8 Interesting facts I learned by watching a public tv program on abstract math
My dad is obsessed with programs like Nova on PBS, and tonight he was watching a program about math. I like spending the evening with my parents when I'm home, so I joined him and actually found the program fascinating. Huh. Who am I becoming?
1. The "invention" of zero revolutionized mathematics
"Conceptualization" or "discovery" might be more apt terms than "invention".
2. Zero is both a placeholder and a number
It's the "number" between -1 and 1, and it's not worth anything on its own. However, it changes the value of other digits; e.g. 52 is very different from 502.
3. Zero becomes particularly problematic when you apply it to division.
0/6 is ok, because everyone gets nothing. But what happens when you divide 6/0? The official answer is "undefined," which I find glamorously mysterious.
4. Zeno's paradox about an arrow in flight radically concludes that it will never reach its destination
Say an arrow is halving its distance to a target every second. No matter how many halves closer the arrow gets, there are an infinite number of halves to go.
5. The idea of zero makes limits possible
This is the conclusion of the above paradox. Limits represent one way to divide by infinity. This, at its core, opens up the field of calculus.
6. Zero and infinity are intimately related concepts
The why here wasn't immediately apparent to me.
7. You can convert a round shape into a rectangle if you use infinity
This helps calculate the area of circles. The way they demonstrated this in the program was by cutting up a pizza into more and more slices and rearranging them into a rectangle each time. As you approach infinity slices, you get a straighter and straighter rectangle and remove the problematic curvature from your shape, enabling you to calculate the area.
8. Some infinities are larger than others
This is a pretty crazy thought. I guess it's because infinity simple means you don't stop counting. That isn't really the same thing as "the largest number."