hmmm...
Georg Friedrich Bernhard Riemann announced in 1854 that there are, in fact, no parallel lines and that every line intersects another at some point in the infinite, thus contradicting Euclid's parallel postulate. If he's actually right, then this would mean that it's impossible for every point on one line to be located exactly the same minimum distance from another line, which, in turn, means that lines are not actually lines but curves (though the slight curvature is only noticeable in the infinite). Makes one wonder why schools teach geometry based on the axioms of Euclid's Elements when there's a theory that doesn't seem to have an inherent defect and therefore can't be discarded as untrue, but that at the same time completely contradicts the foundation of Euclid's theory.
Before you wonder what prompted this, I'm currently reading Paul Hoffman's biography of Paul Erdös, who was probably the biggest mathematical genius of the 20th century.
Oh and: Every day, the Barber of Sevilla shaves those who don't shave themselves. Does the Barber of Sevilla shave himself? ;)
Before you wonder what prompted this, I'm currently reading Paul Hoffman's biography of Paul Erdös, who was probably the biggest mathematical genius of the 20th century.
Oh and: Every day, the Barber of Sevilla shaves those who don't shave themselves. Does the Barber of Sevilla shave himself? ;)