Ask MetaFilter questions tagged with maths
http://ask.metafilter.com/tags/maths
Questions tagged with 'maths' at Ask MetaFilter.Wed, 26 Nov 2014 20:56:38 -0800Wed, 26 Nov 2014 20:56:38 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Seeking advice about teaching maths
http://ask.metafilter.com/272150/Seeking%2Dadvice%2Dabout%2Dteaching%2Dmaths
I'm interested in teaching high school students mathematics through a tutoring agency. I have the required experience in mathematics, but very little in teaching. This doesn't seem to be a massive problem for many tutoring agencies, but I want to know: do you have any specific tips/advice about teaching mathematics? And more broadly, any advice about applying for and going to work for a tutoring agency? I'm a big fan of maths, and very interested in teaching it. I don't simply like it because 'there's only one right answer' etc, I like it for a frajillion reasons: the beauty of elegant proofs, the fun of problem solving, and the fact that it underlies the functioning of the universe as we know it. Heck, I do maths in my spare time. I make lame maths jokes. I am ready to accept that I am a fully-fledged maths nerd.<br>
<br>
I understand that enjoying maths is not the same as being capable to teach it. I have gone through much of the high school maths syllabus (I am in Australia) and understand how to teach it from first principles.<br>
<br>
Anything you can give me that would help me more ably engagingly teach mathematics to potential future students would be much appreciated.tag:ask.metafilter.com,2014:site.272150Wed, 26 Nov 2014 20:56:38 -0800QuilfordMr. Hammond, I should have listened.
http://ask.metafilter.com/271436/Mr%2DHammond%2DI%2Dshould%2Dhave%2Dlistened
I want to calculate a sequence. It's built on some kind of exponential magic. That is as much as I know. Please hope me. Said sequence is <a href="http://www.rhdesigns.co.uk/darkroom/html/f-stop_printing.html">here</a>. Repeated below:<br>
<br>
<pre><br>
1) 4.0, 4.7, 5.6, 6.7, 8.0, 9.5, 11.3, 13.5, 16.0...<br>
<br>
2) 7.5, 8.9, 10.6, 12.6, 15.0, 17.8, 21.2, 25.2, 30.0...<br>
</pre><br>
<br>
I threw some numbers at the screen and I thought I had it solved:<br>
<br>
4.00**0.125 == 4.75<br>
4.75**0.125 == 5.65<br>
5.65**0.125 == 6.72<br>
...<br>
<br>
but that doesn't work with the sequence that starts with 7.5.<br>
<br>
I understand that we have: 4, 8, 16, 32 and 7.5, 15, 30, 60. But how are the 1/4 intervals calculated?<br>
<br>
My brain hurts. Please, could someone hold my hand?tag:ask.metafilter.com,2014:site.271436Wed, 12 Nov 2014 15:17:59 -0800popcassadyWhat are the best textbooks on climate science?
http://ask.metafilter.com/271278/What%2Dare%2Dthe%2Dbest%2Dtextbooks%2Don%2Dclimate%2Dscience
I'm looking for climate science textbooks that take a mathematical approach: that go in-depth with the maths of modelling etc. I'd appreciate if they also had a focus on the science of anthropogenic climate change / global warming. Can you recommend any? Thanks, MeFites!tag:ask.metafilter.com,2014:site.271278Sun, 09 Nov 2014 15:17:39 -0800QuilfordLesser-known women in technology
http://ask.metafilter.com/268520/Lesser%2Dknown%2Dwomen%2Din%2Dtechnology
Who are some important women in technology that are lesser-known in the world? Especially women of color, LGBTQ women, and non-American women? I'm currently editing profiles for a major project on women and technology, and am collecting suggestions for other women to profile. I'm especially interested in women of colour, LGBTQ women, and women outside the US and Europe (though they don't have to be exclusively from those categories). I'm also interested in women that are involved in tech but not directly with computers (e.g. gaming or arts).<br>
<br>
So far we have:<br>
Anita Borg<br>
Ada Lovelace<br>
Juliana Rotich<br>
Rebecca Enonchong<br>
Kimberly Bryant<br>
Hind Hobeika<br>
Rana el Kaliouby<br>
Marissa Mayer<br>
Limor Fried<br>
Hypatia of Alexandria<br>
Marie Curie<br>
Wangari Maathai<br>
Anandibai Joshi / Keiko Okami / Sabat Islambouli<br>
<br>
The women can be historical or contemporary, alive or dead.tag:ask.metafilter.com,2014:site.268520Mon, 15 Sep 2014 13:09:01 -0800divabat4x+y+2z=100, x>y, y>z, x+y+z=j, 3x+z=k, j>k, j+k=100.
