Ask MetaFilter questions tagged with maths

Grapher: How do I animate a parameter?

b1tr0t — Sun, 01 Nov 2009 11:33:28 -0800

How do you animate a parameter in the OSX Grapher utility? There is an example called "Variable Parameter" that has a time line where T varies from 0 to 10. When you move the slider, the graphs are redrawn accordingly.

I'd like to do something similar, with different equations. But I can't seem to animate any parameters. I can create a system of equations with discrete steps (using curly brace notation) or do a parametric equation that varies continuously, but none allow me to animate a parameter.

Simple example:
I'd like to create an animation for y=sin(x+t) or even y=t*sin(x). How do I do that?

Permutations: an extension of the odd sock problem

Beautiful Screaming Lady — Tue, 01 Sep 2009 15:00:02 -0800

I've annoyed myself by getting stuck attempting to work out a silly maths problem relating to permutations. It's an extension of the 'how many odd socks do I have to pull out of a drawer before I find a pair' problem. Only my theoretical sock-wearer has three legs. And a penchant for odd socks. Let's say I'm Jake the Peg. I have s socks in a drawer. There are n different types of sock. On average, how many socks must I remove from the drawer before I get three odd ones?

I've worked this out from scratch using a drawer containing only 5 socks. Obviously, if all 5 socks are different (s=n=5), then there are 5! different ways of pulling the 5 socks from the drawer, and every single one of those leads to me having an odd triplet after only 3 socks.

If I only have 4 types of sock (i.e. in the drawer of 5, there's 1 pair and 3 odd ones), again, there are 120 ways of pulling all 5 socks out of the drawer, but this time there are only 60 unique sequences [I managed to work out from first principles that the number of unique ways of withdrawing the socks is s!/(s-n+1)!, not that that seems to help me at all ]. 84 of these sequences lead me to have an odd triplet after the first three socks. 36 of these lead me to have an odd triplet after the first four socks. At no stage do I need to withdraw all 5. So now the average number of socks I need to withdraw to get an odd triplet is (3x84 + 4*36)/120 = 3.3.

If I now only have 3 types of sock (i.e. in the drawer of 5, there are three black ones, a 'Worlds Best Dad' and a Homer Simpson), there are 20 unique ways of removing them all, and, if I've counted right, 37 ways of getting an odd triplet after 3 socks; 35 ways of getting an odd triplet after 4 socks; 48 ways of only getting an odd triplet after removing all 5 socks from the drawer. This leads to an average of 4.09.

My tiny brain is now too overheated to take this further. There must be a connection between these numbers, but I can't get a handle on a pattern, and am too daunted by the prospect of writing out all the variations of 720 sequences for a drawer of 6 socks to do it by brute force. Can anyone please put me out of my misery and point me towards a general formula for this, to solve the average number of socks necessary to achieve an odd triplet given s socks and n different types?

Help me figure out this sequence

phyle — Sun, 16 Aug 2009 04:55:29 -0800

Ive been tearing my hair out trying to work out a mathematical formula for a sequence of numbers I have. Have a look inside and tell me if you see a pattern. Im trying to reverse engineer a little section of a computer program, I enter the numbers below and get the result out. I have just written out a sample of different numbers I have entered in. I cannot work out what it is doing, there is obviously some rounding in there which is throwing me off..

0.01->2
0.02->3
0.03->3
0.04->3
0.05->4
0.06->4
0.07->4
0.08->4
0.09->4
0.10->5

0.1->5
0.2->6
0.3->7
0.4->7
0.5->8
0.6->8
0.7->9
0.8->9
0.9->10
1.0->10
1.1->10
1.2->11
1.3->11
1.4->11
1.5->11
1.6->12
1.7->12
1.8->12
1.9->12
2.0->12

3.0->14

4.0->16

10.0->22

100.0->46

1000.00->100

Anyone have any idea?

Time as a percentage

cantthinkofone — Thu, 13 Aug 2009 14:42:00 -0800

If something takes 2 hours to complete and is then re-run and takes only 1 hour ... is that 100% quicker or 50% quicker? MathsFilter - maths has never been my strong point! My google-fu has failed me as well.

