Brief Thoughts On Maps

I have been asked in the past if the stated size of a country takes into account the curvature of the Earth and/or its topography. My usual answer was "in reality both affect it but I doubt if the official figures reflect this as historically the data was either not available or the calculation was too cumbersome".

It's very easy for kids to prove this by looking at an imaginary hill/mountain and calculating its surface area. Assuming a hill is a perfect hemisphere it is clear that the surface area is twice that of a flat circular area of the same radius. A conical hill is over 2.4 times the surface area of the flat surface. So obviously anything over perfectly flat will have a larger surface area - its just a question of how much.

I swerved the curve of the Earth question as being only really important for very large countries like Russia, although I suppose you could look at the surface area of the Earth and work out the proportion that country covers.

Since those days God invented computers and airborne/satellite imaging.

I was ploughing through Matt Parker's Stand-up Maths videos and came across this:


Well worth a watch - Switzerland is bigger than it is. I suppose places like Nepal and Tibet must also be bigger than they are.

The Bosnians say that ‘Bosnia would be bigger than Russia if you ironed it...’
 

Zhopa

War Hero
Yes. I'm now looking forward to the YouTube version of several other Arrse threads.
 
Yes. I'm now looking forward to the YouTube version of several other Arrse threads.

They do in fact have a few that have been done on here, including John Snow's cholera map and the non-existent town of Argleton.

I would pay to view the YouTube ARRSE Gingers thread.
 
For some strange reason I seem to have developed an interest in Kaliningrad, the main city in the Russian Kaliningrad Oblast.

Firstly it is an exclave, being part of Russia which is now outside of Russia. Exclaves and enclaves have always fascinated me (yes, I do have a wife and two children, thank you for asking). Secondly it is probably the only "Russian" city to be bombed flat by the RAF in WWII. Thirdly it has the ugliest and most useless building ever built ( kaliningrad house of soviets - Google Search ).

It was the old Prussian town of Konigsberg but the Sovs captured it and renamed it. When the Soviet Empire bit the dust they retained this exclave to give them a naval port in the Baltic that didn't freeze up in winter (which is apparently full of highly radioactive ships due to leakage, pisspoor Sov maintenance and alcoholic sailors).

I was reading a book on maths (irritatingly called Math Without Numbers - How hard would it be to add the "s" FFS) and came across the "Seven Bridges of Königsberg" conundrum. This is a map of old Konigsberg and it's bridges:

Konigsberg_bridges.png


The conundrum was to plan a walk through the city that would cross each of those bridges once and only once.

Give it a bash. It seems easy/obvious but if you can do it you are a better mathematician than Euler who proved it was impossible and in doing so invented the mathematical branch of topology (as distinct from topography - see, I shoehorned in a map and the word topography).


 

Mattb

LE
For some strange reason I seem to have developed an interest in Kaliningrad, the main city in the Russian Kaliningrad Oblast.

Firstly it is an exclave, being part of Russia which is now outside of Russia. Exclaves and enclaves have always fascinated me (yes, I do have a wife and two children, thank you for asking). Secondly it is probably the only "Russian" city to be bombed flat by the RAF in WWII. Thirdly it has the ugliest and most useless building ever built ( kaliningrad house of soviets - Google Search ).

It was the old Prussian town of Konigsberg but the Sovs captured it and renamed it. When the Soviet Empire bit the dust they retained this exclave to give them a naval port in the Baltic that didn't freeze up in winter (which is apparently full of highly radioactive ships due to leakage, pisspoor Sov maintenance and alcoholic sailors).

I was reading a book on maths (irritatingly called Math Without Numbers - How hard would it be to add the "s" FFS) and came across the "Seven Bridges of Königsberg" conundrum. This is a map of old Konigsberg and it's bridges:

View attachment 539834

The conundrum was to plan a walk through the city that would cross each of those bridges once and only once.

Give it a bash. It seems easy/obvious but if you can do it you are a better mathematician than Euler who proved it was impossible and in doing so invented the mathematical branch of topology (as distinct from topography - see, I shoehorned in a map and the word topography).


Good idea for anyone who has eight hours of training time to fill and doesn’t mind being hated, just set it up as a command task.

The DS solution is of course - as Bomber Command showed - the correct application of high-explosive.
 
.....I was reading a book on maths (irritatingly called Math Without Numbers - How hard would it be to add the "s" FFS) and came across the "Seven Bridges of Königsberg" conundrum. This is a map of old Konigsberg and it's bridges:

View attachment 539834

The conundrum was to plan a walk through the city that would cross each of those bridges once and only once.

Give it a bash. It seems easy/obvious but if you can do it you are a better mathematician than Euler who proved it was impossible and in doing so invented the mathematical branch of topology (as distinct from topography - see, I shoehorned in a map and the word topography).

