Tangential Equation of A Point
A linear equation in line coordinates has the form al + bm + c = 0, where a, b and c are constants. Suppose (l, m) is a line that satisfies this equation. If c is not 0 then lx + my + 1 = 0, where x = a/c and y = b/c, so every line satisfying the original equation passes though the point (x, y). Conversely, any line through (x, y) satisfies the original equation, so al + bm + c = 0 is the equation of set of lines through (x, y). For a given point (x, y), the equation of the set of lines though it is lx + my + 1 = 0, so this may be defined as the tangential equation of the point. Similarly, for a point (x, y, z) given in homogeneous coordinates, then the equation of the point in homogeneous tangential coordinates is (lx, my, nz) = 0.
Read more about this topic: Line Coordinates
Famous quotes containing the words tangential, equation and/or point:
“New York is full of people ... with a feeling for the tangential adventure, the risky adventure, the interlude that’s not likely to end in any double-ring ceremony.”
—Joan Didion (b. 1934)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)
“I philosophize from the vantage point only of our own
provincial conceptual scheme and scientific epoch, true; but I know no better.”
—Willard Van Orman Quine (b. 1908)