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Under what circumstances did the Ancient Greeks use algebra, trigonometry, geometry and calculus?

Of these four, the Greeks only did geometry in full. Euclid, who lived in ancient Greece, laid out the geometry we still use today, including the axioms, many of the proofs, and, very importantly, the method of proof. This gave foundation to not only all of geometry, but much of logic, as well, though systematic symbolic logic was a much later (modern) development.

Algebra was unknown to the Greeks. They had the pre-Algebra of fractions, but no notion of the number zero or of irrational numbers. Algebra was created after Ancient Greece, in the Muslim world, around 800 of the Common Era.

The Greeks had some elements of trigonometry, starting in about 200 Before the Common Era. They worked with chords, which are different from today's sine and cosine. They had trigonometric tables of chords, similar to the ones we use today, and developed the 360-degree circle we use today. Trigonometry was essential to Ancient Greek astronomy.

The Greeks struggled with ideas related to calculus, but could not accept some of the fundamental concepts that make rigorous calculus possible. They worked with infinitesimals, but Zeno developed several famous paradoxes, seen unsolvable at the time, that pointed to the notion of infinity, which the Greeks did not grasp as we do today. There was some work with tangents to curves, which are related to differential equations. Calculus was not clearly defined until Newton and Leibniz around 1600.

If you want to learn more, you can look up the history of each of these topics (geometry, algebra, trigonometry, and calculus) on Wikipedia.there's also an excellent book by david foster wallace called "Everything and More - a compact history of infinity' it's highly readable without being dumbed down and quite amusing - amazing how much of DFW toher writings mesh with this book

Thanks, I'll look it up. I've been wanting to get a better grasp on infinity - in many ways!

While this is probably the best answer, is it really possible to live your entire life without knowing what nothing is? 0 is nothing, the mathematicians perhaps left zero out of their enscribings and texts as it is such a self evident concept.

Many concepts we think are evident & essential today did not exist in other periods. Here is a good summary history of zero: http://www.scientificamerican.com/artic … ry-of-zero . We can see that the Greeks struggled for lack of the i

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