Triangles, parallelograms and Shimura curves: Maths!
 Martijn
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Triangles, parallelograms and Shimura curves: Maths!
I did maths at uni. And then I went on to do a PhD and then... well, anyway, there is no maths thread (or, for those accross the pond, a math thread) on Anorak and after I discovered I share a mathematical background with a fellow Anorak, I thought I'd start one. Not that I have anything to say, but that might come now that there is a thread.
 soft revolution
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Re: Triangles, parallellograms and Shimura curves: Maths!
Yes! I dabbled in maths. I'm conviced most of it is entirely made up. Square root of minus one indeed.
Div, Grad and Curl I found a bit enjoyable because it was good to know how shapes worked. Please can someone give me a practical application for Fourier Transforms or Laplace though? They never made sense to me.
Div, Grad and Curl I found a bit enjoyable because it was good to know how shapes worked. Please can someone give me a practical application for Fourier Transforms or Laplace though? They never made sense to me.
And by me, I mean, Flexo.
 Martijn
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Re: Triangles, parallellograms and Shimura curves: Maths!
MP3s. Or digital music in general. Is that practical enough?soft revolution wrote:Please can someone give me a practical application for Fourier Transforms
Here is an article that tries to explain it all.
 soft revolution
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Re: Triangles, parallellograms and Shimura curves: Maths!
Wow, that's totally brilliant. I may have paid more attention if someone had said that, equations always seem so abstract without a practical example.
And by me, I mean, Flexo.
 lynsosaurus
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Re: Triangles, parallellograms and Shimura curves: Maths!
don't they use it in the processing of remotelysensed images, too? don't ask me how, like.
i have this on the wall above my desk.
i have this on the wall above my desk.
we'll be god's tiny carrier pigeons
http://halfmyheartbeats.blogspot.com
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http://halfmyheartbeats.blogspot.com
http://twitter.com/primitive_paint
Re: Triangles, parallellograms and Shimura curves: Maths!
142857 is a cyclic number — you can find its multiples simply by rotating its digits:
* 142857 × 1 = 142857
* 142857 × 2 = 285714
* 142857 × 3 = 428571
* 142857 × 4 = 571428
* 142857 × 5 = 714285
* 142857 × 6 = 857142
http://www.futilitycloset.com/category/sciencemath/
I love numbers me.
* 142857 × 1 = 142857
* 142857 × 2 = 285714
* 142857 × 3 = 428571
* 142857 × 4 = 571428
* 142857 × 5 = 714285
* 142857 × 6 = 857142
http://www.futilitycloset.com/category/sciencemath/
I love numbers me.
My apple pies go off today.
 lynsosaurus
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Re: Triangles, parallellograms and Shimura curves: Maths!
that is fucking cool.
we'll be god's tiny carrier pigeons
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Re: Triangles, parallellograms and Shimura curves: Maths!
i've now got a handy list of everyone on anorak i need to apply a chinese burn to if i ever meet them. carry on.
When the people are being beaten with a stick, they are not much happier if it is called 'the People's Stick.'
 gloom button
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Re: Triangles, parallellograms and Shimura curves: Maths!
assuming you're not playing championship manager at the time.
i may be the fellow anorak mentioned in the first post. my brother and i are doing this thing at the moment where we solve the problems on this website  http://www.projecteuler.net  where he does the computerprogramming parts and i (try to) do the maths part so that the program isn't just bruteforcing its way to a solution but doing something a wee bit more elegant. it's great, actually, it's the first time i've done any problemsolving in forever and the problems are pretty accessible and graded quite nicely as you go along. plus you get to laugh at other people's rubbish solutions once you solve one.
i may be the fellow anorak mentioned in the first post. my brother and i are doing this thing at the moment where we solve the problems on this website  http://www.projecteuler.net  where he does the computerprogramming parts and i (try to) do the maths part so that the program isn't just bruteforcing its way to a solution but doing something a wee bit more elegant. it's great, actually, it's the first time i've done any problemsolving in forever and the problems are pretty accessible and graded quite nicely as you go along. plus you get to laugh at other people's rubbish solutions once you solve one.
the trouble with personalities, they're too wrapped up in style
it's too personal; they're in love with their own guile
it's too personal; they're in love with their own guile

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Re: Triangles, parallelograms and Shimura curves: Maths!
The project Euler website looks great. On paper I should be good at that with a degree in maths and a job that involves computer programming, I bet I'm not though...
I shall return to this thread once I've remembered (asked my boyfriend to repeat to me) my favourite maths joke.
I shall return to this thread once I've remembered (asked my boyfriend to repeat to me) my favourite maths joke.
Re: Triangles, parallelograms and Shimura curves: Maths!
I became extremely moist when I learned that 0.999... is actually 1
http://en.wikipedia.org/wiki/0.999
The proofs are brilliant aren't they?
If I ever have the pleasure to meet JamieC in the flesh, he best not try to chinese burn me or I'll properly stab him up with my 30 60 90 set square.
http://en.wikipedia.org/wiki/0.999
The proofs are brilliant aren't they?
If I ever have the pleasure to meet JamieC in the flesh, he best not try to chinese burn me or I'll properly stab him up with my 30 60 90 set square.
My apple pies go off today.
 gloom button
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Re: Triangles, parallelograms and Shimura curves: Maths!
I have a degree in it as well, and feel guilty if I can't solve those things quickly! I'm quite pleased today though because I managed to solve a quite nice problem about pentagonal numbers and (I think) one about an arithmetic sequence of primes.Nicole Diver wrote:The project Euler website looks great. On paper I should be good at that with a degree in maths and a job that involves computer programming, I bet I'm not though...