http://ask.metafilter.com/265560/4xy2z100%2Dxy%2Dyz%2Dxyzj%2D3xzk%2Djk%2Djk100
4x+y+2z=100, x>y, y>z, x+y+z=j, 3x+z=k, j>k, j+k=100. WolframAlpha can only give me alternative forms or a solution involving 'real and imaginary parts of z'. Is there a solution I can count on my fingers? I wish to buy a thing. The thing I buy will have two desirable characteristics: j, and k.<br>
<br>
j comprises three sub-characteristics, while k comprises four sub-characteristics.<br>
<br>
I have three levels for ranking how important these sub-characteristics are to me - let's say 'super important', 'kinda important' and 'meh, whatever'. Obviously, they are of decreasing importance.<br>
<br>
I have rated the three sub-characteristics for j 'super important', 'kinda important' and 'meh, whatever'.<br>
<br>
I have rated three of the four sub-characteristics for k 'super important', and the fourth 'meh, whatever'.<br>
<br>
This means I have a total of four 'super important', one 'important', and two 'meh, whatevers'.<br>
<br>
Finally, j is a little bit more important to me than k. If further defining these variables help, then I think they'd be about a 60/40 split, though I'm flexible. They can be equal if that helps. At this stage I'd settle for k being less than j if it means a solution pops out.<br>
<br>
I would like to assign positive numbers to x, y and z, because I'm a bureaucrat, that's why.<br>
<br>
So, <br>
<br>
x>y (must)<br>
y>z (must)<br>
<br>
j = x + y + z<br>
k = 3x + z<br>
4x + y + z = 100 (per cent)<br>
j + k = 100 (per cent)<br>
<br>
I can't change the number of characteristics, sub-characteristics, or levels of importance. <br>
<br>
I could make k=2x+y+z, and so change the overall equation to 3x+2y+2z, but I'm not smart enough to know if that helps. It didn't help WolframAlpha.</j>tag:ask.metafilter.com,2014:site.265560Tue, 22 Jul 2014 18:07:45 -0800obiwanwasabiWhat to include in a training on maths for business people?
http://ask.metafilter.com/255311/What%2Dto%2Dinclude%2Din%2Da%2Dtraining%2Don%2Dmaths%2Dfor%2Dbusiness%2Dpeople
I've been asked at work to come up with a list of topics that could be included in a training course around basic maths for business people, and I am finding it hard to find suggestions for topics. It should all be structured around business examples and use cases, so mean, medium and mode probably make sense whereas an intro to calculus doesn't. Anything I put in is supposed to be something they can actually use, either at this stage of their career or later, but the assumption is they remain in sales/marketing and don't go on to be an analyst or anything like that. I think I may just be mentally blocked on the topic. Any thoughts from the hive much appreciated.tag:ask.metafilter.com,2014:site.255311Tue, 14 Jan 2014 15:56:07 -0800StephenFHelp me understand fractions
http://ask.metafilter.com/243209/Help%2Dme%2Dunderstand%2Dfractions
Dear math people: please help me understand fractions and ratios <em>intuitively</em>. I feel really embarrassed about this, but I must have missed a fundamental period when I was learning fractions as a child because I have a really hard time with understanding them intuitively. I am hoping someone can help me to see where my understanding breaks down and how I can make it more intuitive.<br>
<br>
I know what fractions are and I fully understand addition and subtraction of fractions. I can also convert fractions (thought I don't remember the term for this). I think this is because I like to bake so when I think of adding or subtracting fractions, I always imagine cups of flour or something. So 2 1/2 + 1/3 makes perfect sense to me because I can picture it. I know that I need to find a common measurement (denominator) and the easiest way (but not the only way) to do that is to multiply both denominators. So, I would convert so I have this:<br>
<br>
5/2 + 1/3<br>
<br>
make them have common denominators:<br>
<br>
15/6 + 2/6 = 17/6 = 2 5/6<br>
<br>
That part is easy for me! Makes total logical, intuitive sense. <br>
<br>
Multiplying and dividing fractions make no sense (maybe because I never have to do it in real life??). So I have to rely on remembering the "rules" (which I can never remember). I guess (because I looked it up) that to multiply you just multiply both numerators and then multiply both denominators. But to divide you have to flip one of the fractions and then multiply across. Anyway, I get that the rules are simple but this doesn't make logical sense to me (like why you would flip the fraction). <br>
<br>
