**December 12, 2021 **
**Back to Square One**
*A Quiz on Ancient Times and a Quartet: The Answers*
1. Name the famous Babylonian tablet that features derivations of a certain form of triples.

**Plimpton 322 - **The tablet appears to be working what are now known as Pythagorean triples, but it was created more than 1,000 years before Pythagoras was born.

2. A rare and fragile relic of early Egyptian mathematics, written on reeds.

**The Rhind (Mathematical) Papyrus, **circa 1650 BC.

3. An ancient Greek mechanism used to predict astronomical positions and eclipses; it was discovered in a shipwreck in 1901.

**The Antikythera mechanism. **
4. Arab mathematicians and astronomers spent a great deal of time developing and refining this “star taker” device.

**The astrolabe.**
5. The Greek mathematician Hippasus came up with this mathematical construct, so disturbing at the time that it was banned and he was exiled or possibly drowned for his discovery.

**Irrational numbers.**
6. Euclid’s 13-book set, which remains the basis for much of mathematics today.

*The Elements*, circa 300 BC.

7. Among many accomplishments, Persian polymath Muḥammad ibn Mūsā al-Khwārizmī made significant contributions to which branch of mathematics?

**Algebra, **with his publication of

*The Compendious Book on Calculation by Completion* or

*al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah*, from which the math gets its name: al-Jabr.

8. A Platonic Solid is defined as is a convex regular polyhedron in three-dimensional Euclidean space. How many Platonic Solids are there, what are their names, and how many faces do they have?

**There are five Platonic Solids: Tetrahedron (4); Cube (6); Octahedron (8); Dodecahedron (12); Icosahedron (20).**
9. Around 150 CE, Ptolemy wrote the

*Almagest*, an influential treatise on the apparent motions of the stars and planetary paths. What was its major misconception?

**Ptolemy’s ***Almagest* presented (and canonized) a geocentric model of the universe. This misperception persisted for about 1,200 years.

10. Jumping ahead in Geometry: This quaint satire, published in 1884, featured A. Square and his journey to The Land of Three Dimensions. What was the name of this book? Bonus: Who was its author?

*Flatland*, by Edwin A. Abbott
An astrolabe

And a little jazz reprise for a cold night.

For all accomplished and aspiring piano players out there.