hyperbolic elliptic geometry triangle angle sums

A triangle's angles do not always add up to 180°

The familiar 180° rule works on a flat surface. In other kinds of geometry, it changes. On a curved space like a sphere, a triangle can have more than 180°, while in hyperbolic geometry it can have less.

Roman gladiator fights did not have to end in death

Trained gladiators were expensive to buy, train, and maintain, so owners did not want them killed in every fight. A gladiator match could end with both fighters alive. Convicted prisoners sent into the arena were treated very differently and could be expected to die.

Potatoes may have powered nearly half of Europe's early urban growth

~47% estimated contribution

Potatoes produce large amounts of food from relatively small areas of land and can thrive in conditions unsuitable for some traditional grains. After their introduction from the Americas, they improved food supplies across parts of Europe. One economic study estimated that potatoes accounted for about 47% of the increase in urbanization across the Old World between 1700 and 1900.

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hyperbolic elliptic geometry triangle angle sums

A triangle's angles do not always add up to 180°

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