Omar Khayyam · Mathematics

The Fifth Postulate and the Seed of a New Geometry

In his <em>Commentary on the Difficulties in the Postulates of Euclid</em> (1077), Khayyam tried to prove Euclid&rsquo;s troublesome fifth postulate. Studying a special quadrilateral - now called the Khayyam-Saccheri quadrilateral - he proved the first theorems that, centuries later, would open the door to non-Euclidean geometry.

What you'll be able to recall

You learned that Khayyam tried to prove Euclid&rsquo;s fifth (parallel) postulate from the others, using what is now called the Khayyam-Saccheri quadrilateral, and considered three cases for its summit angles - right, obtuse, and acute. Explain his approach and why his rejection of the acute and obtuse cases unknowing…

Leads to Girolamo Saccheri.

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