# The longest straight lines you can sail or walk before hitting the shore

Originally published at: https://boingboing.net/2018/05/01/the-longest-straight-lines-you.html

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straight-line route over land

What about lakes and rivers? Suppose I could RTFA but the headline does say “walk”.

As passive as maps are the underlying tension between what’s real and what’s not is fascinating.

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Now I need a globe and a piece of string dammit.

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The “driving” one says “without hitting a major body of water”. They explicitly mention lakes in this (as they do islands in the sailing) but nothing about rivers. It looks to me like the path they have would have to cross the Tagus somewhere close to the western end.

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But Rob! The lines! They aren’t straight at all!

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There’s probably hundreds of rivers on that path. Rivers can be a bitch to cross when you don’t have a bridge, ferry, or amphibious vehicle. It’s a thing that always bothered me about the show Dark Skies, where they say the bridges were blown by alien invaders, then they toodle up and down the East Coast in trucks, like there weren’t dozens of huge rivers and estuaries to cross.

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Since sailors use compass bearings to determine a course, I wonder if following a geodisic would feel straight.

Sonmiani, Balochistan, Pakistan 25°N
Antarctica and Tierra del Fuego in South America 55°S
Karaginsky District, Kamchatka Krai, in Russia 59°N
OK, I know we are on a globe but I don’t see how going from 25°N to 55°S and back to 59°N is a straight line.

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Yea, it’s weird. But if you think of the math of a circle it starts to make sense. (x – h)² + (y – k)² = r² or more simply y = √(r²-x²)
A great circle is the shortest distance between two points on a sphere and it’s just that, a circle with a radius the same as the sphere.

Now take this example, start in Panama City (near 9°N,80°W) now travel in a straight line to a Columbo, Sri Lanka (near 7°N, 80°E) on the opposite side of the globe.

You could travel there through the north pole (meaning your latitude goes up, then back down as you travel) or you could fly along the equator in either direction. All are basically the same distance (I didn’t find anything exactly on the opposite side to use as a example).

But there are multiple paths and multiple great circles to those points. Some times there are fewer shortest paths, and some of those paths you take travel up and over one of the poles.

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This is a hard problem, if you use your eyes. I would imagine it’s easy as pie for a computer. Two points determine a line. Try all pairs of points. A computer doesn’t need to make a Mercator projection first.

When I backpack my greatest fear is fast, deep water. Not bears, not exposure to heights while crossing mountain passes, not encounters with humans in the back country, but attempting to cross any river, stream, creek etc that is above my knees and moving fast.

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I think it’s a geometry problem mostly, and could be understood abstracted as such. Not that I remember any of the axioms and theorems from 10th grade geometry.

For me if I take a string on a globe to make a straight line. I must realize that in 3 dimensions the “straight” line isn’t really flat and follows the curve of the globe. Straighter (and shorter) would be to remove the constraint of having to travel on the surface of the globe and instead burrow through rock.

It’s kind of like how manhattan distances (travel on a city grid) is longer than a straight line (as the crow flies) distance. But it’s not practical to smash through buildings to take the shorter path.

think of a basketball on your desk and the line across it is the equator you head 90 degrees OR 270 degrees you stay on the centre of the ball line assuming you were on it when you started BUT go up 1/2 way on the ball and go “east” again to stay at the NEW line you are having to TURN as you MOVE forward or you will deviate towards “south” and eventually cross the centre line going from 45 N to the “equator” at ZERO and keep on towards 45 S
to “do this” take your basket ball and position the 45 N to the top and roll the ball straight and the centre “equator” will cross over the TOP and followed by the bottom portion of the ball as it is now partly upside down

So you claim!

[Image credit NikiVandermosten]

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Well there you go.

Less than half of the sphere can be projected onto a finite map.

But if you have an infinite amount of paper, you can include the equator briefly, before gravitational collapse. The other half of the world is beyond infinity, or maybe it’s projected on the ceiling.

another fascinating take on this:
http://andywoodruff.com/blog/beyond-the-sea/

Cartographers are the original nerds.

Most ships use true bearings, via gyrocompass. When you plot a great circle route on a Mercator chart, it is a curve, with regular course changes. The frequency of changes is up to the person plotting the course, since the practical method of plotting it is to use a series of waypoints, determined mathematically, with straight lines in between.
The point of navigating with mercator charts is that a straight line drawn between any two points is a single true bearing. If you are navigating via a rhumbline (single bearing) on a mercator chart, it feels like you are going in a straight line, but you are on a curve. If you are navigating a great circle, you are going in a straight line, but it feels like an arc.

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Slightly off topic. Be shure to bring a life west:

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