** Irina Kogan **

June 22 (Friday)

* A story of two postulates *

“I have traversed this bottomless night, which extinguished all light
and joy of my life. I entreat you, leave the science of parallel
alone”, wrote a Hungarian mathematician Farkas Bolyai to his son
János, horrified at the thought that his son is attracted by the
problem of parallels. János was not deterred, however, and discovered,
simultaneously with Lobachevski, a consistent geometry in which the
Euclidean parallel postulate does not hold. We will zoom through the
path of mathematical thought that took over 2000 years, noticing which
results from a high school geometry text-book do not rely on the
parallel postulate, and which are altered completely in hyperbolic
geometry.