clarification on map size expansion from v.183 to update


Bill Tarling

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Just wanted to verify whether the figures for the map sizes were [with approximation considered] correct. Before I end up passing misinformation, I wanted to find out whether the devs meant the playable map area is doubled - or is it actually in square km comparisons (which would make the playable area almost 4 times the current size, rather than just double)

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I looks to me as the playable area size being doubled, as having increased from 10 km² to 19 km². The coastal highway also looks like having similiar size as the mystery island map... Well, except that a large part of the map is covered with thin-ice of course. (¬_¬")/°

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The reason I wanted to get some clarification is because of the "square" element in the figures. I think the devs just mean the area is doubled, but if the were correctly in using km² in the calculations, then it would be far more.

Again (strictly for example simplicity) using 10 km² compared to 20 km²

10 km² = 10x10 grid = 100 blocks

20 km² = 20x20 grid = 400 blocks

You would be able to fit 4x 10 km² in a 20 km² area

Double the 10 km² size would be approx 14 km²

It's not trying to be picky, but rather that I answer a lot of game questions on streams and wanted to find out if the devs prefer it be said as "double the size of the current play area" or "almost four times the current play area"... it mainly makes a difference gauging how fast the maps are expanding [4 times bigger would be an enormous growth leap] - plus a number of other users spotted the same mathematical confusion.

It's not a big issue, would just help if I know whether to answer "they meant double the size" or not, that's all.

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I was pretty sure that 20km2 is actually twice as large as 10km2. But to be sure I looked it up. Here's a English website with the formula's for calculating the area of mathematical figures like a rectangle. The area of a rectangle is calculated as the width x height.

With that formula, the area of a rectangle (square) of 1km x 1km = 1km2 and a rectangle of 1km x 2km = 2km2 and a rectangle of 2km x 2km = 4km2. A map of 2km2 is twice the size of a 1km2 map.

The current maps together are 10km2. I have a feeling that CH is a little bigger than ML and both maps are square in shape (even if many space around the edges is not accessible) so they could be 2km x 2km and 2.45km x 2.45km, making them 4km2 and 6km2 totalling 10km2.

If the new map is 9km2 and it's square as well, that would make it a 3km x 3km map.

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I was pretty sure that 20km2 is actually twice as large as 10km2. But to be sure I looked it up. Here's a English website with the formula's for calculating the area of mathematical figures like a rectangle. The area of a rectangle is calculated as the width x height.

With that formula, the area of a rectangle (square) of 1km x 1km = 1km2 and a rectangle of 1km x 2km = 2km2 and a rectangle of 2km x 2km = 4km2. A map of 2km2 is twice the size of a 1km2 map.

The current maps together are 10km2. I have a feeling that CH is a little bigger than ML and both maps are square in shape (even if many space around the edges is not accessible) so they could be 2km x 2km and 2.45km x 2.45km, making them 4km2 and 6km2 totalling 10km2.

If the new map is 9km2 and it's square as well, that would make it a 3km x 3km map.

makes sense. thanks!

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double the 10 sqkm size would still be 20 sqkm, obviously. 10 sqkm = 10x1 km grid. it's just 10 squares that are 1km wide on each side. or did school teach me bullshit?

That would be the case with 10 sq km (10x 1km blocks) 0r 20 sq km (20x 1 km blocks)... but 10 km² [10 Km square] is different

example explained:

http://mathcentral.uregina.ca/QQ/databa ... mary1.html

Like I said, not a major thing (just trying to answer questions out there]... but yes 20 sq km would be twice as much as 10 sq km... but 20 km² is much more than double 10 km² (that's why I was surprised km² was being used rather than just the more common area reference of sq km) :geek:

I'm figuring it's meant as double, so mostly curious...

"MATH: 1+1 equals... SQUIRREL!"

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wikipedia says that sq km = km²(http://en.wikipedia.org/wiki/Square_kilometre).

what you mean is (10 km)², not 10 km².