Math? Maths? Mathesises? Mathelesalizes? Mathematisessizes?

fishmasta — Sat, 11 Jul 2009 20:21:17 -0800

When did "Maths" change to "Math" in American English? Or is it the other way around? I'm curious to know more about the origin of the math/maths break in the English language. Growing up in the United States, the shortening of mathematics to "math" has always sounded correct to me. But I know in the UK that "maths" tends to be more common. What I'm wondering is how/when/why this shift happened? Is it based on the long form spelling of "mathematics"? Is it based on the sound when pronounced (and is a teacher of other subjects with the "s" sound treated in a similar manner (e.g. a Sciences teacher rather than a Science teacher))? Or is it just one of those weird differences with no explanation other than that is how it's always been done? Any background you can provide is appreciated. Information on how other slight changes between our English forms happened is also welcome. Not as interested in total word differences (lorry/truck, lift/elevator, etc.) so much as the same word with slight variance.

How to maximise a matrix subject to constraints?

muhonnin — Sun, 14 Jun 2009 05:16:45 -0800

Optimisation problem: trying to find the subset of my data that meets a couple of constraints. I have a data set with 200 columns and 20 rows of numbers. I am trying to find the 20 columns that make the mean of all values in the resulting 20 x 20 data set as large as possible--subject to the constraint that no row in the 20 x 20 set can have a mean value below a particular figure.

I have access to a range of software tools (Excel, Mathematica, SPSS). I know how to specify the constraint if I were going for a brute force solution, but obviously that's not going to be feasible here. All suggestions greatly appreciated. . . . .

Stats/Maths filter: How do I solve a sigmoidal?

doctor.dan — Sun, 24 May 2009 20:53:44 -0800

I am trying to fit my data onto a sigmoidal function. The fit won't be perfect, but I am stuck with it for now. To help with this, I have been (very generously) given a spreadsheet that creates a sigmoidal curve if the values a, b, x0 and x are known. How do I get these values? The excel spreadsheet that I have implements a three-parameter sigmoidal function.

All I know so far is that x is my cutoff (70th percentile) which is solved using the restructured equation.

I've scoured the interwebs for help on this, but I can't for the life of me figure out how to solve for a and b, and what x0 is meant to be. All online resources I have found so far are either really basic (what is a sigmoidal function), or too advanced (how to fit real-time PCR to a sigmoidal function).

Any help would be great.

Getting Bachs number

southof40 — Mon, 13 Apr 2009 17:38:47 -0800

Interested to know more about the 'numbers' in JS Bach's music. Sometime ago I heard a radio programme about how some of Bachs music had patterns in which could be viewed as significant outside of what the music sounded like. I'm interested to know what this area of study/interest might be called and where can I (not a musician or a mathematician) read more about it ?

I realise that this all sounds a bit nutty but apparently this is an established field of interest/study ... !

(That radio programme was produced, I'm reasonably sure, by Deutsche Welle english language service. It was part of a series to mark 250 years since JSB died and it was really good so anyone who knew where that was online would get extra points !)

Game theory for people who like words and pictures?

vizsla — Mon, 26 Jan 2009 13:27:33 -0800

Best books, websites, lecture series on game theory and its applications for smart people who understand mathematics but can't stand trawling through pages of unnecessary complex formulae?

How does this calculator work?

missmobtown — Fri, 16 Jan 2009 12:28:02 -0800

How do mortgage calculations work? As an always-have-been-and-always-will-be renter, I've been free to ignore mortgages and how they're calculated. But now, for work, I need to understand how they're calculated. Specifically, I need to understand how the mortgage calculator on this page works:

https://www.uamc.com/locator/Calculators (select "What Will My Monthly Payments Be?" on the left panel)

Can this be distilled down to a mathematical equation that a programmer on my team would understand?

This is in California, if it makes a difference.

Did the earth move for you too?

genghis — Sat, 10 Jan 2009 12:24:08 -0800

GISfilter -- I have a PostGIS table containing spatial data in the form of a few thousand shapefiles. Anybody know a quick way I can move *all* of them by about 40 metres? Due to a bizarre set of circumstances I need to work with a data set of things contructed from GPS in Ireland. Because of a systemic error, every multipolygon I have is out of whack slightly. Boo!

Yet, because the country I live in is small enough for this to work, I can have a bunch of stuff accurate to within 2m if I globally move every multipolygon 50m to the North and 23.4m to the West. Yay!

But I'm too unfamiliar with both Postgres and Python (I'm working with Geodjango for the first time) to figure out which 10-line loop script will do that lateral translation for me. Boo!

So... um... can anybody lend me a hand here? I don't really care which language the one-use-ever script I need is written in. And my multipolygons are strings of co-ords using WGS84, where each X&Y value is separated by a space, and each pair separated by a comma.

