Useless Fact of Day: Dime & Quarter Mass/Value Ratio

[BobG]

Interesting. However, just thinking about it, shouldn't that be pi/2 and 3/2?

We have a creek on our property and it has been interesting to watch the flow pattern over the years. One hard-learned lesson is that you can't easily steer a creek. I once had a $1000 worth of bulldozer work disappear in about an hour when we had a sudden high flow due to heavy rains.

No. Circumference of a circle is pi*diameter. If you form half the circle over one part of the river and half the circle over the next part of the river, then you've completed the circle over twice the diameter (pi*d/2d= pi/2). Of course, that's assuming the circle formed has the same side to side diameter as the straight line distance for half a loop, and there's really no reason to expect that. In fact, I'm not really sure there would be a reason to expect any particular ratio for an average (well, actually, pi/2 would seem like a reasonable expectation, but ...).

Or, you could have the river to double back in almost a complete circle so the river would look like a circle with diameter d lying next to a line d, which would give you a (pi+1):1 ratio, but that's still making some assumptions about how far a river can go side to side and how often is the river going to completely double back.

The absolute maximum would be almost a (2pi+1):1 ratio if the side diameter were the same as the downriver distance, but the river would have to be doubling back on both sides over its entire length (and once again, there's no real reason the side diameter would be the same as the downriver distance).

 

[Ivan Seeking]

No. Circumference of a circle is pi*diameter. If you form half the circle over one part of the river and half the circle over the next part of the river, then you've completed the circle over twice the diameter (pi*d/2d= pi/2). Of course, that's assuming the circle formed has the same side to side diameter as the straight line distance for half a loop, and there's really no reason to expect that. In fact, I'm not really sure there would be a reason to expect any particular ratio for an average (well, actually, pi/2 would seem like a reasonable expectation, but ...).

Or, you could have the river to double back in almost a complete circle so the river would look like a circle with diameter d lying next to a line d, which would give you a (pi+1):1 ratio, but that's still making some assumptions about how far a river can go side to side and how often is the river going to completely double back.

The absolute maximum would be almost a (2pi+1):1 ratio if the side diameter were the same as the downriver distance, but the river would have to be doubling back on both sides over its entire length (and once again, there's no real reason the side diameter would be the same as the downriver distance).

I was thinking of half circles but I see what you're saying. When I think of aerial views of rivers it makes sense. Our little creek isn't representitive of rivers at large scale. We tend to get half circles.

 

[Kurdt]

Most anti-biotics do not require you to refrain from the consumption of alcohol. I put that in the pub magazine once hoping we could draw back the infected market.