A league is generally the distance traversed in an hour's walking time or about 3 km or 1.5 miles. A furlong is an eigth of a mile in English units.
The Roman mile was 5000 ped (ft) and the league was 7500 ft.
A furlong was 660 ft, used in agriculture and a contraction of forrow' long. The English penchant for a system of measures which were divisible by two and four, petitioned the Queen to change the definition of mile from 5000 ft to 5280ft so that an English mile would equal 8 furlongs.
If we are considering the measurements recorded in Revelation to John, Chap 21:vss 15-17, the angel used a reed to measure the breadth and length at 12,000 stadia, translated in the KJV to furlong.
The stadia is the general dimension of a stadium for footraces interpretted as being anywhere from 185 to 192 meters in length (607-630ft). There might be an interpretation of stadia associated with the process of measurement, so although John 's revelation provided the metric, the identification of that metric to our daily use might have different conversion factors.
1500 miles square seems fairly reasonable as the space used for a city for all the believers in human history.
For what it's worth, Whitley Streiber claims to have been taken to an alien city that vast on another planet. But it would have to be CURVED to follow the curvature of a SPHERICAL planet. If it was a pure pyramid, half of an octahedron, the square base would be some 145 miles below the surface. And only the corners would be at the surface, the sides would also be curved, rising well above 200'.
As an architect, an object HALF the diameter of the moon(3000 miles)seems outlandishly LARGE for a planet only 8000 miles in diameter. Furlongs, stadia, leagues....with the number 12,000....obviously the writer was playing with decimals. A city 1.5 miles x 1.5 miles, with 200 foot high walls sounds about right. That's about the size of a mountain, still HUGE by human standards.
Stick around long enough though and you'll see it coming down on anti-gravity pads, made by computers and robots on the planet mercury(w/o hands)where there's LOTS of AU 79.
As to GOLD being the material-of-choice, PEOPLE value it because it doesn't rust/oxidize. It has a single outer electron which gives it excellent electrical/thermal(phonons) conduction properties, as well as excellent reflective albedo. It has some 10 isotopes, all being short-lived except AU 79 which is stable.
Other than its SCIENTIFIC values in instruments, technology, I have no use for it. I'm not one that LUSTS after it as so many do, the love of MONEY is the root of all evil. How many have KILLED others over a pile of gold? And yet all the known gold reserves on the earth would fill a 50'x50'x50' cubical volume.
Or as our lord said : what doeth it profit a man to own all the GOLD in the world, and lose his own SOUL? As a BUILDING material though, it has its pluses and minuses, perhaps not the best choice for a MOUNTAIN sized building. But then I'm a mere architect, not the SUPREME architect....
Here is the verse:
Rev 21:16 : 16 And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal. KJV
I always pictured the city itself as a cube, since the walls are mentioned separately. Do you all not see it that way? I ask because I am going to require considerable space for my mansion. :)