ADVERTISEMENT
  About the SA Blog Network

Posts Tagged "Euclid"

Roots of Unity

What’s the Deal with Euclid’s Fourth Postulate?

An illustration from Oliver Byrne's 1847 edition of Euclid's Elements. Euclid's fourth postulate states that all the right angles in this diagram are congruent. Image: Public domain, via Wikimedia Commons.

In February, I wrote about Euclid’s parallel postulate, the black sheep of the big, happy family of definitions, postulates, and axioms that make up the foundations of Euclidean geometry. I included the text of the five postulates, from Thomas Heath’s translation of Euclid’s Elements: “Let the following be postulated: 1) To draw a straight line [...]

Keep reading »
Roots of Unity

The Math Wars, Lewis Carroll Style

Lewis Carroll in 1863, photographed by Oscar Gustave Rejlander. Image: Public domain, via Wikimedia Commons.

In 1879, Charles Dodgson, better known as Lewis Carroll, published an odd little book called Euclid and his Modern Rivals (available for free at the Internet Archive). Though it takes the form of a play, it is a defense of Euclid’s Elements as the best textbook for geometry. Carroll’s introduction lays out his purpose and why [...]

Keep reading »
Roots of Unity

Chasing the Parallel Postulate

If you'd like to see these again, accept the parallel postulate. Image: Webber, via Wikimedia Commons.

Euclidean geometry, codified around 300 BCE by Euclid of Alexandria in one of the most influential textbooks in history, is based on 23 definitions, 5 postulates, and 5 axioms, or “common notions.” But as I mentioned in my recent post on hyperbolic geometry, one of the postulates, the parallel postulate, is not like the others. [...]

Keep reading »

More from Scientific American

Scientific American Dinosaurs

Get Total Access to our Digital Anthology

1,200 Articles

Order Now - Just $39! >

X

Email this Article

X