I shall return to this thread once I've remembered (asked my boyfriend to repeat to me) my favourite maths joke.
(The only good maths joke I know is the one about the two cats on an inclined plane..)
the trouble with personalities, they're too wrapped up in style
it's too personal; they're in love with their own guile
it's too personal; they're in love with their own guile
 lynsosaurus
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Re: Triangles, parallelograms and Shimura curves: Maths!
that is one of my favourite jokes ever.gloom button wrote: (The only good maths joke I know is the one about the two cats on an inclined plane..)
we'll be god's tiny carrier pigeons
http://halfmyheartbeats.blogspot.com
http://twitter.com/primitive_paint
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 gloom button
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Re: Triangles, parallelograms and Shimura curves: Maths!
So actually in solving this problem I think I have something at least mildly interesting (or something I didn't know about before, at any rate). The problem is about arithmetic sequences of 4digit primes whose digits are permutations of each other, and given one (1487, 4817, 8147) you're asked to find the (only) other 4digit ascending sequence that there is.gloom button wrote:and (I think) one about an arithmetic sequence of primes.
And it turns out that the constant between the elements in that first sequence (3330) is the same as the constant between the elements in the other sequence, which seemed completely counterintuitive to me. Why should two moreorless unrelated sequences of primes have the same difference between each member. So we extended the program to look at sequences of more than four digits, and it turns out that that same difference, 3330, or multiples of it, keeps turning up as the constant between elements of sequences of primes. You get other constants as well  1450, 2970, etc  whose digits always sum to a multiple of 9, and I think I understand that part at least, because, taking a simple case, if you have a 2digit number 10a+b and you reverse the digits (10b+a) and subtract, you get 9(ba), and you get versions of that for other numbers.
And that's true of all numbers, actually, not just primes, but I still think that this is all a bit mysterious, and that there ought to be some interesting application to it somehow (so that, for instance, if you have a very large prime in an arithmetic sequence with a 3330 constant difference, you can tell where the next prime is  or something).
I did do other things this weekend too.
the trouble with personalities, they're too wrapped up in style
it's too personal; they're in love with their own guile
it's too personal; they're in love with their own guile
 indiehorse
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Re: Triangles, parallelograms and Shimura curves: Maths!
A few weekends ago, I started trying to explain a mathematical concept in the pub to a selection of other anorakers. I did a diagram and all. At no point did JamieC attempt to give me a Chinese burn.
Re: Triangles, parallelograms and Shimura curves: Maths!
And in any base.gloom button wrote:So actually in solving this problem I think I have something at least mildly interesting (or something I didn't know about before, at any rate). The problem is about arithmetic sequences of 4digit primes whose digits are permutations of each other, and given one (1487, 4817, 8147) you're asked to find the (only) other 4digit ascending sequence that there is.gloom button wrote:and (I think) one about an arithmetic sequence of primes.
And it turns out that the constant between the elements in that first sequence (3330) is the same as the constant between the elements in the other sequence, which seemed completely counterintuitive to me. Why should two moreorless unrelated sequences of primes have the same difference between each member. So we extended the program to look at sequences of more than four digits, and it turns out that that same difference, 3330, or multiples of it, keeps turning up as the constant between elements of sequences of primes. You get other constants as well  1450, 2970, etc  whose digits always sum to a multiple of 9, and I think I understand that part at least, because, taking a simple case, if you have a 2digit number 10a+b and you reverse the digits (10b+a) and subtract, you get 9(ba), and you get versions of that for other numbers.
And that's true of all numbers, actually, not just primes, but I still think that this is all a bit mysterious, and that there ought to be some interesting application to it somehow (so that, for instance, if you have a very large prime in an arithmetic sequence with a 3330 constant difference, you can tell where the next prime is  or something).
I did do other things this weekend too.
Octal :
71  17 = 52 (7)
Hex :
C1  1C = A5 (F)
Binary :
10  1 = 1
My apple pies go off today.
 Gordon
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Re: Triangles, parallelograms and Shimura curves: Maths!
Can be simplifed to "who are divisible by 9", surely.gloom button wrote: whose digits always sum to a multiple of 9
Toot toot.
 soft revolution
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Re: Triangles, parallelograms and Shimura curves: Maths!
That depends on whether your mathsglass is half full or half empty.
And by me, I mean, Flexo.
 Gordon
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Re: Triangles, parallelograms and Shimura curves: Maths!
No, I meant if the digits of x add up to a multiple of 9, then x is a multiple of 9.
Toot toot.
 Martijn
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Re: Triangles, parallelograms and Shimura curves: Maths!
It did so to me at first, but then, if you look at lengththree fourdigit arithmetic sequences, whose members are permutations of each other, then there is only a small number of possibilities for the difference. Knowing that the numbers all have to be prime leaves you with even fewer possibilities (because, for instance, the final digits either have to be all different, or all the same). So the fact both sequences have a difference of 3330 (and not, say, 450, which a priori is possibly too) still surpises me, but it's not as strange as it seems at first.gloom button wrote:And it turns out that the constant between the elements in that first sequence (3330) is the same as the constant between the elements in the other sequence, which seemed completely counterintuitive to me.
Random maths fact of the day: the only three arithmetic sequences whose members are cyclic permutations of each other and who are of maximal length are the ones starting with 148, 259 and 012345679.
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