Does "land area" assume a country is perfectly flat? 

Hi 👋 I just need need weekend

hahahahaha I need to show my uncle this video, he's from Liechtenstein

@@sebastianpeheim8851 Let us know the results 😉

All 9 of them!

Liking just for that intro music

Oh no, what have you done

So for simplicity i suppose we start at average sea level. Do the Netherlands then end up at negative volume?

@@arandacil you extrude the board down to the center of the earth

And then how about when the volume changes due to erosion, construction, or land reclaimation? Now there are 4 dimensions.

Also fractal. As you increase resolution you get to elementary particles, and these have undefined (fractal) volume.

Are they finally out now?

@@A.Lifecraft last i heard, no, but it's possible something happened super recently and we're suddenly Out now

@@mozarteanchaos I hope this charade will be over soon. My guess is this will ultimately result in Britain rejoining once people realize what they did to themselves. So lets get it over and done with, because there are people who have to suffer from all this uncertainty.

That's been the UK for the past 200 years probably more

That's EVERY government.

And Limburg

Vergeet de dijken niet

​@@mimi3570 ah, yes, dutch

Netherlands have bedrock above terrain

dremples, if I'm not mistaken

I've seen this anime before

Are you the evil genius that's going to do it purely for wanting to flatten the Earth to make the flat-Earthers right?

@@Axartsme Was it both Fooly and Cooly?

O

Hey! I watch you're videos

This comment is underrated

Exactly what I thought.

Wow, I didn't even notice at first

Yes, Matt, your mic range is bounded

I was surprised he made it that far without mentioning it

Not only would the 2d coastline problem appear, but then a much worse 3d terrain fractal-ish problem would appear and ruin everyone's day

Skanderbeg not with volume!

@@skanderbeg152 Yes, that is mentioned in the video.

Internally I was like: "Father, here I command my soul to the eternal infinity of the heavens", when he mentioned the coastline problem... But when mentioned that the coastline problem could be extended to 3D, I felt as if I had become god itself that created reality itself just so that line would be delivered with a close-up shot on the crevices of that wall. Complete mathematical enlightenment: The surface area of every country is infinity. 🤣

Facts

Is it sad that I actually understand what was said???

@@makatogonzo no, i do too, hes saying online information is so diverse and available, that college is not that necessary to have the knowledge to make something happen

@@artratengo3685 I'm pretty sure OP is amazed at how willing this person was to donate time and effort to this cause which OP(maybe erroneously) attributed to them being a part of academia. I don't understand how you ended up at your conclusion.

@@ruukinen well if you read the last part, the for free at the end of OOP' s post tells the same thing as i said more compactly

The movie? Nah, the trilogy! And judging by the amazing landscape pictures in this video, the first one is going to be: The Fellowship of the Torus.

@@wolframstahl1263 American π

@@apocalypsepaul Harry Parker and the Mathematician's stone. Harry Parker and the Vector Space of Secrets. Harry Parker and the Theorem of Azkaban. Harry Parker and the Goblet of Fractals. Harry Parker and the Order of Operations. Harry Parker and the Half-Blood Primes. Harry Parker and the Mathly Hallows.

@PAUL BAILEY Fermat Wars: The Last Theorem? Alice in Fractal Land? Matt Parker and the Philosopher’s Geoid?

i'm ready for the Parker Cinematic Universe

It's goofy and epic at the same time!

Wait a second, I recognize you...

it supposed to be soundtrack for parker wars, but it turned out that spreadsheet is not very good way for rendering a movie.

I am hoping for an ost

@@Irondragon1945 No seriously, I'm subscribed to you... I must know you somehow

Lmaoo

...are there any places with any fractal buildings?

@@TinyDeskEngineer Yes, every building. Look at stone or paint under a microscope.

@@karlhendrikse that wouldn’t be a fractal

@@murpledeer A fractal just needs to have detailed structure at arbitrarily small scales. If you want it to look the same all the way down at different scales, that's a Mandelbrot set.

Awh shucks.

BOOOO music too short BOOOO ENCORE! Where's the rest?

Two teachers I greatly respect... Nice. 🍉

I love seeing educational RU-vidrs commenting on the videos of other educational RU-vidrs.

