|HPS 0410||Einstein for Everyone| Back to main course page John
D. Norton Department of History and Philosophy of Science
University of Pittsburgh In the last chapter, we explored the
geometry induced by the postulate 5NONE by means of the
traditional construction techniques of geometry familiar to
Euclid. We drew lines and found points only as allowed by the
various postulates. The outcome was a laborious construction of
circles and triangles with some quite peculiar properties. We
constructed a circle with center O and circumference G, G', G'',
G'''. Its circumference is only 4 times is radius (and not the
2π times its radius dictated by Euclid's geometry). Its
cirumference is both a circle and a straight line at the same
time. Each of its quadrants are triangles with odd properties.
The triangle OGG', for example, has three angles, each of one
right angle. So the sum of its angles is three right angles (and
not the two right angles dictated by Euclid's geometry). You
would be forgiven for thinking that the