Closest 3dis to 2dis

[Alps]

In Portland, I-405 is a loop just a mile west of I-5. Where else does a child Interstate stay so close to its parent?

[ap70621]

Well, I-287 is combined with I-87 for several miles in New York. And I don't believe I-895 ever strays too far from I-95 in Baltimore, MD.

[PHLBOS]

Well, I-287 is combined with I-87 for several miles in New York.

Yes, but it continues further south into New Jersey; as state that I-87 doesn't even touch.

In Philadelphia, PA & Gloucester City, NJ; I-676 doesn't stray too far from I-76.

In the Wilmington, DE area; I-495 doesn't stray too far from I-95.

In the Manchester, NH area; I-293 doesn't stray too far from I-93.

[Alps]

Well, I-287 is combined with I-87 for several miles in New York. And I don't believe I-895 ever strays too far from I-95 in Baltimore, MD.

895 gets 2 miles away on the south side of the harbor.

Well, I-287 is combined with I-87 for several miles in New York.

Yes, but it continues further south into New Jersey; as state that I-87 doesn't even touch.

In Philadelphia, PA & Gloucester City, NJ; I-676 doesn't stray too far from I-76.

In the Wilmington, DE area; I-495 doesn't stray too far from I-95.

In the Manchester, NH area; I-293 doesn't stray too far from I-93.

I-676 is about 3 miles from I-76.
I-495 is about 2 miles away from I-95.
I-293 is farther than that.

Anything inside 1 mile?

[Quillz]

I-580 at one point shares freeway with I-80 on a wrong-way concurrency.

[agentsteel53]

as far as the largest distance from a 3di to its parent ... well, I-175 and I-375 only stray about a mile from their parent in Florida.

for a loop example, I-15 and I-215 are very close in Salt Lake City - about 3 miles apart at most.

[1995hoo]

I-395 in Baltimore doesn't get more than two miles from I-95.

I-277 in Charlotte is similar except it's a three-quarters loop.

[jcarte29]

I-277 in Charlotte is similar except it's a three-quarters loop.

True story, plus a couple more NC examples...

I-240 in Asheville doesn't stray too far from I-40, maybe a couple miles but I have never measured.
I-795 from Wilson to Goldsboro stays close parallel to I-95.
I-840 (Future) only exists as a one to two mile stub on the East and West side of Greensboro.
I-295 (Future) only exists as a couple mile stretch in Fayetteville, like G-Boro
I-140 in Wilmington only spurs 6 or so miles WSW from Wilmington
I-440 in Raleigh used to share pavement with I-40, but no longer.

[oscar]

Interstate H-201 stays within about two miles of Interstate H-1.

[Duke87]

I-470 in Wheeling, WV doesn't get much more than a mile away from I-70.

[Hot Rod Hootenanny]

I-470 in Wheeling, WV doesn't get much more than a mile away from I-70.

Looks like a 1 1/2 at the widest betweent the two.
I-277 (in Akron) is 2 1/2 from I-77/76.
I-670 gets nearly 2 miles from I-70 before both diverge around Bexley (in greater Columbus)

[NE2]

There seems to be some confusion about whether we want the maximin or minimax.

[The High Plains Traveler]

St. Joseph MO is pretty small to have a 3-di in any event, so I-229 is real close to I-29.

[bigboi00069]

In Miami, Fl I-395 only extends 1.2 miles from I-95. It is not even a loop, it just goes east for 1.2 miles and ends.

[bugo]

I-444 is close to I-244.

[kurumi]

I-395 in MD only strays about 0.72 miles from I-95, but only because it's a short spur. I think what the OP is looking for is:

A = area enclosed by the 3di that meets its 2di twice (or an imaginary shortest-distance straight line completing the connection)

L = longest "shortest straight line" between 3di and 2di -- how far apart they are.

We want the largest value of A/L (I would actually go with A/L^2 since it's dimensionless).

[DTComposer]

I-980 in Oakland is about 1 1/2 miles from I-80, which I would guess is the closest 3di that doesn't actually touch its parent.

[vtk]

I-395 in MD only strays about 0.72 miles from I-95, but only because it's a short spur. I think what the OP is looking for is:

A = area enclosed by the 3di that meets its 2di twice (or an imaginary shortest-distance straight line completing the connection)

L = longest "shortest straight line" between 3di and 2di -- how far apart they are.

We want the largest value of A/L (I would actually go with A/L^2 since it's dimensionless).

I think the OP was interested in the smallest L, but the other metrics are interesting.  A/L would favor loop 3dIs with long distances between their ends (I-405 CA), and A/L² would favor loop 3dIs which enclose (with their parents) highly-elongated regions (I-470 OH-WV-PA).  Personally I think W would have been a better letter for Kurumi's L variable, but whatever.  Also, calculating A for Baltimore's I-895 could be interesting, as a strict mathematical approach would have the region northeast of the harbor cancel out part of the region southwest of the harbor...

[NE2]

There's nothing unstrict about using absolute values.

[vtk]

Okay fine, but absolute values inside integrals can be inconvenient sometimes. Maybe not in this case (since we'd be integrating numerically anyway) but sometimes.  Anyway, most general-purpose expressions for calculating the area of a region don't have an absolute value inside the integral, because they expect the boundary to go in one direction around the whole thing.  Common sense and awareness of this special case would fix the situation and it could still be "strict", yes.  Maybe the word I was looking for was "naïve" or "automated".

[vdeane]

I'm surprised I-790 hasn't been mentioned yet.

[roadman65]

I-895 in New York is a spur of its parent and maybe is just over a mile from its sprouting.

[hbelkins]

There seems to be some confusion about whether we want the maximin or minimax.

Depends on how heavy the bleeding is. 

[TheStranger]

I-980 in Oakland is about 1 1/2 miles from I-80, which I would guess is the closest 3di that doesn't actually touch its parent.

Aren't the 6th Street ramps off of I-280 in San Francisco about 2 blocks from the 5th Street ramps from I-80?  I'd think that's even closer.

805/5 probably is the closest (about 4 miles at full width) for a loop 3di in California though.

[flowmotion]

First thing that comes to mind is I-670 in Kansas City MO/KS. Looks to be about 0.6 miles from I-70 at it's closest point.