@@standupmaths Now we have another challenge for you, which also strikes at the issue of geoids. Take the flight distances between A: London, B: New York, C: Tokyo, D: Johannesburg, E: Melbourne and F: Rio De Janeiro. [1] Show the distances for {A,B,C,D} make a tetrahedron of *positive* volume (hence they are not co-planar and the Earth is not flat). [2] Show the distances for {A,B,C,D,E} can *not* exist in *any* Euclidean geometry of *any* number of dimensions! (Instead, they lie in a 3+1 dimensional geometry - a Minkowski geometry). [3] Account for the Earth's curvature by assuming all flight distances are actually arcs along circles of diameter d and use the corresponding chords instead (with the conversion Chord = d sin(Arc/d)). Prove that: [3a] for d ranging from (2/pi x the longest flight distance) to a fixed value, the chords for {A,B,C,D,E} can only exist in 4 dimensions, [3b] for d ranging beyond this fixed value, the chords for {A,B,C,D,E} can only exist in a 3+1 dimensional Minkowski geometry and not in Euclidean space, [3c] for a very specific d, the chords for {A,B,C,D,E} can be embedded in a 3 dimensional Euclidean geometry. [3d] what is d? [4] Do the same with all 6 cities {A,B,C,D,E,F} and show: [4a] for d ranging from (2/pi x the longest flight distance) to a fixed value #1, the dimension required is 5 (signature +++++ in the 5 coordinates), [4b] for d at the value #1, the dimension is 4 (signature ++++0), [4c] for d ranging from value #1 to a second fixed value #2, the dimension is 4+1 (signature ++++-), [4d] for d ranging from value #2 to a third fixed value #3, the dimension is 4+1 (signature +++-+), [4e] for d at value #3, the dimension is 3+1 (signature +++-0), [4f] for d beyond value #3 as well as for flat geometry where d = infinity, the dimension is 3+2 (signature +++--) - an anti-deSitter geometry, [4g] at d = value #2, attempts to fit the chords of {A,B,C,D,E,F} *diverge* (the signature approaches +++00 but at least two of the cities must diverge to infinite null vectors before the signature is reached), [4h] value #2 is almost exactly equal to the diameter found in [3]. [5] Use the results of 4 to show that the flight distances of {A,B,C,D,E,F} do *not* fit on a sphere at all but require an irregularly-shaped geoid, like an ellipsoid. Find the ellipsoid that allows the flight arcs to be embedded in a 3D Euclidean space, and use it to also determine the *latitudes* of the cities! This requires converting from *elliptical* arcs to chords, which requires elliptical functions. [6] Add in a 7th city, G: Nome. Repeat all of the above with {A,B,C,D,E,F,G} assuming a sphere, then assuming an ellipsoid. Compare the results to those of [4] and [5]. In particular, does it fit the same ellipsoid that was found in 5, with the *same* absolute latitudes and relative longitudes for the subset {A,B,C,D,E,F}?

NationalAntheming is my new favourite verb

I think it was more CountryFile-ing, tbh, but I lolled!

That intro music just kills me.

Everyone Everyone around is

That intro caught me off guard lol

Hey Andrew, didn't expect to see you here!

They have the original song available on the website, but can’t find the remixes

What hey andrew

I hate it, I cringe every time I hear it lol

@@MBKill3rCat that's weird

Greetings from Conway!

That’s the way you do it

Just have to watch out for Gowrow.

@@garrysekelli6776 'inland water counts as land' Dutch: 'hold my Ijselmeer'

@@baskoning9896 _Waddeneilanden has entered the chat_

If you want to verify, there's elevation data available at half a meter resolution: downloads.pdok.nl/ahn3-downloadpage/

I think people are underestimating the Netherlands. Anyone who has ridden any substantial distance in the Netherlands know the county has hills. The lowest point in the Netherlands is about 7 meters below sea level while the highest point is a bit more than 320 meters, for a total variation of about 327 meters. According to Wikipedia, the flattest country is the Maldives, with a total variation of about 1.5 meters. (As a result, you can see why the Maldives are concerned about rising sea levels as a result of global warming.)

@@baskoning9896 "We're not trapped in by the ocean, the ocean is trapped in by us" - The Dutch presumably

I like that someone once said, "In the 18th century, the British should have all moved to Australia and left the criminals behind!

@@timbeaton5045 On vacation in Australia, Douglas Adams realized that England is a cold, rainy, dreary, and cramped place, Australia is a sunny, beautiful, wide open place, and England had the bright idea to use Australia as a prison. No wonder there's a special smile Australians reserve for the English.

