[Closed] Favourite maths thing

We might be describing the same thing here, but one of my favourites is the ‘Napkin Ring Problem’

Copied from wiki, as I can’t find the words to explain -
In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere (i.e., the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere). It is a counterintuitive fact that this volume does not depend on the original sphere's radius but only on the resulting band's height.

I like it!

If you wrote down a Googolplex without using powers, the paper would be larger than the universe.

Thats the best I can do at the moment, its the 3.14/PIE one

Bloody hell, it only worked!

That if you take the sum of all integers, ie: 1+2+3+4+5+.........n

the answer is -1/12

(it clearly isn't, there's an error / assumption in it that sort of makes sense but it's almost like a bit of misdirection in a magic show. But, and the amazing bit, is that the sum of all integers is used commonly in physics / quantum physics, and using this 'approximation' ........ THE PHYSICS HOLDS UP AGAINST THE OBSERVED MEASUREMENTS!)

The speed of light thread reminded me of my favourite bit of maths. If you got a piece of string and wrapped it round the equator, then lifted the string by 1 inch the whole way round, the distance between the two would be exactly the same as if you did the same with string round a tennis ball.

I'm not sure I understand that, of course it is, it's an inch.  Was that a typo, do you mean "difference"?

My favourite maths thing:  If you take a pizza of thickness "a" and radius "z", its volume is pi.z.z.a

e^i*pi+1=0

Beautiful equation.

Alexander Grothendieck, one of the greatest mathematicians in history, was talking with a student who said 'If we consider any prime number..' 'You mean an actual number' 'Yes' 'OK, 57 then'.

Not very interesting intepretation - the greatest mathematician in the world has made a glaring elementary error.

Far more interesting interpretation, and the true one according to some - Grothendieck was unaware that 57 is not prime as he just didn't think on that level.

Euler's identity is another brilliant mathematical expression - five most important numbers in maths related by a simple identity. A virtual pint to anyone who can put that up with correct formatting on the board right now.
[ETA good effort Jon]

As [sup]superscript[/sup] tags still don't seem to work, my best effort at formatting:

 [size=10]iπ[/size]
[size=40]e +1=0[/size]

Aaargh broke it just as the edit window ran out (preview doesn't work for me at all, so I have to try it live)

[size=10]  iπ[/size]
[size=20]e +1=0[/size]

I’m not sure I understand that, of course it is, it’s an inch. Was that a typo, do you mean “difference”?

Gary Numan is actually two weeks older than Gary Oldman

Dec 25 = Oct 31

proof by induction was always a  favourite.

5318008

2x6 has always been a favourite of mine.

^^ 🙂

<span style="display: inline !important; float: none; background-color: transparent; color: #444444; font-family: 'Helvetica Neue','Helvetica',Helvetica,Arial,sans-serif; font-size: 12.8px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; line-height: 15.36px; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">I mean the distance between the two ends of the string

This is a really interesting bit of maffs and one that's quite hard to get your head around.

Imagine a piece of string wrapped around the earth, which obviously has the same length as the earth's circumference.  You now take the string and uniformly raise it by one inch along it's entire length.  Obviously it gets longer (by about a foot), as the diameter of the circle it encloses has increased by 2 inches.

Now imagine doing the same thing to an apple.  Wrap the string around the apple.  Now you need to orbit your string one inch above it, just like the earth.  How much extra string do you need?  The answer, remarkably, is also about a foot (12.57 inches).

This

https://czep.net/weblog/52cards.html

Imagine a piece of string wrapped around the earth, which obviously has the same length as the earth’s circumference.  You now take the string and uniformly raise it by one inch along it’s entire length.  Obviously it gets longer (by about a foot), as the diameter of the circle it encloses has increased by 2 inches.

Now imagine doing the same thing to an apple.  Wrap the string around the apple.  Now you need to orbit your string one inch above it, just like the earth.  How much extra string do you need?  The answer, remarkably, is also about a foot (12.57 inches).

