, fine, beautiful sound of an earth-bound creature who grew wings and flew up high and looked straight into the face of the future. And caught, just for an instant, the unbelievable vision of a free man in a free world.”
—Dalton Trumbo (1905–1976)