@@tparadox88 That special smile on an Aussie bowler's face at the GABBA when the next English batsman is coming to the crease when they are 5 for 70, perchance? 🤣

Ah, the brilliance of children. not quite smart enough to know the answers but smart enough to know how to ask good questions, and then they know the answers.

my dads strategy was to just promise that the "hütte" (restaurant on or near a mountain top in europe usually supplied by helicopter, cable car or on foot, i dont know if thats a thing in america) was right around the next corner, or across that hill, basically just out of sight.

GPS can include altitude data when connected to more than 4 satellites, so, depending on the software, that's a real possibility

@@CMDR_Hadion Yes. My telephone (app Geo Tracker) includes altitude but I think the distance is calculated as a projection in x-y only.

My Garmin watch can track distance and spee in 2D or 3D.

ha! I saw that too

Look at the % increases given on screen. They match the written version, which also are intuitively more credible. You people are wasting your time looking at a maths channel.

He puts these in to see if we’re paying attention.

I thought the cord on my headphones was broken. XD

xenontesla122 same lol

And @6:39 (and elsewhere!) we also found the limits of Matt's camera's Autofocus settings. Panasonic G5, possiblement?* *Ahh. The Panasonic Pony of Hope

I thought it was the cheap HDMI cable I bought.

Well, i have good news!

@@LeventK What's the good news! Tell us!

Well, I have good news!

I know right. I'm literally from the Netherlands and we have a higher "mountain" than Denmark.

@@Leyrann Really? I used to think that the Denmark is a bit more hilly than the Netherlands but I admit that I've never visited Denmark.

Technically, both Netherlands and Demark have their highest point in overseas territories

Our tallest peak is 170.86m unless we count monuments on top, in which case there's one at 183m and several other structures reaching even higher. Which brings up the general question if topographic area should include the exact shape of various buildings, including balconies and broken windows that extend the surface into the inside rooms.

Well, Netherlands is only 1,4% larger than Switzerland whereas Denmark is 4,4% larger (according to Wikipedia). Both countries are pretty flat (although with hills). Also, it doesn't matter how tall the tallest peak is, just how much it goes up and down.

Your comment made me so happy until I saw your comment was made one year ago 😂😫

Sadly it now says 2 years ago...

That sounds pretty cool. It's like you're an old timey surveyor *BUT FROM SPACE*

Matt just has a lot of questions and doesn’t want to bombard you

@@robertstuckey6407 nah, modern datasets are almost all from survey planes. (One of the standard global elevation datasets however was made by the space shuttles synthetic aperture radar experiments)

@@RobertSzasz A whole host of methods are used to generate geospatial datasets. Including GPS (measurement of asset locations/heights), surveying/lidar (land/property), aerial imagery/elevation from planes, but its also very common to use raster datasets derived from constellations of remote sensing satellites (ie SPACE, think > LandSat, Digital Globe, PlanetLabs, etc) to map/model our environments with all kinds of variables (we can even determine soil moisture levels "from space"). Would be great to see Matt cover differential GPS, where they use ground stations/mobile networks and a lot of maths to obtain ultra-accurate locations.

@@fieldo85 I some how missed the first couple words of your post .. 😳 sorry bout that

"And that is something you might not have known"

I don't think there's a red tshirt that measures 247,719km²

Parker Tom Scott

It IS a thing that I may not have known

Numberphile did touch on the coastal area problem before!

It's not. You built a house vertically, or with a floor whose plane vector matches the vector of the force of gravity (if you use good enough builders). That means that for each floor you build you have consumed the 2D footprint of it in real-estate. Agriculture now... That's a whole different thing...

@@ExMachinaEngineering woosh

@@ExMachinaEngineering Also you should never mix up 2D footprint of your roof (which is important calculating the amount of rain water) and actual surface area of your roof (which is important when ordering new rooftiles).

Thank you, fellow Dutchman. See my comment on removing seawater with Dutch canals to gain land area in the Netherlands.

@@A.Lifecraft what’s the difference?

So to measure the surface area of each country, build an impermeable barrier around each, fill it with hydrogen, then do a bunch of mathematical calculations...

And if you were to gather results for such a project to measure the areas of countries, you'd find they tend to infinity, and probably strongly correlate with physical properties of the countryside's materials. Not to mention the errors from the hydrogen getting absorbed or reacted by things.

