Intersection of A Pair of Lines
Let L1 and L2 be a pair of lines, both in a projective plane and expressed in homogeneous coordinates:
where m1 and m2 are slopes and b1 and b2 are y-intercepts. Moreover let g be the duality mapping
which maps lines onto their dual points. Then the intersection of lines L1 and L2 is point P3 where
Read more about this topic: Incidence (geometry)
Famous quotes containing the words intersection of a, intersection of, intersection, pair and/or lines:
“If we are a metaphor of the universe, the human couple is the metaphor par excellence, the point of intersection of all forces and the seed of all forms. The couple is time recaptured, the return to the time before time.”
—Octavio Paz (b. 1914)
“If we are a metaphor of the universe, the human couple is the metaphor par excellence, the point of intersection of all forces and the seed of all forms. The couple is time recaptured, the return to the time before time.”
—Octavio Paz (b. 1914)
“You can always tell a Midwestern couple in Europe because they will be standing in the middle of a busy intersection looking at a wind-blown map and arguing over which way is west. European cities, with their wandering streets and undisciplined alleys, drive Midwesterners practically insane.”
—Bill Bryson (b. 1951)
“With two sons born eighteen months apart, I operated mainly on automatic pilot through the ceaseless activity of their early childhood. I remember opening the refrigerator late one night and finding a roll of aluminum foil next to a pair of small red tennies. Certain that I was responsible for the refrigerated shoes, I quickly closed the door and ran upstairs to make sure I had put the babies in their cribs instead of the linen closet.”
—Mary Kay Blakely (20th century)
“The opera isn’t over till the fat lady sings.”
—Anonymous.
A modern proverb along the lines of “don’t count your chickens before they’re hatched.” This form of words has no precise origin, though both Bartlett’s Familiar Quotations (16th ed., 1992)