I've seen this before - I think it's in one of Martin Gardner's books. If you're interested in this sort of thing I'd recommend anything with his name on the front. Loved them when I was at school, but they're written to appeal to all ages.
 
I have a metric sh1tton of his books so very much in agreement re Gardner.

I started reading his maths posers in the back of Scientific American about fifty years ago.

He is also very good on anti-woo and general skepticism.
 
I have a metric sh1tton of his books so very much in agreement re Gardner.

I started reading his maths posers in the back of Scientific American about fifty years ago.

He is also very good on anti-woo and general skepticism.

He died quite recently. I was surprised to read he wasn't a professional mathematician. "STEM" needs more communicators like him.
 

TamH70

MIA
For some strange reason I seem to have developed an interest in Kaliningrad, the main city in the Russian Kaliningrad Oblast.

Firstly it is an exclave, being part of Russia which is now outside of Russia. Exclaves and enclaves have always fascinated me (yes, I do have a wife and two children, thank you for asking). Secondly it is probably the only "Russian" city to be bombed flat by the RAF in WWII. Thirdly it has the ugliest and most useless building ever built ( kaliningrad house of soviets - Google Search ).

It was the old Prussian town of Konigsberg but the Sovs captured it and renamed it. When the Soviet Empire bit the dust they retained this exclave to give them a naval port in the Baltic that didn't freeze up in winter (which is apparently full of highly radioactive ships due to leakage, pisspoor Sov maintenance and alcoholic sailors).

I was reading a book on maths (irritatingly called Math Without Numbers - How hard would it be to add the "s" FFS) and came across the "Seven Bridges of Königsberg" conundrum. This is a map of old Konigsberg and it's bridges:

View attachment 539834

The conundrum was to plan a walk through the city that would cross each of those bridges once and only once.

Give it a bash. It seems easy/obvious but if you can do it you are a better mathematician than Euler who proved it was impossible and in doing so invented the mathematical branch of topology (as distinct from topography - see, I shoehorned in a map and the word topography).



I looked at that diagram for about thirty seconds and decided that it was impossible to solve. How long did Euler take?
 
For some strange reason I seem to have developed an interest in Kaliningrad, the main city in the Russian Kaliningrad Oblast.

Firstly it is an exclave, being part of Russia which is now outside of Russia. Exclaves and enclaves have always fascinated me (yes, I do have a wife and two children, thank you for asking). Secondly it is probably the only "Russian" city to be bombed flat by the RAF in WWII. Thirdly it has the ugliest and most useless building ever built ( kaliningrad house of soviets - Google Search ).

It was the old Prussian town of Konigsberg but the Sovs captured it and renamed it. When the Soviet Empire bit the dust they retained this exclave to give them a naval port in the Baltic that didn't freeze up in winter (which is apparently full of highly radioactive ships due to leakage, pisspoor Sov maintenance and alcoholic sailors).

I was reading a book on maths (irritatingly called Math Without Numbers - How hard would it be to add the "s" FFS) and came across the "Seven Bridges of Königsberg" conundrum. This is a map of old Konigsberg and it's bridges:

View attachment 539834

The conundrum was to plan a walk through the city that would cross each of those bridges once and only once.

Give it a bash. It seems easy/obvious but if you can do it you are a better mathematician than Euler who proved it was impossible and in doing so invented the mathematical branch of topology (as distinct from topography - see, I shoehorned in a map and the word topography).


This conundrum featured in the BBC R4 series " A Brief History of Mathematics " presented by Professor Marcus du Sautoy .... all episodes are still available .... BBC Radio 4 Extra - A Brief History of Mathematics - Available now ... a very interesting series of broadcasts .

ETA IIRC Episode 2 explains
 
He died quite recently. I was surprised to read he wasn't a professional mathematician. "STEM" needs more communicators like him.

He actually died ten years ago.

He did have a degree in philosophy, which probably came in handy as so much of modern maths and physics seem almost philosophical to me.

There are a bunch of his articles available here: Martin Gardner's Articles on Skepticism

Including one of his very first articles The Hermit Scientist, a criticism of Hubbard and Scientology.
 
He actually died ten years ago.

He did have a degree in philosophy, which probably came in handy as so much of modern maths and physics seem almost philosophical to me.

There are a bunch of his articles available here: Martin Gardner's Articles on Skepticism

Including one of his very first articles The Hermit Scientist, a criticism of Hubbard and Scientology.

Ten years, was it? I should have doubled the number I first thought of - I'm sure there's another conundrum there!
 

Mattb

LE
I looked at that diagram for about thirty seconds and decided that it was impossible to solve. How long did Euler take?
It took him until 1944, when the RAF made it possible by bombing several of the bridges. It was a slightly phyrric victory, with Euler having been dead for 160 years at that point.
 
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