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(and yes, it's upside-down)
Question: What student, even the math-devoted one, doesn't ask this question? (OK, so it's a weak question. I'll be asking more later...)
Comment: It's interesting to see how much Euclid expanding our understanding of mathematics, especially since he lived such a long time ago (about 2300 years). It's pretty funny how little has changed since Euclid's time. Math has advanced, but people haven't changed. I was also wondering why 1 doesn't fit into the accepted view of prime numbers. If 1 fits the bill, what about 1 doesn't work in prime theory? The book expressed little about why the mathematicians find that one doesn't fit the prime number bill... It listed a brief math equation to demonstrate, but it wasn't candid enough to show why (I feel). I also thought that it was funny that, although amicable numbers are more populous than perfect numbers, they still seem to be very few in number (esp. considering that we had only 1 pair for centuries until Euler and Descartes discovered a few more (Euler making some 30 discoveries [minus some for the wrong ones]). It doesn't seem like there are a whole lot more friendly pairs than perfect numbers.
Sorry, I didn't realize there was actually a previous reading due here...
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Question: The Julian Calendar did not have the zero issue associated with it because of its dating origins. What year, on the Julian calendar, was the Gregorian calender adopted?
Comment: I thought that it was weird to think about the fact that there is no year zero. Of course, as the book mentions, zero is not usually used as a counting number, and just as the years go from 1 B.C to 1 AD, so, too, do the centuries jump from the first century B.C. to the first century AD, which, of course has a zero in the hundreds, or "centuries" position. However, as strange as the mix-up between B.C. and AD is, the fact remains that, had the Pope decided to include a year zero, the concept, even with the knowledge of the logic behind it, would be stranger still. I suppose that, no matter which way we turn, we will be stuck in this matter.
Another part I found interesting about the reading is how late in the game the concept and notion of zero comes into play. This is 1582. Shakespeare is on the up and up, the Ottoman are rising to power just a few years after conquering the Byzantines, and the Renaissance in Europe has already started. And zero is still [insert zero equivalent expression here], nowhere to be seen. Such a strange thought that Shakespeare, though granted the knowledge of zero as a number and a concept and as a digit used to hold place value, did not understand it in the same way that we do today.
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Question: Does a [modern] calculator operate on the same basic principle as an abacus?
Comment: I thought that the idea of Romans using binary to solve math problems is pretty cool, especially when binary seems like such a modern invention in terms of ways to think about and express numbers. Especially when you consider the thought that advanced abacus users could utilize the simplicity of the binary-based abacus to do incredibly quick mental calculations. I also thought it interesting to note that calculus, the name of this class, comes from calculus ponere. Ponere means "to put" (in Spanish, it is poner), so our Calculus class is really just about pebbles (OK, so not really, but you get the idea behind this comment). Sometimes our origins are not as flattering as they ought to be....
(and yes, it's upside-down)
