Geometry at Infinity

Extract

Mr. Hatton in the March number of the Gazette (p. 43) has given an interesting discussion of the “geometry at infinity” with the object of reconciling Euclid's definition of parallel straight lines with Desargues' conception of lines “meeting at infinity.” There seems to me, however, still to be considerable confusion, and the young geometrical student who finds difficulty in grasping the statement that all the points at infinity in a plane lie on one straight line will scarcely be reassured when he is informed that two planes may under certain circumstances intersect in a region which is neither a straight line nor indeed a curve.