That's where the confusion started because the Hinterland chart (top post) is in "10 km²"

I read it as sq km at first too until I was reading an article which used km squared references instead.

*lol* Really didn't wanna do a lot of math stuff, so it's funny how - SQUIRREL!... ummm, what was I just saying? :lol:

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  • 2 weeks later...

This is an interesting topic and one that is easily misunderstood. So, for anyone who is really interested:

The basic definition of area comes from a square. So, let's say that a square has sides of length x units (where the units could be in meters, feet, cm, angstroms, or whatever distance unit we happen to use or need). Then, by the definition of area, the area of that square is:

(x units) times (x units) which equals x2 units2.

Note that the x is multiplied by itself and so are the units. (That is, we get units2 as our "area unit".)

For simplicity, let's assume that the available area in TLD is A units2 and that our units are in kilometers (km). So we can say that the area in the map is A km2. If we were to double the area of the map, then all we would need to do is to multiply this area by 2. So, letting the symbol * mean "multiply", we have:

2*A km2 .

That is, if the current available area is 10 km2, then doubling the area would give us

2*10 km2 = 20 km2 .

Note that no new units were introduced--instead, all we did is "scale up" the amount of area involved by a factor of 2. So this seems easy enough--but a lot of questions in school geometry ask about things like, "How would the area of a rectangular region change if the lengths of the sides were doubled?"

Okay, so now we need to be thinking about the side lengths being doubled, so we'll need to keep that in mind. As we'll see, doubling the side lengths doesn't simply double the area--instead, as Bill was suggesting, it has a more dramatic effect on the area.

We'll start again with a square which has side lengths of x km and thus has an area of x2 km2. Now, if we double the lengths of the sides of this square, then each side is now equal to 2x km.

Hence, the area of our region is (2x km)*(2x km) = 4x2 km2. That is, the new area would be four times as big as " x2 km2 " was and, therefore, the area is four times bigger than it was at the beginning.

If we generalize this to a rectangle with length l and width w , then the "starting" area would be

A = l*w .

But if we were to double the lengths of these sides, then the new sides would have lengths of 2l and 2w, which would give an area of

A = 2l * 2w = 4*lw

which is again four times as big as the original area would have been.

In short, if the Devs have said that they're doubling the previous area of 10 km2, then the new total area should be somewhere around 20 km2. But it's very easy to misinterpret information in cases like this and I hope that this was helpful for at least some folks--and not too pedantic!

Regards,

--Gibbon

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"Just to tease the next update a bit -- we'll be adding an entirely new region, accessible from the Coastal Highway. The new region will be 3x3 kms, so it'll be the largest region we've built yet, and will take the world from 10km/sq to 19 km/sq. "

How are those lengths calculated? It seems to me that the lenght of one side of the map and the time it takes to travel it does not correspond. In hiking the time to get somewhere is calculated with 5km/h, every 12 minutes a kilometer.

The two current maps are 10km2 in total, that means one is 5km2 with 2x2.5km side length. It shouldn't take more than 30mins ingame to get from one side to the other. But I need longer already to just cross the Mystery Lake (only the lake, not the region). And that's when sprinting and not walking, which is calculated somewhere between 20-30km/h.

Because of this I was quite suprised when I've first read that the current regions are "only" 10km2, given the time it takes to cross it, it sure feels bigger.

Having said that, I'm just recalling from memory, I haven't actually tested it but I will once I'm home (boss won't allow me to game TLD at work :D).

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Don't forget that the in-game clock is sped up something like 10x normal, so to travel 1 km at 5 km/h would actually take 2 hours of in-game time...
It shouldn't take more than 30mins ingame

4 sec in RL is 1mins ingame so it's actually 15x as fast. And that's what I am saying, the INGAME clock should not pass more than 30mins if the numbers would be correct, but it actually takes hours. But when I think about it again, because time flies by but we walk in normal speed the numbers can't ever match, we would need to run 15 times faster.

So, sry for the fuzz :D

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So I did a couple simple measurements out on the ice on Coastal Highway.