If you could have a chamber where you can pump gas in and out to achieve constant pressure, with circulation to provide convection, and a heating system for the gas, would it be possible to measure some fractal metric by selecting a pure gas, then changing the temperature and measuring the outflow of gas? Obviously you'd need to factor out chemical reactions and account for adsorption, but this should allow you to test the sizes of gaps and crevices continuously, as hotter, less dense particles might avoid reaching into those crevices more than expected. You could sort of imagine the particles "acting bigger" when at the same pressure and lower density. This would drive out more gas than should be driven out than temperature increase alone should provide (remember the system has constant pressure), as the small crevices are not packed as efficiently because the particles are "acting bigger." A really clever model could perhaps also look at the cohesion of the gas (and how that cohesion changes with temperature), but the mathematical relations for that could be a respectable nightmare. With or without such extra modelling, this effect would perhaps be nearly impossible to measure, and the errors would still drive out any meaningful data, but it's fun to think about. Some large (particle size) inert gas and a very tight (average bonding distance) material object could make some of these considerations more possible. The large particle size and tight material in the solid might decrease adhesion, while having large particle size also limits resolution to ignore whatever wierd physics shenanigans might happen if particles get into very enclosed spaces while the particles are very close to the solid's surface. Making the gas inert should also pretty much eliminate cohesion, I think.

In WWI they tried it with Chlorine gas

Peter LeRoy Barnes there’s lots of interesting ideas in here! Using pressure is only realistic on smaller scales, especially because things like reactions but also because different materials adsorb gas on the surface at different concentrations so you would essentially get a free variable out the other end that would be difficult to manage-not to mention the difficulties of such an experimental setup!

That’s hilarious

The Vatican might as well be called the flatican, despite being built on a hill. Although of course for the Vatican, the topography of the buildings would actually make a difference. Hey I think I just stumbled onto a related problem, I suppose it would only really be a thing for the Vatican, Monaco and maybe Singapore, but those little countries are basically completely full of urban development, and buildings are about as extreme as topographic features get.

@@AlRoderick if you're interested, the data used here seems to be DTMs (digital terrain models) of various resolutions rather than DSMs (digital surface models). A DTM represents the elevation of the bare earth whereas a DSM represents the surface including any buildings etc. So, it's unlikely the buildings in the Vatican were taken into account this time.

How are DTMs generated?

@@TheAlison1456 I'm not entirely certain but, from what I understand, DTMs are taken from DSMs with building heights and vegetation etc. subtracted. A common method for scanning elevation is using LiDAR. It's like radar except using lasers instead of radio. With LiDAR, you can tell how far something is but also what sort of thing you're detecting. So I guess it can be determined if a height is of a building or land and then the rest is figured out somehow.

I've been watching your content all day and was not expecting you here too!

@@MrBroady02 He *is* the official RU-vid Nerd Representative for Australia, so of course he's here.

Always nice to see somewhere in comments mate!

@@chemputer oh man, there are lots of nerdy Australian RU-vidrs. Heck, Both Matt Parker and Brady Haran are partly from Australia.

added difficulty: use DaveCAD.

Ah, an "influencer" here on business then, carry on! 😉

Funny, but it's Britain; you can usually find all those terrains within 5 miles of any given spot.

It significantly increases the total biomass, since plants dont really care. Also, you ever seen animals in mountainous areas? those dont care at all, so an increase may not help you, but it increases the grasing area for farm animals, which does influence you. But obviously, it's not only farm animals, it's all kinds of organisms that benefit from this, humans are really only partially an exception, as in those mountainous countries, even cities may extend more than a meters up a mountainside

But paved roads etc can be tilted and therefore more area

@@siangchengpang772 roads takes topography as relevant and they do their work mapping the region before constructing

You can totally make verticality into livable area. You can engineer a building to attach to, or join into, a sheer cliff face. Then, if the cliff is tall enough, build one above it. Look at cliff dwellings of the Pueblo People in the American Southwest. But that starts opening up a whole other issue of underground/in-ground area that's still technically "above" ground level. Still, you can construct on the side of a cliff for livable area.

*drones everywhere*

**...and it's so large that Matt has to exit the room and film this video outside.**

Obnoxiously so.

Still managed a Parker Microphone moment, though.

Great intro sequence for a great question! Please keep this epic music for your videos!! Where can I download this epic track in full length without voice-over?

@@engywuck85 I would like to know that too!

For real, this was like watching a short film.

The grass is always greener...

@@ErwinPommel ...on the other side of the planet.

You must never have been to Tassie, or Gippsland...

You guys need to visit India

@William White Agreed!! Not an expert, but I find India too, having climate varying place to place. I'm sure Australia is same. I visited Melbourne once and the weather was changing everyday.😄 Awesome place!!

Same!

We need a marching band version as well.

So epic. I love it!

bardcore it!