So to bring this into real life matters where it is really bothering me is something like the P/E ratio. Here are the "rules" I know about it:<br>
<br>
- market value of share divided by earnings per share<br>
- a higher P/E means people think the company has better potential for future earnings growth<br>
- PE ratios are only comparable to similar companies<br>
<br>
What I don't understand is the logic. So if someone asks me - "what happens to the PE ratio if a company's earnings per share falls?" I see this as what happens to the fraction itself if either the numerator or denominator or both rises or falls. The ONLY way I can figure this out is literally by trial and error using normal numbers. This is literally what I do:<br>
<br>
20/5 = 4<br>
20/4 = 5 <br>
<br>
So if the <strong>numerator falls</strong>, the fraction solution <strong>rises</strong>. So if the above were a PE ratio, the PE ratio would go up, which means the market thinks the company has better future growth prospects than it did before (extrapolating, if the EPS has gone down but the share price stays the same, the market thinks the lower EPS is temporary, but still has faith in the company because the share price hasn't changed and the EPS doesn't fully reflect the value of the company or whatever. THIS PART DOESN'T REALLY MATTER FOR THE PURPOSES OF MY QUESTION).<br>
<br>
Another example would be financial/balance sheet ratios where understanding intuitively how fractions work and what it means when the numerator or denominator changes is super important to understand the balance sheet and the company. So if I wanted to look at net profit margin, the ratio is:<br>
<br>
Net income/revenue<br>
<br>
And if someone asked what decreased revenue means for a company's net profit margin, I would like a way to understand this intuitively through my understanding of fractions (and not my understanding of how companies and economies work) without having to use my manual trial and error divisions of twenty that I used above, Does that make sense? To make it perfectly clear:<br>
<br>
Variable A/Variable B = Bigger Picture XYZ<br>
<br>
What are the implications for Bigger Picture XYZ if Variable A changes?<br>
<br>
PLEASE HELP. Where is my understanding of fractions breaking down???tag:ask.metafilter.com,2013:site.243209Wed, 19 Jun 2013 16:34:52 -0800Anonymousminimise syntax errors in secondary school maths exams using Mathematica
http://ask.metafilter.com/242795/minimise%2Dsyntax%2Derrors%2Din%2Dsecondary%2Dschool%2Dmaths%2Dexams%2Dusing%2DMathematica
In high school maths exams students when use Mathematica to solve problems, a syntax error that costs a lot of time to find can lose a student a lot of marks. What strategies can teachers use to reduce the risk or cost of syntax errors to students sitting high-stakes exams? I'm asking this one for Mrs Kandinski. She's a substitute maths teacher in an Australian (Victorian) secondary school that uses Mathematica both in lessons and in exams. Students have to sit a maths exam using Mathematica as a tool to solve problems. Students in many schools use CAS calculators instead, like the TI-Inspire line. Compared to using CAS calculators, the school believes that Mathematica offers the students a better learning environment and the opportunity to acquire some skills that are transferable and will be more useful in the future. <br>
<br>
The problem with using Mathematica is that, in an exam situation, students risk losing a great deal of time to syntax errors. The exams are state-wide and very high stakes for the students and the school (university entry relies on these exams). CAS calculators are not as "risky" to use, in this regard, as Mathematica. So she is asking whether anyone can explain their strategies to minimise the cost to students of making simple syntax errors in exams.<br>
<br>
This must be a problem for teachers in IT or programming subjects at similar levels (end of high school, start of university). So maybe teachers in other fields would have some insight or suggestions.<br>
<br>
The school is heavily invested in using Mathematica for this, and believes that the overall benefits outweigh the risks, so just changing back to CAS is not an option for solving this problem.tag:ask.metafilter.com,2013:site.242795Wed, 12 Jun 2013 20:44:12 -0800kandinskiDealing with percentages: noob question
http://ask.metafilter.com/241788/Dealing%2Dwith%2Dpercentages%2Dnoob%2Dquestion
I've recently decided to transition to a new career path, accounting. Most firms round here do an online numeracy test as part of the application process.