Walking, you travel 100m in ~26 seconds (real time, not game time). That's 260 seconds per km, or 13.8 km/h (about 8.5 mph).

Running, you travel 100m in ~14 seconds. That's about 25.7 km/h, or about 16 mph.

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Its not really an interesting topic.

Raphael van Lierop posted:

New Region, New Wildlife, New Features

Just to tease the next update a bit -- we'll be adding an entirely new region, accessible from the Coastal Highway. The new region will be 3x3 kms, so it'll be the largest region we've built yet, and will take the world from 10km/sq to 19 km/sq.

So whoever wrote an article that said it would be 4x larger is obviously the one that is confused.

km2 wasn't even used.

Please don't let that sites (whoever they are) ignorance wear off on you Bill. :P

Maybe you should send them an email to have them redact their statement.

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Its not really an interesting topic.

Lux,

Perhaps it's not an interesting topic to you, but it is quite an interesting topic to me, as would be nearly any topic regarding a misunderstanding of mathematics or its notational conventions--which is fundamentally what this thread is about, albeit in the context of TLD and the upcoming map expansion.

km2 wasn't even used

That is true, in that the symbol "km2" wasn't explicitly used. However, when it was stated that

The new region will be 3x3 kms...and will take the world from 10km/sq to 19 km/sq

it seems fairly clear that the intent was to convey that the new map will have dimensions of 3 km by 3 km, implying that the new are will measure 9 km2. This was confirmed in the last part of the quoted phrase, as the world would expand from its current area of 10 and increase to 19--except for the use of the units "km/sq" which are not standard units but, based on the rest of the post and our conventions regarding how distance units are expressed when referring to area, there appears to be no reason that we cannot safely infer that both the "10" and "19" were intended to be expressed using area units, which in this context would be km2.

That is, while km2 wasn't used explicitly, it seems quite clear that those are the units that were intended.

Regards,

--Gibbon

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In the context of the original question, "is the game world going to be nearly 2x larger or over 4x larger" it seems a simple answer is all that's needed. How the tangential conversation began is irrelevant as any of that information can be easily disseminated from a quick web search about units and their usage.

Sooo...whatever you say. I guess, if it interests you it interests you. For me at least its similar to an argument about grammatical usage. There's he said/she said but really all that matters is the content of the message which in this case was "3x3" so that alone should clear up any misunderstanding anyone has about what a square kilometer is (i.e. its irrelevant since we know the answer is 9 km/sq being added which answers the question all by itself). Everyone with basic mathematical skills knows that 3x3=9.

Only on TLD forums could this become a 2 page thread. Sarcasm intended. :P

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Lux,

I really don't disagree with anything you just said--and I concur that it should indeed be just a simple answer.

Nonetheless, there was some confusion--and I've observed similar confusion on related topics before, which is what really interested me. The misunderstanding seems to have been centered around the concept of "doubling the area" versus "doubling the side lengths (of a given rectangular region)" and the resulting change in the area after doing so, as well as the units involved and what they imply. Personally, my only intention was to provide some clarity--though it's entirely possible that I failed to do so!

Only on TLD forums could this become a 2 page thread. Sarcasm intended. :P

Lol, you may well be right about that! :)

Regards,

--Gibbon

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While the math terms aren't necessarily correct ['x sq km' and 'x km sq' aren't equally interchangeable and mean different things/measurements], the devs did give the intention of size in their announcement re the next update after the v.183 version to mean double the size.

I probably wouldn't have even brought up the math, except by coincidence one of my clients from a law firm is representing a client who bought some property in another country, and there's a legal dispute because they purchased [contracted] an 'x km sq parcel of land', and after the deal was closed and completed (all payments fulfilled) the seller then claimed they actually only intended 'x sq km' of land [which worked out to approx 8 sq km of land rather than 64 sq km parcel of land which was purchased]

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I probably wouldn't have even brought up the math, except by coincidence one of my clients from a law firm is representing a client who bought some property in another country, and there's a legal dispute because they purchased [contracted] an 'x km sq parcel of land', and after the deal was closed and completed (all payments fulfilled) the seller then claimed they actually only intended 'x sq km' of land [which worked out to approx 8 sq km of land rather than 64 sq km parcel of land which was purchased]

Interesting. Now I cant help but wander about 2 things:

1. What country?

2. Did they actually use "km sq" or "km2"?

Because in many countries (like the Netherlands, where I live) km2 is how you would write sq km. So if you were to buy a piece of land in NL that is the size of 8km2, you would be getting a piece of land that is say 2km x 4km.

