| |
| |
Caption: Mathematical Models by Arnold Emch - Series 1 (1920)
This is a reduced-resolution page image for fast online browsing.
EXTRACTED TEXT FROM PAGE:
It arises in connection with the study of cyclides. If w e consider the quadric locus of the centers of all double tangent spheres associated with one of the five systems by which the cyclide m a y be generated, the centers of all circles of the system on the cyclide lie on two quartic curves cut out from the quadric by the quartic ruled surface. Cauchy Surfaces If we consider a function oe a complex variable w = f (f) = u + iv, in which f = x + iy, and at every point (x, y) erect a perpendicular to the complex f — plane equal to the value of u2 + v2 at each point, and denote this value by z, w e obtain an equation F {x, y, z) = 0 which defines a so called Cauchy surface This surface i . the locus of the endpoints of those perpendiculars. s t-1 10. Surface for w = i+i Cartesian equation: (x2 + y2 - I)2 + % 2 [ (x + I)2 - y2}2 a quintic. 11. Surface for w = f3 — 1.
| |
