ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

18. Teaching and Popularization of Mathematics

1991 MS Classification: 14,51 Fjelstad, Paul A picture for Real Arithmetic By mapping the real line plus ∞ onto a circle, drawing the line through 0 and ∞, and the line tangent to ∞, one can use geometric means, namely a straightedge, to determine the product and sum of 2 numbers. This is an example of a very general result where a conic and a line determine a group for the points on the conic that aren’t on the line, and this group is isomorphic to 1)real number arithmetic when the line intersects the conic in 2 points. 2)real number addition when the line intersects the conic in 1 point. 3)complex number multiplication on the unit circle when the line intersects the conic in no points.