There is a type of % change question that often comes up and I can't find a proper answer about how to calculate it.
There are two formulae suggested by different websites, but they give different answers. Which is right? (details inside) A common question is: <br>
<br>
"The share price of Mapple Inc is 545. Last year it was 15% lower. What was the share price last year?"<br>
<br>
<strong>Method one:</strong> 545 x 0.85 = 463.25<br>
<br>
Although this is recommended by a couple of (fairly reputable!) places it seems to be wrong. Trying to reverse the percentage change to check it, 463.25 x 1.15 does NOT equal 545.<br>
<br>
<strong>Method two:</strong> 545 / 1.15 = 473.91<br>
<br>
This looks like the correct method. <br>
<br>
I've never been numero uno for maths. So mathematically inclined folks, is the second method definitely the right one?tag:ask.metafilter.com,2013:site.241788Tue, 28 May 2013 04:02:17 -0800NoiselessPenguinMasters in maths? Difficulty level: Have bachelors in graphic design
http://ask.metafilter.com/238267/Masters%2Din%2Dmaths%2DDifficulty%2Dlevel%2DHave%2Dbachelors%2Din%2Dgraphic%2Ddesign
Dear Mefites, a long time ago I got a degree in graphic design but never worked in the industry. Along the way I somehow (don't remember how or why or when) became interested in math and I finished a <a href="http://www.londoninternational.ac.uk/courses/diploma-graduates/lse/diploma-graduates-mathematics">graduate diploma in maths</a> as a distance learning course in my free time. I am considering applying for masters programmes in maths or related subjects but ... can I? Should I? To give a little more background, I'm interested in what I perceive as stuff related to applied maths: meteorology, language processing, cryptography, etcetera. But I'm also wondering how I can relate these sorts of interests to jobs or careers ... <br>
<br>
I've seen <a href="http://www.math.smith.edu/center/">center for women in mathematics</a> and <a href="http://www.bu.edu/eng/academics/special-programs/leap/">LEAP</a> but I'm not a US citizen and I can't afford to attend those. Also, I have no access to education I'm interested in where I live, hence I'm considering becoming an international student in the EU. I have some savings but by no means can I afford to get a second bachelors degree ...<br>
<br>
I've also tried looking for work in related fields so I could get a feel for them but right now I'm just stuck at an awful data entryish job that I hate so much.<br>
<br>
And also sometimes I feel like I'm so stupid that I just shouldn't be attempting this at all ... argh!<br>
<br>
I'd appreciate any advice! Thank you!tag:ask.metafilter.com,2013:site.238267Sun, 31 Mar 2013 11:08:49 -0800Cat Set GoWeighted mean
http://ask.metafilter.com/232176/Weighted%2Dmean
Mathematics-filter: If there are seven funds with various charges, how can I work out the allocation to these funds of a fixed amount so that the weighted mean charge is below a certain level and the allocations are of similar sizes? Background: I'm looking at putting some of my savings in index trackers. In order to try and balance risk, I would like to spread my savings around various tracker funds, which have varying levels of charges. I would like to keep charges below a certain level, and try and keep the investment in each fund roughly similar (otherwise the risk isn't so evenly spread).<br>
<br>
The seven funds have the following charges:<br>
Fund 1: 0.57%<br>
Fund 2: 0.57%<br>
Fund 3: 0.59%<br>
Fund 4: 0.62%<br>
Fund 5: 0.62%<br>
Fund 6: 0.65%<br>
Fund 7: 0.71%<br>
<br>
My (admittedly extremely limited) maths skills are failing me - the closest I could get was the allocation of savings (i.e. weighting) for each charge rate, but then this leaves those funds with the same rate receiving half of the relevant allocation, which means that the amount in each fund is not balanced.<br>
<br>
How can I work out what percentage of my savings should be placed in each fund so that the average charge is 0.58% or lower, whilst the amount in each fund is as similar as possible?tag:ask.metafilter.com,2012:site.232176Mon, 31 Dec 2012 10:07:48 -0800djghHuman Random Generator
http://ask.metafilter.com/231631/Human%2DRandom%2DGenerator
Can you think of a method that allows an individual to pseudo randomly create a sequence of numbers (at the very least the randomness is opaque to the minds of other people) assuming said individual may only use his mind and body (no physical tools are allowed)? Some use cases to test this method:<br>
* tell someone a number between 1-100<br>
* select 10 out out of 20 doors and select 5 out of those 10<br>
* create a string consisting of 10 ascii characters<br>
* select a date and time (YYYY-MM-DD, HH:MM)tag:ask.metafilter.com,2012:site.231631Fri, 21 Dec 2012 16:47:33 -0800Foci for AnalysisSherlock as a Mathematical Logician?
