Incidence (geometry) - Determining The Line Passing Through A Pair of Points

Determining The Line Passing Through A Pair of Points

Let P1 and P2 be a pair of points, both in a projective plane and expressed in homogeneous coordinates:

Let g−1 be the inverse duality mapping:

which maps points onto their dual lines. Then the unique line passing through points P1 and P2 is L3 where

Read more about this topic:  Incidence (geometry)

Famous quotes containing the words determining the, determining, line, passing, pair and/or points:

    Our civilization has decided ... that determining the guilt or innocence of men is a thing too important to be trusted to trained men.... When it wants a library catalogued, or the solar system discovered, or any trifle of that kind, it uses up its specialists. But when it wishes anything done which is really serious, it collects twelve of the ordinary men standing round. The same thing was done, if I remember right, by the Founder of Christianity.
    Gilbert Keith Chesterton (1874–1936)

    I esteem it the happiness of this country that its settlers, whilst they were exploring their granted and natural rights and determining the power of the magistrate, were united by personal affection. Members of a church before whose searching covenant all rank was abolished, they stood in awe of each other, as religious men.
    Ralph Waldo Emerson (1803–1882)

    The middle years of parenthood are characterized by ambiguity. Our kids are no longer helpless, but neither are they independent. We are still active parents but we have more time now to concentrate on our personal needs. Our children’s world has expanded. It is not enclosed within a kind of magic dotted line drawn by us. Although we are still the most important adults in their lives, we are no longer the only significant adults.
    —Ruth Davidson Bell. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 3 (1978)

    Hats off!
    The flag is passing by!
    Henry Holcomb Bennett (1863–1924)

    Like to a pair of loving turtle-doves
    That could not live asunder day or night.
    William Shakespeare (1564–1616)

    Wi’ joy unfeigned brothers and sisters meet,
    An’ each for other’s weelfare kindly spiers:
    The social hours, swift-winged, unnoticed fleet;
    Each tells the uncos that he sees or hears;
    The parents, partial, eye their hopeful years;
    Anticipation forward points the view:
    Robert Burns (1759–1796)