It would seem to me, as a layman, that if you would take the price paid in the land deal and divide it by the average price per km2 in that region (for the same type of land) and the result is around 8km2, the buyer is getting what he paid for, if it's around 64km2 he is indeed being ripped off.

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Interesting. Now I cant help but wander about 2 things:

1. What country?

2. Did they actually use "km sq" or "km2"?

Because in many countries (like the Netherlands, where I live) km2 is how you would write sq km. So if you were to buy a piece of land in NL that is the size of 8km2, you would be getting a piece of land that is say 2km x 4km.

It would seem to me, as a layman, that if you would take the price paid in the land deal and divide it by the average price per km2 in that region (for the same type of land) and the result is around 8km2, the buyer is getting what he paid for, if it's around 64km2 he is indeed being ripped off.

Can't say where due to current litigations and privacy - but that's not important... in contract, the areas were spelled out in full.

The price would have been 4 to 5 times the value of the current market value at the time if it had only been for square kilometers (plus would have been insufficient for the buyer I imagine)... Under the contracted parcel being km sq, it was pretty much on par or slightly less given that not all the area was expected to be completely workable for use.

Like I said - I'm not privy to specific details, it just stood out because of timing as well when the TLD chart was released. I had originally assumed the same as you: "km2 is how you would write sq km", but happened to be talking on the phone to my client who pointed out that there is a difference between sq km and km sq.

Anyhow - not overly important... like I said, the devs clarified they meant double the size, and that was the only clarification I was originally looking for. Although it is interesting to see how the math debate has grown on this side-subject :lol:

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  • 2 months later...

There is a lot of confusion with this even in my country where it's the official unit, taught to kids from 2nd grade. Americans need not think they are dumb if they have problems. Though I think the confusion remains even if you use feet or miles and square them, so maybe it's worth relating what we did in our firm.

First off it's very simple: 1 km² = 1km x 1km. A square with 1km sides.

And 10km² = 10 x 1km²

But contrary to intuition that's not the same as 10km x 10 km (that would be 100 km²)

If it's still not clear paint it on quadrille paper.

There is really only 1 thing you need to keep in mind: when A is the area, the side length s is always the square root

A = s²

=> s = √A

1km² = 1 quadrille (s = √1)

10 km² = 10 quadrilles (s = √10 = ~3.33)

100km² = 100 quadrilles (s = √100 = 10)

Now in my firm, which deals a lot with m² (we have a say how much other firms get paid per square), people were simple unable to understand how much where 0.1 m² or 0.01m². Employees who normally have technical college degree can't get things right once they deal with fractions.

By intuition they tend to think 0.1 m² = 0.1m x 0.1m. Totally wrong by a factor of 10.

But correct is: 0.1m² = √0.1m x √0.1m (Remember what I say above, side length is √A)

I printed a huge graph with the squares and hung it to the wall so that people always have it in front of their eyes. The area and side length for is 0.1 m² is much larger than people think, it's ~0.316m squared, or quite close to a sqaure foot, , or 31.6cm.

0.1m x 0.1m is tiny in comparison, just 0.01m² or 1/10 of 0.1m².

I don't know of this helps anyone who is not willing to invest some time thinking it over, but I think it contains enough clues to better understand areas. Again, if you are still not sure better always use quadrille paper before you embarass yourself in your job ;) I have seen people with good degrees look absolutely embarassed because they were wrong by 1000% on a pretty basic calculation.

Which is to say, Hinterlands claims are correct and it never occured to me that they couldn't.

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