http://ask.metafilter.com/230997/Sherlock%2Das%2Da%2DMathematical%2DLogician
A colleague alluded to a passage from Sherlock Holmes where all the evidence is re-written as formal logic propositions, leading to a mathematical solution that matches Holmes' solution (and is far from trivial). Does anyone else know where I could find this passage? I'm a maths teacher and will be teaching Logic to top level year 11s in the new year, and this sounded interesting. Unfortunately, my google-fu is only turning up introductions to logic with quotes from Sherlock Holmes, rather than the full passage with formal logic notation beside it - I would *really* appreciate any help.<br>
<br>
Thanks :)tag:ask.metafilter.com,2012:site.230997Wed, 12 Dec 2012 19:01:43 -0800Anon YmousWhat should my sample size be?
http://ask.metafilter.com/228707/What%2Dshould%2Dmy%2Dsample%2Dsize%2Dbe
Say that I have a bag which contains 100 balls and every ball in the bag should be red, but it's possible that one or more of these balls is the wrong colour. How many balls should I look at to be 90% sure that all the balls are red? Or 95%? Or 99.9%? Talk me through how to work this out, please?tag:ask.metafilter.com,2012:site.228707Mon, 12 Nov 2012 08:36:03 -0800xchmpPercentage Calculation
http://ask.metafilter.com/227053/Percentage%2DCalculation
I know the price of something now and what the price was 2 years ago - how do I calculate that as an annual percentage increase? I live in Argentina where inflation is (unofficially) estimated at 25% annually. I remember that 2 years ago a kilo of ice cream at my local shop was 29 kilos. It's now 48 pesos. That's a 71% increase over 2 years - how do I calculate that on an annual basis (assuming the same increase each year)? <br>
<br>
I've worked it out using trial and error, but I'm looking for a formula I can use and apply to other figures.tag:ask.metafilter.com,2012:site.227053Fri, 19 Oct 2012 16:15:51 -0800jontyjagoWhat part of the earth gets the most moonlight?
http://ask.metafilter.com/226118/What%2Dpart%2Dof%2Dthe%2Dearth%2Dgets%2Dthe%2Dmost%2Dmoonlight
Is there any place on Earth that gets the most moonlight? Hey astronomers! I don't know if this even makes sense to ask, but my partner and I have been kicking around whether there is any place on Earth that gets what could be described as the most moonlight. Moonlight only counts as times where it is only the moon showing, not also the sun (since it's reflected light from the sun, I know this seems arbitrary, but I'm not looking for just visible moon, since the light really does look different). <br>
<br>
Is there any way to determine this?<br>
Does the whole Earth get the same amount of moonlight per year? <br>
How would one even start to figure this out (astronomy was many years ago)?tag:ask.metafilter.com,2012:site.226118Sat, 06 Oct 2012 15:49:35 -0800zinfulHow do I calculate the probability of a specific sum of repeated die rolls?
