X 3 Y Z 3 Y 3 Z X 3 Z 3 X Y 3 Youtube Complete cubic parametrization of the Fermat cubic surface w 3 x 3 y 3 z 3 = 0 This is a famous Diophantine problem, to which Dickson's History of the Theory of Numbers, Vol II devotes many pages It is usually phrased as w 3 x 3 y 3 =z 3 or w 3 x 3 =y 3 z 3, with the implication that the variables are to be positive, as in the integer solutions 3 3 4 3 5 3 =6 3 (an amusing3 Describe geometrically the set of points (x,y,z) that satisfy y = −3 4 Describe geometrically the set of points (x,y,z) that satisfy x y = 2 5 The equation x y z = 1 describes some collection of points in R3 Describe and sketch the points that satisfy x y z = 1 and are in the xy plane, in the xz plane, and in the yz plane 6 (x-y)^3 (y-z)^3 (z-x)^3=3(x-y)(y-z)(z-x)
