Triangle Inequality

[chendabao]

As my life now has been boring beyond belief, this journal has been left to collect dust and spider-webs. Time to inject a bit of life here to remind everyone that I'm still well and alive :D but since there's nothing particularly interesting to blog about from my life, I decided to write about something that I've pondered over. It's not exactly a

Comments

[gohyc2003]

weh weh, you are bending the logic to suit your argument, my fren.. The thing is you are not really walking directly towards your target end point by going the BA way in your last diagram. You are detouring and go towards end point and repeat that cycle till you reach. So the triangle inequality thing still holds, just that your problem does not fit the situation..

As for the last question, it is just a matter of choice. Some prefer certainty, some prefer adventure.

[chendabao]

Haha and I think you just summarised what I was trying to say XD

[huangpei]

LOL... your arguement is flawed in the sense that u assume that there are no paths that are parallel to BA. Actually, in order for your assumption to hold true, every path u take from BA MUST be parallel to either BC or AC. Otherwise, BA will still be a shorter path =D.

[chendabao]

Yup yup that is the assumption I made, and if we're talking about city areas that would somewhat be the case. Even if they are not exactly parallel to BC or AC, as long as they are sufficiently close to the two directions, and if points A and B are sufficiently far apart, difference between the two routes would not be significant enough :p

[ronald_05]

OKay lets summarise the arguments XP

Theoretically speaking the AB route can still be shorter cos there are small pockets of road parallel to AB.

However practically speaking, the effort taken to identify all these routes which are parallel to AB will cause you to spend more time in the end and thus AC + BC should be the practical choice especially in unfamiliar places.

Having said that, when time is not a constrain, travelling around all those buildings in the middle is much more fun to some people and thus could end up being the better choice.

In conclusion, we just had a lesson in maths, logic and economics :D

[chendabao]

hahaha nicely summarised :p

[williamkwan]

I don't quite see how the grid-like layout makes it excellant city-planning automatically, because I feel that good city-planning should incorporate and expresses the pre-existing natural contours (say random hils?) etc. and not the other way round.

As for the rest of the argument, didn't even read carefully to be honest.

Haha this sort of "problem-lesson-discussion" posts look like what I will post

[chendabao]

Haha when I said "excellent planning" I wasn't really referring to the planning, but more to the perfectly perpendicular layout :P