Useless World Expansion Information for Math Geeks
Posted: Thu Jan 02, 2014 6:31 am
I'm fascinated by mathematics and when Pri said the 1.7 world was increasing by +60% I immediately drew a picture in my mind and thought it wouldn't be enough. Now that it's done, the math tells me that we are now WAY bigger than a +60% factor here. Take a look:
Lets say for argument's sake that the old world had a radius of 2000 units. According to my visual representation (below), the new world now has a radius of approximately 3150 units--I know those numbers may not be exact but whats important here is the relation between these two numbers, not the actual values.
Anyone with a 6th grade education knows that the area of a circle is equal to the radius squared times 3.14:
Old world was 2000 units in radius.
2000 squared is 4,000,000.
4,000,000 X 3.14 = 12,560,000
So the old world was 12,560,000 units in area.
New world is 3150 units in radius.
3150 squared is 9,922,500.
9,922,500 X 3.14 = 31,156,650
So the new world is 31,156,650 units in area.
The area of the new world minus the area of the old world:
31,156,650 - 12,560,000 = 18,596,650 units
Granted, "units" are not necessarily blocks or meters... just units as they relate to the picture shown below.
The new area that has been added, by itself, is actually larger than the entire old world! Area-wise, the world has more than doubled in size!
To put it in percentage terms, the new world is about 248% the size of the old world.
(31,156,650 / 12,560,000 = 2.48 or 248%)
Astounding!
Lets say for argument's sake that the old world had a radius of 2000 units. According to my visual representation (below), the new world now has a radius of approximately 3150 units--I know those numbers may not be exact but whats important here is the relation between these two numbers, not the actual values.
Anyone with a 6th grade education knows that the area of a circle is equal to the radius squared times 3.14:
Old world was 2000 units in radius.
2000 squared is 4,000,000.
4,000,000 X 3.14 = 12,560,000
So the old world was 12,560,000 units in area.
New world is 3150 units in radius.
3150 squared is 9,922,500.
9,922,500 X 3.14 = 31,156,650
So the new world is 31,156,650 units in area.
The area of the new world minus the area of the old world:
31,156,650 - 12,560,000 = 18,596,650 units
Granted, "units" are not necessarily blocks or meters... just units as they relate to the picture shown below.
The new area that has been added, by itself, is actually larger than the entire old world! Area-wise, the world has more than doubled in size!
To put it in percentage terms, the new world is about 248% the size of the old world.
(31,156,650 / 12,560,000 = 2.48 or 248%)
Astounding!