BEGIN:VCALENDAR
PRODID:-//eluceo/ical//2.0/EN
VERSION:2.0
CALSCALE:GREGORIAN
BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/163
DTSTAMP:20230914T125913Z
SUMMARY:Non-euclidean Algebra
DESCRIPTION:Speaker: Vaughan Pratt\nStanford University\nComputer Science D
epartment\n2215 Old Page Mill Road\nPalo Alto\, CA 94304\n\nAbstract: \nEu
clidean geometry today is most naturally understood as affine geometry equ
ipped with a suitable bilinearity as a basis for notions of length\, angle
\, area\, rectangles\, circles\, etc. In this talk we express the affine
content of Euclid's Postulates 2\, 5\, and 1 algebraically in that order.
In our account Euclid's Fifth or Parallel Postulate is expressed as an eq
uation parametrized with the number 6. Parameters in the range 3 to 5 yiel
d discrete notions of elliptical geometry while 7 and beyond do the same f
or hyperbolic geometry. Had the tools of the past half century of univers
al algebra been available to Euclid\, the first of his thirteen books coul
d have been both simpler and more general\, and the conceptual obstacles t
o hyperbolic geometry overcome more easily.\n
URL:https://www.tcs.tifr.res.in/web/events/163
DTSTART;VALUE=DATE:20110214
LOCATION:AG-66 (Lecture Theatre)
END:VEVENT
END:VCALENDAR