http://ask.metafilter.com/225560/How%2Ddo%2DI%2Dcalculate%2Dthe%2Dprobability%2Dof%2Da%2Dspecific%2Dsum%2Dof%2Drepeated%2Ddie%2Drolls
I'm looking to learn how to calculate probabilities for a multi-round dice game. I've researched this question some, and it looks like I might need to know how to use the multinomial distribution, but I can't find any good introductions. Please point me to the most layman-accessible educational material on this subject, and help me to help myself. The game I'm playing can be abbreviated like this:<br>
<br>
I roll two six sided dice and add them.<br>
I then subtract a (fixed) penalty value, and score as many points as remain.<br>
I cannot score less than 0. If I would score less than 0 points, I score 0 instead.<br>
I repeat this process several times, without altering the penalty between rolls.<br>
<br>
How do I predict the probability of any 1 particular cumulative score?<br>
I am not interested in simulating this event and taking a random sample; I want to calculate all possible outcomes and their precise probabilities. Examples follow:<br>
<br>
<br>
Example #1:<br>
My penalty value is 0, and I repeat the die roll 36 times.<br>
Each roll will produce a number between 2 and 12 inclusive, and my final score will be between 72 and 432. What is the chance that I will score 7 points exactly 6 times.<br>
<br>
Example #2:<br>
My penalty value is 11, and I repeat the procedure 40 times.<br>
Each roll will produce a value between 0 and 1 inclusive, and my final total score will be between 0 and 40, and likely closer to 0 than 40.<br>
I wish to predict the chance that I will score a cumulative total of exactly 2 points across the sum of all 40 trials.<br>
<br>
Example #3:<br>
My penalty value is -5, and I repeat the procedure 5 times.<br>
Each roll will produce a value between 7 and 17 inclusive (negative penalty). I wish to plot the probability of a arriving at each possible total: 35 through 85. <br>
<br>
Again, I think maybe this is a case of the muiltinomial distribution, but everything I can find about it (wikipedia) is confusing and not written as educational but as reference material. <br>
<br>
I'm familiar with MS Excel and have a basic Liberal Arts understanding of calculus and probability/statistics, though I'm quite rusty. I'm willing to re-learn what I have forgotten, and also to learn new skills - within reason. If this procedure requires me to learn lots of new math, I would appreciate links or book titles to pursue as well as a general outline of what the fields of study are called, and what I'll need to know to pursue them intelligently (i.e. help me ask questions without sounding ignorant/clueless). <br>
<br>
I gather that the program R might be helpful in this, so please feel free to recommend a good introduction to both R and Statistics.<br>
<br>
Thanks for any help you're able to give!tag:ask.metafilter.com,2012:site.225560Fri, 28 Sep 2012 22:16:58 -0800Richard DalyGetting my math(s) right.
http://ask.metafilter.com/219663/Getting%2Dmy%2Dmaths%2Dright
Maths (math) people of the US: I need your help in working out if certain British conventions would be understood or standard in the US classroom. I'm working on some text that will be read by schoolkids in the US. There is a fair bit of math involved, and while I'm confident I've "translated" most of it properly there are a few things I'm not sure about:<br>
<br>
1. "The formula that describes the steps can be applied to find any triangular number, where T(n) is the sum of the numbers from one to n"<br>
<br>
Is T(n) correct in the US here?<br>
<br>
<br>
2. "Firstly, Newton developed differential calculus, a method for calculating the gradient of a curve on a graph."<br>
<br>
Should "gradient" be "slope" here?<br>
<br>
<br>
3. Vectors/coordinates. I have the sentence "To calculate the vector that describes the movement of an object between two points, like an aeroplane, the coordinates at point A are subtracted from point B" illustrated with something like:<br>
<br>
B(2, 10, 4) - A(5,0,5) = AB (-3,10,-1)<br>
<br>
<em>except that there the numbers in the parantheses are piled on top of each other rather than being separated by commas, as in the numerous examples<a href="http://www.netcomuk.co.uk/~jenolive/vect17.html"> in this link</a><br>
AND <br>
there is a right-facing arrow above "AB"</em><br>
<br>
Is this how this should be presented in the US?<br>
<br>
<br>
4. "The gradient of a straight line is calculated by dividing the change in vertical height by the change in horizontal distance. At first, the flat ocean bed has a zero gradient – there is no slope at all. Despite moving only a few millimeters each year, folds develop over time, and a slight gradient of 0.1, or 10%, builds up. Over millions of years the fold mountain continues to grow and, as the gradient gets steeper, it rises above sea level. "<br>
<br>
Again, should all of these "gradient"s be "slope"s? Or should they be "grade"s, because we're talking about mountains? Or a mix of the two?<br>
<br>
<br>
Thanks for your help!tag:ask.metafilter.com,2012:site.219663Tue, 10 Jul 2012 08:53:13 -0800cincinnatus cTaking the random out of racking
http://ask.metafilter.com/212195/Taking%2Dthe%2Drandom%2Dout%2Dof%2Dracking
After tens of thousands of games of pool, every time I rack the balls I seem to switch about half of them around. I know I'm wasting time. So, I want to know exactly how many balls I should <em>normally</em> expect to swap (the median), and what is the most I should <em>ever have</em> to swap. For those of you who aren't pool nerds like me, I've explained the 8-ball racking process inside. A "proper" rack should look something like <a href="http://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Rack_8-pool.svg/567px-Rack_8-pool.svg.png">this</a>.<br>
<br>
There are 15 balls. 7 "stripes", 7 "solids", and one black ball.<br>
<br>
You dump them into the triangle at random, then swap them around until you have the "correct" pattern. There are two different recognised patterns (European and American), but we'll pretend there's just one. <br>
<br>
You can either start that pattern with stripes at the front, or solids. You can also reverse the pattern in terms of symmetry. As such, I think there are four ways of racking the balls correctly.<br>
<br>
However, once the balls are in, you can spin the triangle into three positions, giving you 12 total possibilities. <br>
<br>
There is a complication: the black is the only ball that has to sit on one of the inside three spots.<br>
<br>
So, if the balls happen to land in the worst possible way, what are the most number of ball swaps that you'll ever have to make? I'm talking about straight swaps — no moving three at a time.<br>
<br>
A second, perhaps more-important question: what's the median starting position, in terms of how many ball swaps I'll have to make?tag:ask.metafilter.com,2012:site.212195Wed, 04 Apr 2012 16:24:22 -0800omnigutWhat is the difference between floating point accuracy and precision?
