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)
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)
“By many a legendary tale of violence and wrong, as well as by events which have passed before their eyes, these people have been taught to look upon white men with abhorrence.... I can sympathize with the spirit which prompts the Typee warrior to guard all the passes to his valley with the point of his levelled spear, and, standing upon the beach, with his back turned upon his green home, to hold at bay the intruding European.”
—Herman Melville (1819–1891)