Waited for this.

Well, the topography part is intuitive and for many countries curvature is irrelevant. Therefore you are wrong and could also cause smirks. So be more careful next time :)

Very dangerous to make measurements near the edges. Many surveyors have fallen off,,, never to be seen again.

If you are talking about flerfers, you could have just said "We don't understand."

@@Gladaed *gasp*, smirks? How awful

It was an epic opening theme

@@neurofiedyamato8763 epically awesome

I love the implication that the entirety of Liechtenstein was, prior to this video, subscribed to Stand Up Maths.

What have we learned? A country can have infinite area, and an infinite border, but maintain a finite volume. I started thinking about this a couple weeks ago, and it gave me a headache to say the least.

Exactly ! He didn't even mention Nepal!

Although high, isnt there a huge plateu in nepal, which is flat (ish)

@@paulquaife7974 fair point, there is sizable lowlands on Nepal's southern borders. Perhaps Bhutan or Lesotho may be better contenders?

@@davegrimes3385 my guess was chile

I have to imagine Chile and Argentina are up there too.

idk it doesn't seem weirdly punctuated to me, what's missing? a comma before and? I don't think it's necessary

@@macizogalaico I think all that was missing was context. You can easily get confused by the long name of the dataset if you don't know it beforehand. If you know that "GEODATA COAST 100k 2004 data" is to be read as just one entity, you're trying to insert some kind of break inside there (as it's usually unlikely that a single term is made of so many words, and our brains work on likelyhood). But then you wonder where's the break? _Obviously_ there's some punctuation missing to make that break clear ;) And honestly, punctuation _would_ help, though it's not grammatically necessary. Replace the "and" by a period and make it two sentences. Or replace the "and" by ", so" to show that the latter part is the conclusion and all of the former part is one subsentence. The sentence was written by someone who was rightfully assuming that the reader would know what "GEODATA COAST 100k 2004 data" would mean and wrote the sentence with that in mind, but it was read by someone who didn't. The only one at fault was Matt for not providing the required context ;)

some italics would help

Epic music upgrade!

Yes!

Stand Up Maths: The Movie

No,it just makes me amazed that their are such curious people in the world.

Exactly! I have actually previously wondered the 1D->2D equivalent of this, namely: does Google Maps quote you the "flat" distance when travelling, or does it take into account topography. Never went into enough of a rabbit-hole to find a definite answer, and also never considered expanding it to a 2D->3D problem!

@@EcceJack Hmmmm I never thought of that either, but I would assume Google Maps uses the topographical distance, since I would assume they get their distance data from surveys of the roadways, which I would assume are done by someone driving along the roadway and measuring every so often. That's a lot of assuming though, lol.

No, not wasting my time on this question doesn't make me feel silly because taking topography into account makes no sense when the calculation seems to be intended as a means for comparing the relative size of countries. If I dig a large hole in my backyard and pile up the dirt, thereby increasing the surface area of my yard, would it make sense to say the size of my property increased relative to my neighbors? In a strong field, this is the strangest Matt Parker video I've seen and the first one I've turned off because the premise is lost on me.

@@tompaine4044 "thank you for coming to my ted talk"

So that's where Flatland takes place. I always thought it was here in Florida

Wrong, Sir, WRONG ! You need to count all the damned dams in the Netherlands !

Rock, in the Netherlands? It's all sand, peat and clay, my friend.

Wait until sea level rises and they start to dome their entire country. In the 22nd century they will have the biggest submarine navy in the world.

@@HappyBeezerStudios We (dutch) would just call them cars

Well he did mention that it was corrected for the _local_ shape of the geoid and that it's not the same over the whole globe. He just didn't explain why that is, and the mention was just a side-note, so it's easily missed.

@@sourcererseven3858 Also it mentioned they use the Australian Geoid, which is probably slightly different to geoids designed to minimize error for the whole globe (Eg WGS84 used by GPS) as many are local standards that only care about accuracy within a given region usually a country.

The "solid" ground being measured also deforms constantly due to tidal force, just like the ocean, but without the large delay due to sloshing.

Thanks for this comment! I didn’t think about different densities

There is no point, you would get a percent at most from that

Apparently Parker Square can also refer to some sort of arithmetic operation he screwed up in that computation as well as an NxN square of numbers with some special property.

I assumed 7 because it didn't seem like the measurement would jump by 200.

I'm guessing 7. He has done this in a few other videos lately, too, where he said the wrong number but the correct number was displayed on screen.