Wut? <goes off to do some maths to prove this can't be true>

Pretty much right except pi x 2inches isn't a foot

C1 = pi*De

C2 = pi *(De + 2")

C2- C1 = pi*De + pi*2" -pi*De

C2 - C1= pi*2"

That's the proof.  The difference in circumference is only a function of the increase in diameter, not the value of the diameter.

Favourite bit of maths - Möbius strip - just weird

<span style="display: inline !important; float: none; background-color: transparent; color: #444444; font-family: 'Helvetica Neue','Helvetica',Helvetica,Arial,sans-serif; font-size: 12.8px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; line-height: 15.36px; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">Gary Numan is actually two weeks older than Gary Oldman</span>

proper lol

dammit if only I knew the equation for quoting on the new forum

Pretty much right except pi x 2inches isn’t a foot

Yeah that bit had me confused. So the difference is always just pi*the change in diameter. Straightforward once you write the equations down but like you say totally counter-intuitive when you first hear it.

My favourite thing to wind my missus up is to tell her that .99999 recurring is exactly the same as 1. As an engineer, she won't have it.

I've seen the same used to describe racing around the M25. Assuming that it's a circle to make it easier, and the road is 10m wide, how much further is it going clockwise on the outermost lane vs anti- on the innermost, ie if 2 cars set off at the same time and drove at the same speed (making progress, obviously) how much would the anticlockwise car win by.

Distance (ie circumference) of the 'short' route = pi* D

Circumference of the long route = pi* (D+20) = pi*D * pi*20

Difference is pi*20 irrespective of diameter and therefore the anti-cw car wins by about 60m, which when you're making progress at 200km/h is about one second.

And if you shorten the track to give him a better chance - he still always loses by the same distance.

[i]My favourite thing to wind my missus up is to tell her that .99999 recurring is exactly the same as 1. As an engineer, she won’t have it.[/i]

On a similar note almost all numbers contain a 3

[quοte]dammit if only I knew the equation for quoting on the new forum[/quοte]

Gives:

dammit if only I knew the equation for quoting on the new forum

(though not if you copy and paste that, you'll have to retype what you see - for obvious reasons I've broken the tag translation with funny characters)

So, so many, that nothing springs to mind.

But one interesting titbit is that you only need 23 people to be in a group (suitably random), for the probability to be more than a half, that at least 2 of them share a birthday.

"If you got a piece of string and wrapped it round the equator, then lifted the string by 1 inch the whole way round, the distance between the two would be exactly the same as if you did the same with string round a tennis ball."

I'm guessing one inch?

Ok- I see it's been answered. I am amazed that you would need an extra foot for the apple string, but there you go! 🙂

There are more numbers between 0 and 1 than integers ( ...-2,-1,0,1,2...)

Ok- I see it’s been answered. I am amazed that you would need an extra foot for the apple string, but there you go!

There was a mistake with that answer, it's about 6.3 inches I think (same for both).

So I just had a go at this with an apple and a piece of string (actually a roll of kitchen towel and a USB charging cable) and I'm not convinced.

Maths:

Diameter of Earth: 12,742,000.000 metres
Circumference = pi x diameter = 40,030,173.592 metres
Circumference plus two inches = pi x 12,742,000.051 = 40,030,173.752
Increase of 0.160 metres.

Diameter of apple: 0.070 metres
Circumference = 0.220 metres
Circumference plus two inches = 0.380 metres
Increase of 0.160 metres.

Well I'll be darned. Crazy!!

<span style="display: inline !important; float: none; background-color: transparent; color: #444444; font-family: 'Helvetica Neue','Helvetica',Helvetica,Arial,sans-serif; font-size: 12.8px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; line-height: 15.36px; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">On a similar note almost all numbers contain a 3</span>

7?

1?

1913760 used to be a favourite...

Used to be 65536 but got past that. Recently [s]learnt[/s] read about Grahams Number. It eats a googolplex for breakfast. There are larger numbers but I couldn't make any sense of them, Grahams Number doesn't require any fancy maths to understand.

7?

1?

You don't appear to have disproved the "almost all" premise there. There are a lot more numbers than 7 and 1 (hint: even if you're only considering integers, then almost all numbers have more than 100 digits, so 7 and 1 aren't particularly typical...)

oh and:

528-491

Oh, and:

528-491

There are more numbers between 0 and 1 than integers ( …-2,-1,0,1,2…)

I love the proof of that too, easy way to demonstrate that there are different sizes of infinity.

