(no subject)

[bellinghman]

A kilometre is not a unit of area.

C'mon guys, do you mean 60 square kilometres, 60 kilometres square, 60 kilometres radius, or what? Unfortunately, being somewhat literalist, my mental image involves the area being covered by a Peano curve approximation using a strip the width of a road and 60 kilometres long. My mental abilities won't tell me how much area that actually is.

Comments

[songster.livejournal.com]

Don't thank me - I'm bullshitting ;-)

I just thought it's a bit bizarre to use your road to approximate a Peano curve, when the whole point of a Peano curve is that it uses a zero-thickness line.

Best way to area-fill with a road is just to lay it out boustrophedonically across a square, at which point the curved segments at the edges become negligible in comparison to the straight segments going across.

I have no idea if this would apply to a Peano-approximation (which is almost all corners and infinitesimally short straight segments), or even if it's meaningful to postulate a Peano-approximate road.