Gap geometry - Begin with the Euclidean plane and then slice out the strip betwe
ID: 2899917 • Letter: G
Question
Gap geometry - Begin with the Euclidean plane and then slice out the strip between x=0 and x=1. The points in the geometry are all those in the Euclidean plane except those (x, y) with 0 lessthanorequalto x lessthanorequalto 1. (So, the y-axis is in the geometry but the vertical line x=1 is not.) Lines are defined to be the same as in the Euclidean plane except that for any non vertical line y=mx+b, the part in the missing strip is deleted. The distance between two points that are on the same side of the gap is our regular Euclidean distance. The distance between two points that are on opposite side of the gap is d_Gap (AB) = d_Euclid (AB)-d_EuclidCD), where C is the point where the segment AB meets the y-axis and D is the point where the segment meets the vertical line x=1. Does Gap Geometry satisfy the postulates of neutral geometry? What parallel postulate does Gap Geometry satisfy? For the Gap geometry, what is a circle?Explanation / Answer
a) According to gap geometry a straight line can be drawn at any point,a finite straight line can be produced in a straight line and circle can be described any point as center any distance as radius,and also all right angles equal to each other..these all satisfyed by neutral geometry..
parallel postulate:If a transversal falls on two lines in such a way that the interior angles on one side of the transversal are less than two right angles, then the lines meet on that side on which the two angles are less than two right angles.by this we can say it satisfys the gap geometry.
b) in ap geometry a circle may be described with any point as center and any distance as radius.
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