The application of your collective genius is warmly appreciated.

"Beware of the Physicist."

daisyk — Fri, 12 Dec 2008 05:33:42 -0800

What might |000> + |111> mean, on a garden gate? This morning on the way to work, I passed a house where the garden gate bore a sign reading: |000> + |111>. (This isn't too surprising in Cambridge. My other favourite signs include "Silence" in Latin, Ancient Greek and Babylonian and "Don't lean bicycles here" in Latin and Ancient Greek.)

I'm at work now staring at a database, and it's been a few years since my last physics or pure maths courses. Can anyone suggest what the houseowners meant by their sign?

Help me relearn mathematics and its practica applications

dcbarker — Fri, 01 Aug 2008 05:19:32 -0800

Applied Math Filter: Help me use math! I'd like to learn more about mathematics and it's practical applications - particularly in Computer Science I'm a Computer Networking graduate (under 25) who never really done much math at university. My course was somewhere between computer science and communications engineering so maths sort of slipped through the cracks.

Now, I'm looking to re-learn math. I know that a lot of mathematics is abstract but I'm having difficulties seeing practical applications.

Where I'm at:
I took calculus at high school but just scraped through (I spent more time fighting with the teacher than learning). I don't remember a bit of it. I'm pretty much at "square one" so will be learning from the start. I consider myself a quick learner in most areas but had a horrible foundation in math so never picked it back up. I've bought a couple of math books which should teach me the theory I need. I've always thought graphing calculators were pretty interesting but lack the mathematical knowledge to necessitate their use (or purchase). I'm currently in the process of ditching my "college job" to go for a "real job".

What I want:
I want to learn math with a view to using it practically (preferably in computer science).

How you can help:
I'd like suggestions on how I should go about learning mathematics and its practical applications. Which areas should I look at if I want to use mathematics in computing? I think my problem is that I can't see a practical application for math that I'd like to explore but I have a strong urge to develop my mathematics skills.

Any help would be greatly appreciated! Thanks!

How can I help my (nearly) seven year old son "get" maths?

h00py — Wed, 30 Jul 2008 03:00:14 -0800

How can I help my 6 1/2 year old son to *get* maths? It hasn't clicked with him at all and I find myself getting frustrated with having to repeat really basic stuff when helping him with his homework. I'm not a maths genius myself and I really don't want to put him off by getting cranky because he's just not getting it. How do I help him get it? He's a really very bright little fellow who can read exceptionally well and his vocabulary is excellent. He's good with words. It's numbers that he hasn't come to terms with yet. Reading the clock, money, simple addition (and subtraction); all of these things are not within his frame of reference at the moment. How can I help him get the decimal system? I figure that once he's got the whole 'there's only 9 numbers and zero and then you go up a notch and then another notch and so on' at least he'll have somewhere to work from.

He doesn't have to become a mathematician, I just want him to find a good place to start so it all makes some sense. At the moment, he's baffled.

%

dydecker — Fri, 13 Jun 2008 13:41:08 -0800

I am useless at mathematics. If company A grows at 5% a month, how much bigger is it after one year? Answers in percentage terms

Best way to tile a sphere ?

silence — Mon, 02 Jun 2008 07:07:53 -0800

How can I tile a sphere using the minimum number of differently shaped units? I have a 3 meter diameter sphere and I need to tile it using units that are each about 400 square cm (ie like a 20 x 20cm square). The units must be flat (ie, not spherical triangles). I'm currently thinking of using a geodesic tiling, but a (for instance) a 5V geodesic tiling results in (i think) 6 different tile shapes, and also has the problem that the density of tiles isn't constant over the surface - there are obvious visual artefacts where the tiles bunch up. I need to try to minimise the number of different types of unit, and to optimise the appearance so that it's as even as possible. Are there any better ways of tiling a sphere?

How can I implement an s-curve function in excel?

matholio — Wed, 16 Apr 2008 17:48:00 -0800

How can I implement an s-curve function in excel? I have some programming experience, but my maths is crap.
I want a generic function to use to to effect a smooth transition between two numbers. Asigmoid funtion seem useful.

I have read throught these pages :
http://en.wikipedia.org/wiki/Sigmoid_function
http://www.computing.dcu.ie/~humphrys/Notes/Neural/sigmoid.html

But my poor math skills stop me from implementing it.
I do not understand how to transfer the equations I see in to code, or excel.

Much of the problem is I can't properly read and understand the notation used in math functions.
I did ask in an IRC math channel, but several people laughed.

