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Shortest Route Possible to connect 4 points

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I hope this helps in cutting costs for motorways, roads or whatever, because I know every meter costs a huge amount of money. There is some mathematics involved,

Here is a scenario: You have built up 4 towns (or buildings or whatever) and now you need to join them up. These 4 towns (or buildings in the picture) happened to form a square (let's assume) 1 by 1 Kilometer or mile if you are British. A picture of the

Stupid governments or road planners will then draw the 4 lines (if you did this no offense), but we want the shortest route. Another possibility is connect them along the diagonals of the square with the roads joining the middle. This shortens the distance of the road system by A LOT (if you are a maths whizz you get 2 by the square root of 2, which equals to 2.82, way smaller than 4 km) Diagonals

However, another problem is that the government has only enough money to buy 2.75 km worth of road. So what's the answer?

To use the shortest amount of road, you should make the roads meet at junctions of 120 degrees. The picture below shows the roads connected, meeting each other at 120 degrees.

Better

To calculate the length will be too long if you do not like trigonometry and pytho, so to cut short, the line in the middle is abt 0.43, while the others are equal at 0.575. Add together to get abt 2.73 km, less than 2.75km.

I hope this encourages better planning for future mappers. Of course it is impossible to draw 120 degrees (Unless you have a protractor) everytime, but just estimate as you draw your roads. This is only recommended for buildings or towns that are only a short dist. apart, not for straight motorways which goes 100 of miles to connect 4 towns. Otherwise things will become unrealistic.

This 120 degree rule does not just work with squares or rectangles, it applies, to any network of things that need linking up. If you want to connect a series of 6 water fondtains, the shortest arrangement of pipes needed should all meet at 120 degrees.


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