# Useless fact of the day

turbo
Gold Member
Comments from a doctor's wife "why aren't YOU a teacher?" and from the purchasing agent's assistant at a local mill that I sold to like "my daughter loved that! Why don't the teachers teach that?"

Etymology can make learning new words a whole lot more interesting than rote memorization of meanings and spellings.

Drakkith
Staff Emeritus
Comments from a doctor's wife "why aren't YOU a teacher?" and from the purchasing agent's assistant at a local mill that I sold to like "my daughter loved that! Why don't the teachers teach that?"

Etymology can make learning new words a whole lot more interesting than rote memorization of meanings and spellings.
Hah! Awesome...

turbo
Gold Member
Hah! Awesome...
I had a good time with that. When you've got pre-teen girls letting each other in on cool stuff like that, it's a sign that you have reached them in a way their teachers haven't.

BobG
Homework Helper
The ratio between a river's length as measured along its actual path to the straight line distance between a river's source and mouth tends towards the value, pi, as the river gets older and older.

The reason for this is that if there's any curvature in the river, the current on the outside of the bend tends to be faster than the current on the inside of the bend, causing more erosion on the outside of the bend than inside, which causes even more curvature of the river. The amount of curvature is limited by the fact that if the river curves back enough, it cuts right back into the upstream side of the bend, cutting the bend out of the river completely (as an ox bow lake), resulting in a straight line path for the river with the curving process starting all over again.

In practice, most rivers, icluding younger rivers, average a ratio of 3:1 between the actual distance and the straight line distance (with rivers bounded by a gorge/canyon/etc having much smaller ratios).

Ivan Seeking
Staff Emeritus
Gold Member
The ratio between a river's length as measured along its actual path to the straight line distance between a river's source and mouth tends towards the value, pi, as the river gets older and older.

The reason for this is that if there's any curvature in the river, the current on the outside of the bend tends to be faster than the current on the inside of the bend, causing more erosion on the outside of the bend than inside, which causes even more curvature of the river. The amount of curvature is limited by the fact that if the river curves back enough, it cuts right back into the upstream side of the bend, cutting the bend out of the river completely (as an ox bow lake), resulting in a straight line path for the river with the curving process starting all over again.

In practice, most rivers, icluding younger rivers, average a ratio of 3:1 between the actual distance and the straight line distance (with rivers bounded by a gorge/canyon/etc having much smaller ratios).
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. BobG Science Advisor Homework Helper 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).

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Ivan Seeking
Staff Emeritus
Gold Member
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
Staff Emeritus