Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20130201 12:05:41
The King and his Four Cities.There is a King who has just built four cities. This king is a very peculiar king as he built these four cities so that each individual city made up the corner of a perfect square. In addition all four cities are on perfectly level ground. Though there is a slight problem; the king forgot to build the roads. This king, in all of his peculiarity, decided he wanted all of his roads to be straight, and he wanted to be able to get from one city to any other city using these roads. How can you design the king's roads so that you use the least amount of road possible, while still meeting his criteria? Spooooon!!! #2 20130201 17:42:09
Re: The King and his Four Cities.This is a well known problem and is easily solved using soap bubbles. Interestingly enough, if you dip two frames connected by four pegs in a square position into soap watter, the soap film that forms around the pegs will try and minimize its surface so you'll get something that looks like this: >< The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #3 20130201 17:49:51
Re: The King and his Four Cities.I love it when nature solves mathematical puzzles for us! "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #4 20130201 17:56:43
Re: The King and his Four Cities.Hi MIF The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #5 20130205 20:54:03
Re: The King and his Four Cities.I think I'm oversimplifying it, but wouldn't a direct road to and from each city suffice? The roads would make the shape of a square with an "X" in the middle. #6 20130205 21:23:57
Re: The King and his Four Cities.hi pRo9aMeR You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20130205 21:49:35
Re: The King and his Four Cities.Hi pRo9aMeR The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20130206 18:56:57
Re: The King and his Four Cities.I did slightly misunderstand the question...But now I'm confused. Why wouldn't a simple "X" be shorther than the "><"? I 'looks' like it takes longer to travel that way... #9 20130206 19:16:46
Re: The King and his Four Cities.hi pRo9aMeR You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei 