termine which of the following interpretations of the undefined erms are models
ID: 2256864 • Letter: T
Question
termine which of the following interpretations of the undefined erms are models of incidence geometry. In any case, indicate which (i) Points are points on a Euclidean plane, and lines are nonde- (ii) Points are points on a Euclidean plane, and lines are all parallel alternative is exhibited by the interpretation. generate circles in the Euclidean plane. those lines on the plane that pass through a given fixed (ii) Points are points on a Euclidean plane, and lines are con- (iv) Points are Euclidean points in the interior of a fixed circle, point P. centric circles all having the same fixed center. and lines are the parts of Euclidean lines that intersect the interior of the circle. (v) Points are points on the surface of a Euclidean sphere, and lines are great circles on the surface of that sphere.Explanation / Answer
(i)
The interpretations Points are points on a Euclidean plane, and lines are nondegenerate circles in the Euclidean plane are
not models of the incidence geometry because the non-degenerate circles in the Euclidean plane are circles with some finite
radii.
(ii)
The interpretations Points are points on a Euclidean plane, and lines are all those lines on the plane that pass through a given fixed point P are models of the incidence geometry because points are points on Euclidean plane as well as the lines on the planes are also lines in
Eclidean plane.
(iii)
The interpretations Points are Euclidean points in the interior of a fixed circle, and lines are the parts of Euclidean lines that intersect the interior of the circle are not models of the incidence geometry because points in the interior of a fixed circle are points in Euclidean plane but lines are the parts of Euclidean lines that intersect the interior of the circle are not lines in Euclidean plane.
(iv)
For this part also answer is NO with the same reasoning in part (iii).
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