Oh and on Graham's number, we know it ends in a 7.  Not a clue what it starts with.

Plus Wiles' work to prove Fermat - it brings together apparently unconnected branches of maths to prove such a simple looking theorem.

<span style="color: #444444; background-color: #eeeeee;">If you wrote down a Googolplex without using powers, the paper would be larger than the universe.</span>

But surely the paper would have to be that big before you wrote anything on it.

And if we're using 'the universe' as a means to measure a piece of paper does this mean you've extended Flat Earth theory to one of a completely Flat Universe?

My favourite Maths thing (as a non maths-y person) was mathematician on radio 4 describing how he tried to explain infinity to his young son.

Dad: "what do you thing the biggest possible number in the whole universe is - a number so big you couldn't make it any bigger"

Son: " *thinks* ten million, 900 thousand and seventy three"

Dad: "well if I added 1  and made it ten million, 900 thousand and seventy four then that it would be biggers still wouldn't it"

Son: "Well I was close"

Not really relevant to the thread but I'll mention it anyway since it made me slightly happy.

My brain's been going downhill over the last few years mainly due to work stress but the last few months have been better.

The other day I managed to calculate the number of seconds in a year in my head without writing anything down. Got it exactly right (or at least right if you consider 365.25 days)

Was pleased that I still had some cognitive ability after a shot couple of years.

I like the paper folding on its self.

Any more than a 103 times it will be bigger than the universe. Handy for writing a Googolplex on.

I like the paper folding on its self.

Yes, that's the secret to Millefeuille

That would be some custard slice.

One I like is that your phone number is somewhere in the digits of pi. And my phone number, and everyone else's.

Do you think there's some sort of Greg's at the end of the universe that stocks these delicacies?

I like that a half-step in an Octave has a frequency ratio of 2^(1/12). It just seems just the right size.

Dam how do you do powers?

One that I find quite useful in my work as an accountant is the fact that if you swap two digits in a number then the difference between this and the original number will divide by nine.

It's a good way of finding errors in adding up numbers.

So for example 1050 and 1005 difference equals 45, divides by 9.

or 4743524 and 4734524 difference equals 9000, divides by 9.

or 27854934 and 72854934 difference equals 45000000, divides by 9.

One that I find quite useful in my work as an accountant is the fact that if you swap two digits in a number then the difference between this and the original number will divide by nine.

The ancient Celts and Vikings were obsessed with the number 9 because it does so many cool things like that.

I like that a half-step in an Octave has a frequency ratio of 2^(1/12)

Or to put it another way, the frequency ratio is 2^-(1+2+3+...) 😉

Like the anecdote about von Neumann in the book [i]A beautiful mind[/i] - two grad students thought they'd get one over on the Great Man by asking him the following - imagine two cyclists 20 miles apart, who begin cycling toward one another at 10 mph [in a straight line]. At the same instant, a fly on the wheel of the first rider buzzes off toward the second at 15 mph. When it reaches the wheel of the second, it turns round and flies back to the first, and then turns round and so on and so on. How far does the fly travel before getting smushed between the two wheels of the cyclists meeting in the middle of their journey?

von Neumann instantly replies 15 miles. Somewhat crestfallen, the students ask him if he's heard it before then? No, replies a quizzical von Neumann, I just summed the infinite series...

<span style="color: #444444;">One I like is that your phone number is somewhere in the digits of pi. And my phone number, and everyone else’s.</span>

If you printed the whole of Pi (and therefore everyones telephone numbers ever) on a piece of paper the size of the universe and folded it 103 times it would make for a better TV spectacle to see Geoff Capes tear it in half than it would the slim A5 pamphlet that got posted through my door recently pretending to be the Yellow Pages

also about a foot (12.57 inches).

Oops.  Divide by two and all is well.

I like that a half-step in an Octave has a frequency ratio of 2^(1/12)

That's for convenience. Musical scale used to be based more on what was pleasing to ear. Maths doesn't quite do as well.