I liked that you gave the 7th graders a sheet of mysteriously complicated looking formulas, instead of just including ones they would understand. It gives them a sense of how much further they could go with math if they wanted to. That sort of pedagogical move should have a name.
Very cool, Eric. I don't know Python, but since you do, how about throwing in a bit of code that counts cycles? It would be interesting to know how fast the series reach arbitrary degrees of accuracy.
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The pi = f(shape of surface) reminds me of my introduction to non-Euclidean geometry. It was a charming little Dover book entitled "Taxicab geometry." Distances were measured n to by taking sqrt[(x2-x1)^2 + (y2-y1)^2] but just by (x2-x1) + (y2-y1)--in other words, the way a cab would drive in a city whose streets are laid out on an infinite square grid. The results are interesting, too. For example, what does a circle look like? An ellipse? A hyperbola? The answers weren't intuitive to me until I started calculating them. Then the patterns became obvious. And fun.
I don't recall whether I mentioned how (or that) pi figures heavily into Sagan's love, Contact. But it does, and it's central to what, to me, was a central message in the book. Cannot recommend it highly enough.
I liked that you gave the 7th graders a sheet of mysteriously complicated looking formulas, instead of just including ones they would understand. It gives them a sense of how much further they could go with math if they wanted to. That sort of pedagogical move should have a name.
Ill have to remember those till next February.
Very cool, Eric. I don't know Python, but since you do, how about throwing in a bit of code that counts cycles? It would be interesting to know how fast the series reach arbitrary degrees of accuracy.
***********
The pi = f(shape of surface) reminds me of my introduction to non-Euclidean geometry. It was a charming little Dover book entitled "Taxicab geometry." Distances were measured n to by taking sqrt[(x2-x1)^2 + (y2-y1)^2] but just by (x2-x1) + (y2-y1)--in other words, the way a cab would drive in a city whose streets are laid out on an infinite square grid. The results are interesting, too. For example, what does a circle look like? An ellipse? A hyperbola? The answers weren't intuitive to me until I started calculating them. Then the patterns became obvious. And fun.
I don't recall whether I mentioned how (or that) pi figures heavily into Sagan's love, Contact. But it does, and it's central to what, to me, was a central message in the book. Cannot recommend it highly enough.