Hey, it's March 14! And, I've been doing a bunch of arguably grown-up things in the physical world, so I need a super-straightforward topic if there's going to be a Monday Quiz. Therefore, today's topic is:
π
1. What is π, anyway? Not the numbers, but their significance.
2. What's 2πr?
3. What's πr2?
4. What's 4/3 πr3?
5. If all you had was the 2πr formula, you could reason out pretty quickly that π was going to be between two and four. How?
6. If all you had was the πr2 formula, you could do the same thing. How would that work?
7. True or False: Although it had long been established that π must be between 3 and 3.25, it could not be calculated with precision until the advent of modern computers.
8. True or False: Because each successive digit of π requires an order of magnitude of computer power to calculate, an accurate figure to 1000 decimal places reached in 1970 has, as of 2015, only been extended to 1200 decimal places known with absolute certainty.
9.
10. A fellow named Rajveer Meena holds the world record for memorizing and reciting π to the greatest number of decimal places. About how far out do you suppose he got? Oh, go on, guess. It's only the Monday Quiz.
3 comments:
Grown-up things? Ugh!
1. The proportion of a the circumference of a circle relative to its diameter.
2. Wait, did you just ask me the same thing again?
3. The area of the circle.
4. The volume of a sphere?
5. Hrmm...maths proofs, ugh. Well...Since the circumference of half a circle 2πr/2 (πr) is obviously longer than the diameter 2r, π > 2. And...the 'circumference' of a square of sides 2r (which would be the smallest square that the circle could fit inside) would be 8r. The circle must have a lesser circumference than that, so 2 < 8 and thus πr <4.
6. I dunno, man. Area of that big square is 4r² (2rx2r), and the area of the circle is less than the square too, therefore π < 4. The >2 bit has me baffled.
7. Depending on your definition of precision, false. Greeks were pretty smart.
8. Ummm...very false.
9. That's a well known piem.
10. 7000? Guy had skills, probably.
1. It's a constant that you can use to compute the circumference or the area of a circle given its radius. Or, given question 3, the area of a sphere.....
2. circumference of a circle, given the radius (r)
3. area of a circle, given the radius (r)
4. volume of a sphere given radius r?
5. mmmmmm . . . pie!
6. probably something involving cutting out squares and trying to fit them inside the circle.
7. I guess that would depend upon your definition of precise, no? But that begs the question - how are they computing it? Given that there's no fraction that you can create that equals pi, and therefore, no exact measurements of a circle that you could measure even with the most precise measuring instrument that would give it to you, where are they getting it from? What numbers are they placing into their supercomputer and saying, "go to town, HAL" with?
8. false-a-roonie!
9. mmmmmmmm.. . ... pie!
10. 1000 places?
1. It's a greek letter. The lower-case "pi" also represents the circumference of a circle divided by its diameter. It can also represent, for example, a function representing the density of the primes. There are fewer letters than there are mathematical concepts that we'd like to represent succinctly, as it turns out.
2. That's the circumference of a circle, if "r" is the radius of the circle.
3. That's the area of a circle, again with "r" being the radius.
4. That's the volume of a circle.
5. A value of 2 would be good for measuring the length of the diameter twice, as if we were marching around the outside. A value of 4 would be good for measuring the perimeter of a square. Since a circle is bounded horizontally the same as both of these shapes, extends further vertically than the line, but is more confined vertically than the square, we can conclude that pi is somewhere between 2 and 4 (this is not a rigorous proof by any means).
6. We can draw a square completely inside of a circle with area pi*2^2 (put the corners on the circle) and a square completely containing a circle with area pi*4^2 (put the center of each of the lines on the circle).
7. False. It's a straightforward mathematical procedure. We did it in my high school geometry class.
8. False. It's pretty easy to increase precision.
9. I'm not really sure how that's a "True or False".
10. I'd guess on the order of magnitude of 100,000, but it could very possibly be much higher.
Post a Comment