# "Crow Flies Distance" On a Rectangular Grid -- Definition?

1. Oct 29, 2015

### WWGD

Hi all,
I am looking for a precise definition of " Crow Flies Distance" on a rectangular grid. I have not found a precise definition yet, but from what I have read, I think it would be the standard Euclidean distance $d((x_1,y_1),(x_2,y_2)) = \sqrt {( (x_1-x_2)^2+(y_1-y_2)^2})$ Is this correct?
Thanks.

2. Oct 29, 2015

### LunaFly

This seems correct to me. My understanding of "as the crow flies" is a direct straight-line path from one point to another, in which case the distance would be given by the expression you have written.

3. Oct 29, 2015

### WWGD

Excellent, LunaFly, thanks.

4. Oct 30, 2015

### zoobyshoe

I am confused as to why you are looking for a "precise definition" of a very informal term. "As the crow flies" is an expression invoked when someone wants to point out that the straight line distance from one location to another is much shorter than the road or path a person is required to take. The person never knows or gives the exact "as the crow flies" distance. Example: "From here to Fitzwilliam, it's 7 miles by the Old Mill Bridge road. As the crow flies, though, probably 2 miles. Gotta go out of your way to get to the bridge over the Old Mill River." That sort of thing.

5. Oct 30, 2015

### WWGD

No, I had never heard the expression before and was curious after reading about it. EDIT Actually, I was talking with someone about points farthest apart within the U.S mainland and the term came up. I looked it up but could not find any precise definition, at least not one I could get right away..

6. Oct 30, 2015

### zoobyshoe

OK. Generally it's just an expression brought into play when a practical route is much longer than it would be if you could get to the destination in a straight line.

Regardless, you can avoid using the expression altogether when someone asks you for directions by taking this approach:

7. Oct 30, 2015

### Staff: Mentor

Of course, we're talking about idealized crows here. Real crows are probably likely to deviate from a straight-line path if they see some food along the way.

8. Oct 30, 2015

### zoobyshoe

Might be better if we update the saying to, "as the drone flies," and then actually use drones to collect the data associated with a given route.