If someone could show me how to implement the sigmoid function in excel, it would help me learn.

Thanks

Silly question about flashing...

twine42 — Wed, 06 Feb 2008 07:44:13 -0800

I have a question about persistence of vision and flashing lights... There will be maths and biology involved. Imagine you have two LEDs. They each produce one hypthetical unit of light (1 HUL if you will). If they're both turned on, they produce a combined 2HUL.

Now imagine that they flash at a rate greater than 25fps in a way that when one is on the other is off.

Ideally they are producing 1HUL. In reality the light up time probably means it's a little less than this. But here is my question:

What does the human eye *think* they are producing? Do you see the equivalent of 1HUL, 2HUL or somewhere in between? Does it matter if you are looking directly at the LEDs or at a surface being illuminated by them?

I've used 25 fps here since with cartoons a frame rate above 25 fps creates a moving image... it may be a red herring.

Tips for university teaching

onoclea — Wed, 12 Dec 2007 12:25:09 -0800

Teaching a university course for the first time: any tips or suggestions? A friend of mine is preparing to teach his first university course, calculus for non-math majors. He has given single lectures and many seminars before on other more advanced topics, but this is the first time he will be carrying a whole course, on calculus, and with an audience of this size. He's a quiet guy, works really hard, takes this commitment very seriously, wants to continue in academia, and obviously wants to do a good job! Any tips, suggestions, warnings, recommendations, revelations, wake-up calls, etc. would be very much appreciated! Thanks.

Why the inconsistent derivatives?

PuGZ — Sat, 03 Nov 2007 01:01:37 -0800

Where am I going wrong with this (very simple) implicit derivative? I have an equation: xy + y^2/x = 2. I solve it this way:

(1 * y) + (x * dy/dx) + (2y*dy/dx * x^-1) + (y^2 * -x^-2) = 0
dy/dx(x + 2y/x) = y^2/x^2 - y
dy/dx((x^2 + 2y)/x) = (y^2 - x^2 * y)/x^2
dy/dx = (y^2 - x^2 * y)/(x^2) * x/(x^2 + 2y)
dy/dx = (y^2 - x^2 * y)/(x^3 + 2xy)

Now, the answers I have before me say the correct method is:

x^2 * y + y^2 = 2x
(2x * y) + (dy/dx * x^2) + (2y * dy/dx) = 2
dy/dx(x^2 + 2y) = 2 - 2xy
dy/dx = (2 - 2xy)/(x^2 + 2y)

Both of these appear correct to me, but the end result is different in each case? Can someone explain the ludicrously obvious mistake I am making?

Maths: Help me!

cholly — Wed, 24 Oct 2007 18:26:57 -0800

Time for a ridiculous math question: I've got F=255M^(-1.08) and I need to work out M. It is driving me crazy that I can't work this out.

[[not a homework question]]

Thanks in advance!

Inequalities and direction-flipping

PuGZ — Fri, 19 Oct 2007 22:00:46 -0800

Why is it that when I solve the inequality 0 ≤ arccos(x) <> cos(π/4)? Why do the operators switch direction? I understand that when multiplying or dividing by a negative number, the operators switch direction - but why is this the case for functions?

mathematics chess book?

randomizer — Thu, 18 Oct 2007 16:21:49 -0800

is there a book on the mathematics of chess? i've been looking for a book that deals with the mathematics or/and game theory of chess, but i'm not having much luck. is there a chess book that deals with the mathematics/game theory?

Difficult as ABC

londongeezer — Sun, 16 Sep 2007 14:35:54 -0800

ABC x D = BADC. What single numbers (1-9) do the letters represent? Is there any way to arrive at the answer (a) by logical deduction all the way rather than with some trial-and-error and (b) so that a 10-year-old can follow the logic? By trial-and-error I mean, for example, having deduced that C might be, e.g., 5 (whereas it couldn't be, e.g., 3), then experimenting with various values for D (3, 7, 9) and so on. That's one way to get to an answer, but I'm hoping there's a more purely deductive route.

Equation solving help for the intellectually challenged

prentiz — Mon, 04 Jun 2007 06:49:22 -0800

(x + y)-(x*y)=79. What are x and y? I know that, once upon a time I knew how to do this - sadly it must be in one of the parts of my brain knocked out by decades of alchol. Apparently neither are allowed to be 0 - which ruled out my boss' solution. Any help much appreciated - particularly if you show your working out!