Which questions can you answer? No cheating by using Google or whatever. Go from memory only.

1. Is America a democracy or a republic?

2. What Englishman and English writing were a big influence on our Founding Fathers?

3. What system(s) of government did ancient Athens have?

4. How did Socrates die? Who was Socrates?

5. Where did the modern battery come from?

6. Can you prove that the area formula for a triangle is correct?

7. Why is 3^0 = 1? (That’s “why is 3 raised to the zero power equal to 1?”)

8. What math makes cell phones possible?

9. What are Mill’s Methods?

10. What is a proof of the Pythagorean Theorem?

I’m pondering how good our education was, and how well-prepared we were to navigate the complexities of life and to reason things out independently and objectively.

*Update (4-29-09, 1:00 PM): Answers below.*

*I think I learned the answer only to question #6 in school. Maybe I learned #3; I don’t recall. I learned a proof to the Pythagorean Theorem in school, but I did not get it at the time. The rest I learned after school, on my own.*

Answers:

1. Constitutional Republic.

2. John Locke and his Second Treatise of Government — but as the question is general I’d have to take Blackstone, Magna Carta, etc. as answers. I might even settle for Thomas Paine and his Common Sense — though this does not qualify as being an English writing.

3. Athens had different forms of government. It was most well-known for being a democracy, but it was also ruled by oligarchies and tyrants.

4. Socrates died by being put to death by majority rule; the democracy he lived in, in ancient Athens, tried and convicted him of corrupting Athenian youth. Socrates was the teacher of Plato, who was the teacher of Aristotle. Socrates played a major role in developing philosophy; he made major contributions to the theory of definition (and therefore to epistemology, the theory of knowledge) and he was known for the Socratic Method — basically, driving thinking by asking and answering questions.

5. The battery developed from experiments touching metal spoons and forks to people’s foreheads and tongues, and (more directly) from experiments into the cause of twitches in the legs of frogs when they were touched with metal probes. In both cases, people found the essentials were a metal and a moist object (a wet piece of paper or a brine-like solution in a glass container).

6. Put two triangles together to make a parallelogram, which has an area of base x height. The triangle is half that, of course. All you need is everyday, “common sense” reasoning — but most of us were not told that in school. You get bonus points if you remember that you have to depend on the idea that two (nonparallel) lines intersect in one and only one point.

7. This could be shown in a few ways. One way is to see its logical necessity by seeing that 1 = (3^2)/(3^2) = 3^(2 – 2) = 3^0. Which relationship will work for any number (except 0), so you could use “x” instead of 3 to be general about it.

8. Different answers here. Calculus is necessary, for one thing. And algebra, too, of course. But I was thinking of the sinusoidal functions we need to grasp, measure, and control the electromagnetic waves which transmit our voice, video, and text messages.

9. Mill’s Methods are methods of induction, methods of determining the cause of an effect.

*10. There are many — 20 or 30, I think. President Garfield gets credit for one proof — hey, can any of our Presidents today prove the Pythagorean Theorem, much less state it, much less prove anything in geometry??? Jefferson, Lincoln, and Garfield could!!! One demonstration involves comparing the areas of two squares: one square (a + b on a side) is cut up into a smaller square of area c^2 and four right triangles with legs of length a and b; the other square (also a + b on a side) is cut up into two smaller squares of area a^2 and b^2 and four right triangles with legs of length a and b. Take away the triangles, and you are left with c^2 = a^2 + b^2.*

*I picked these questions — among others I could have chose — for their importance in understanding our country and our history, or for their importance in teaching us how to reason and think independently, or for their importance in understanding how the physical world works, the world in which we live, act, and strive for values.*