@@tomtrask_YT It's the fabled Parker Number!! :)

It's entirely plausible that he deliberately places mistakes into his work, just like in his book humble pi. Either that or I diagnose early onset dementia

Yes. Where's the full length standalone version? Came to rewatch the view for the music, not the math.

I would imagine that's probably unknowable realistically. You'd have to measure every single building, every person, every animal, every tree, it would be absurd. And not just one by one, but simultaneously in an instant, or else all your measurements would be wrong again by the time you finished.

@@TheRealHungryHobo I think he just means the land volume... It shouldn't be too hard to calculate depending on how the topographical data is recorded. The land area is already calculated from land at mean tide.

@William White The perimeter of a 2D fractal is infinite. It seems the area of a 3D fractal would similarly be infinite, no?

@William White Take a 2d fractal. Give the fractal depth by giving it a finite thickness, say 1m. You now have a 3d object with infinite surface area (infinite linear perimeter x 1m is infinite area) and finite volume.

@William White 1) You say draw a box that's x by y miles, well you have to include z as well since we're including the 3rd dimension. 2) I can draw a 2D box around the island that has a finite perimeter, but the 1D fractal perimeter of the coast is still infinite. I can draw a 3D box around the island with a finite area, why does that imply that the 2D fractal area is finite?

I saw that, 14:04 precisely. Think he needs to do more proofing before publishing. Other than that good research as per usual. HAPPY DAYS.....

He acknowledges this in the description- the on screen numbers are correct.

Probably what's written is correct seems to fit with the % maybe he didn't wanna redub the audio.

It's the Parker Area of the UK

@@Varil81lol

Imagine if you calculated the surface of the _leaf cells_

*R E S O L U T I O N I N T E N S I F I E S*

*computer science intensifies*

Or cave systems

FRACTALS!

Forklift17 very few subjects solve problems faster than creating them

That's the nature of problem solving.

The americas as a whole would be interesting to see how much of a difference each has given that both North and South America’s have rather sprawling countries that have distinctive mountian ranges to them.

I would expect all three of Chile, Peru, and Equador to gain quite a bit, all of them with their mountainous areas near the coastline.

Not that anyone should try that, wales are a protected species! XD

By the same logic, if you flattened our England, the ranking would be the same as it was. There is a lot of stored area in the Pennines, Lake District, and various wolds.

Wow, 6 to 10 points per square meter is impressive. Not sure if it is sufficient againts the one of Switzerland with resolution of 0.5m though: shop.swisstopo.admin.ch/en/products/height_models/alti3D

@@niemandwirklich Then we might lose out, Although not completely flat, the Netherlands is likely to have much gentler slopes than Switzerland.

Okay, that data is detailed. You can see individual plants in someone's garden!

Funny thing is that the highest elevation in NL is higher than in DK ;)

Wow the standard deviation is 5cm? Netherlands really IS flat! Oooooooooooh you meant the SD of the error not the dataset itself??

Speed bumps are the Dutch mountains.

Well, it goes into the negatives. Even your airports are below sealvl

Exactly. And I even live in Friesland which is, apart from Groningen, petty much the flattest landscape possible. When I use my bike the only times I have to cycle uphill or downhill is when there is a man-made height difference for a bridge or underpass. Any other road is as flat as it could be xD

@@duncanhw exactly, Saba contains our highest point

*Flat earth vibe intensifies*

The Danes thought that a hill that's 147 m was their highest peak until 1847. Said hill is called "The Sky Mountain" in Danish. I just find that hillarious.

I wouldn’t be proud of beating the danish. They don’t have many things. Let them have this

@@Spoon80085 Whoah mate! Unnecessary shade much?

@@kisteglad Well, I mean, they don't even have the Danish pastry. Lego is good stuff, though.

@@fanbuoy9234 They’re best traditional food is just bread, or sandwich in other langusges

But when the leaves fall off in autumn ...

Yeah, caught that too.

How about c) the volume between its actual surface and a section of a sphere with the country’s average border height as its diameter?

@@wsshambaugh That would be fun, too! I guess once you got the data to answer one of those questions, it'd be a simple task to answer the others.

Considering many countries have mines and such I think mineable earth should be included, which theoretically would include all the crust which is about 18 mi thick over the continent’s (deepest borehole is 7.6 mi)

Each country goes to the center of the earth. So therefore the actual relief of each country is negligable. Only land area and latitude matter then.

Wouldn't b) make the volume 0? There will be as much of the country above and below it's average height, after all...