The Maths Orgy Thread - The Bear and Badger

Yossarian

acemuzzy wrote:

Pix or it didn't happen

Surely in this thread it's 'show your working or it didn't happen'.

voices

n0face wrote:

I just used Pythagoras theorem at work, who says maths is useless.

I use numbers at work all day, but hadn't thought of myself as using maths until I thought about your post. As it turns out, I'm doing maths all day. Not hard maths, but still maths (mainly probability, stats and financial stuff). Exciting times!

Yossarian

When I worked in retail, I never used to key in the amount of cash I was handed at the till, I just worked out the change in my head. I was mathsing like a mofo.

n0face

You can shove your Euler's identity, this is grass roots maths.

acemuzzy

Division itt. Who'd have thought it.

dynamiteReady

I like teh maff'...

But I'z always ask for consent 1st.

...

Yeah... I've brought a brolly'

Blue Swirl

Ladies and gentlemen, introducing Belphegor's Prime, a palidromic number, consisting of the number of the beast with 13 zeroes (and a one) on each side. Total number of digits is 31, which is 13 backwards. YOU SCARED YET? YOU SHOULD BE.

1000000000000066600000000000001

cockbeard

I think he's stopped now but the guy who ran this blog was brilliant for interesting maths

http://matheminutes.blogspot.co.uk/2013/02/why-gove-is-wrong-about-long-division.html?m=1

Also loves digging on Gove, so win all round really

The Daddy

Each person that puts money into a charity collection tin puts in 3 coins amounting to 6p more than the person immediately preceding, if there was one. At the end there is exactly £1, it was empty to begin with.

How many people gave?

How do we know there can't have been 2 or 3 donors?

How do we know there can't have been 6?

Blue Swirl

The Daddy wrote:

At the end there is exactly £1, it was empty to begin with. How many people gave?

Sweet fuck all, given that there's only a quid in the tin.

cockbeard

Spoiler:

cockbeard

I remembered the word median part way through, I trust my answer but not my command of the terms or whether my working was most efficenct

Blue Swirl

cockbeard wrote:

Must be 5 people then

Dude, spoiler tags.

cockbeard

Oops, didn't think actually, these spoiler tags are new to me

Sorry

acemuzzy

Ironically, one more thing needs to be spoilered...

acemuzzy

I always like that the three next primes after 5 (i.e. 7, 11 and 13), which I kind of view as yucky numbers, multiply together to give 1001.

acemuzzy

OK another question.

You have a circular ring, and the temperature around it varies continuously (ie no jumps).

Prove there must be some point on the ring which is the exact same temperature as the ring directly opposite.

RamSteelwood

i like maths up to the limit of my mental arithmetic, which is just about the countdown numbers round. beyond that i find the concept interesting, but as soon as i see something along the lines of 'and then we put an imaginary number in and the formula works' i see at as a total swindle

Obviously i'm not really dismissing it all, but to my mind i can grasp pi and e cos they can be shown as 'proper normal real decimal numbers to an accuracy that is acceptable to me' (not sure what the official term for that is!)

i appears to be 'whatever 'number/concept' is convenient to make the formula work'.
playing around Euler's identity, i = (pi * i)/ pi
total scam!

cockbeard

I can't prove it, but logically it makes sense. The highest and lowest points must be directly opposite and therefore perpendicular to that the opposite temperatures must be halfway between each temperature and so the same

I kinda hear you Ram, but none of the numbers are imaginary, just sometimes tricky to conceptualise. I love the way it can introduce the ability to truly abstract, something I struggle with in more classic forms of art

RamSteelwood

acemuzzy wrote:

OK another question. You have a circular ring, and the temperature around it varies continuously (ie no jumps). Prove there must be some point on the ring which is the exact same temperature as the ring directly opposite.

cos (appropriate?) the temp would map to a sin/cos wave line that would repeat atleast once every 180 degrees?

cockbeard

Technically it repeats 360 degrees, but yeah that's a much more math way to describe it. It has the temp twice because once is on way up and once on way down. I could visualise it, but completely forgot about wave forms and the fact that they are math

acemuzzy

But the question wasn't limited to a sin/cos wave - what about a wigglier variation in temperature round the ring (but still with no jumps)?

voices

OK, this thread is dangerous. I'm going to stop there because I get sucked into these things and end up doing no work.

I'll map out what I expect the proof to look like, but I'm not sure if it really works. It relies on another proof.

Map the circle to a function defined between 0 and 1, which repeats between each number (like sine and cosine do). I can't remember the proper way to define this, but it's number that wrap round anyway.

We know f(x) = f(x+1)
We know that f(x) is a continuous function.
if there doesn't exist a point where f(x) = f(x+0.5) then either:

1) f(x) - f(x+0.5) > 0 for all x
2) f(x) - f(x+0.5) < 0 for all x
3) f(x) - f(x+0.5) < 0 for some x, f(x) - f(x+0.5) > 0 for the rest of the x

Under scenarios 1 and 2, we use a similar contradiction:

if f(x) - f(x+0.5) > 0 then (f(x) - f(x+0.5)) + (f(x+0.5) - f(x+1)) > 0, but this is equal to 0 by definition, so there is a contradiction (because f(x) = f(x+1) because it's a circle essentially).

Scenario 3 we can see that there is a discontinuity in the function f(x) - f(x+0.5) where it swaps between < 0 and > 0, but the sum of a continuous function is continuous, so there is another contradiction.

There's probably a way more elegant proof. Not 100% sure mine is correct.

davyK

We are going to need a better tag system to deal with the maths.....

RamSteelwood

acemuzzy wrote:

But the question wasn't limited to a sin/cos wave - what about a wigglier variation in temperature round the ring (but still with no jumps)?

clearly i just meant any kind of wave, when you apply the 'ramsteelwood constant of convenient curve repeats'...

cockbeard

So if min=0 and max=1, max at 12 if viewing as a clockface
1 wave means min at 6 therefore 0.5 at 3 and 9
2 waves mean min at 3+9, max at 12+6 and 0.5 at 1:30, 4:30, 7:30, 10:30
3 waves however place max at 12, 4 and 8, min at 2, 6 and 10, 0.5 at all odd hours, ah ok that seems like it would work actually
Ignore me now, I'm a foo'

Blue Swirl

cockbeard wrote:

Oops, didn't think actually, these spoiler tags are new to me Sorry

Actually, I was joking, but fair play. Just in case someone wants to work it out themselves.

voices

The more I look at my proof the happier I am with it. I work with lots of other maths type people (actuaries) and since this is much more interesting than actual work, it's likely to get discussed at lunch today.

voices

We reckon it's alright, and can't be bothered to sort it out so that it doesn't rely on the other proof.

What's the proper answer then?

dynamiteReady

Out of interest, What are proofs?

Howdy, Stranger!

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