http://ask.metafilter.com/204661/What%2Dis%2Dthe%2Ddifference%2Dbetween%2Dfloating%2Dpoint%2Daccuracy%2Dand%2Dprecision
What is the difference between floating point accuracy and precision?tag:ask.metafilter.com,2012:site.204661Mon, 02 Jan 2012 14:54:45 -0800conrad101Maths for tiny people?
http://ask.metafilter.com/193323/Maths%2Dfor%2Dtiny%2Dpeople
How to teach math to a 3.5 year old? Posting for a friend:<br>
<br>
A friend of mine has asked me to give maths lessons to his 3.5 year old son, and I'd like to help - but I don't know where to start.<br>
<br>
What sort of "math" is it reasonable to try to teach to someone so young? And what would be the best way of teaching it? Are there maths games I could use?<br>
<br>
Thanks in advance!tag:ask.metafilter.com,2011:site.193323Sat, 13 Aug 2011 08:32:05 -0800nj554If an geeky child is traveling South at 839 MPH, and his nerdy dad is going North at...
http://ask.metafilter.com/187878/If%2Dan%2Dgeeky%2Dchild%2Dis%2Dtraveling%2DSouth%2Dat%2D839%2DMPH%2Dand%2Dhis%2Dnerdy%2Ddad%2Dis%2Dgoing%2DNorth%2Dat
My son, who is finishing up third grade, loves math and especially the basic Algebra he's been doing. He is actually sad to be leaving school for the summer because he's so into it. How can I keep this going for him over the summer? Fun books, board games, computer (on-line and OSX) games? Seriously, Jason Fox is this kid's idol. He desperately wants to learn Calculus, though I don't think he even knows what that is. For now he's happy doing algebra such as "2x + 5 = -7 + 10x" (Those are just random letters and numbers. I have not checked if that's a legit equation. I spent my summers avoiding math, you see)<br>
<br>
He's finishing up 3rd grade at a Montessori school, ready to go into forth, or "Upper El" as they call it. While I want him to have the usual summer of playing Minecraft, chucking rocks at beehives, and frolicking merrily outside I'd like to keep him entertained with whatever math he's willing to do.<br>
<br>
So what can I give him? While computer games are fun I would prefer non-computer things if they exist. Interesting books (not just books of random problems), board games, TV-shows, YouTube videos, activities, etc. I'm happy to know about any computer games as well. We're Mac people, at least at home. Really anything that will engage him and help him to <em>understand</em> the math he's doing.<br>
<br>
He is a nine year old, and while he's advanced in math for his age he is still a kid, so anything should be somewhat age appropriate.<br>
<br>
Everything I give him will be optional for him over the summer, of course. I'm not interested in pushing him where he doesn't want to go.tag:ask.metafilter.com,2011:site.187878Wed, 08 Jun 2011 10:43:33 -0800bondcliffDid Anyone Invent Some New Math Stuff So They Could Solve A Problem Which Then Lead To a Technological Breakthrough?
http://ask.metafilter.com/182770/Did%2DAnyone%2DInvent%2DSome%2DNew%2DMath%2DStuff%2DSo%2DThey%2DCould%2DSolve%2DA%2DProblem%2DWhich%2DThen%2DLead%2DTo%2Da%2DTechnological%2DBreakthrough
Can you cite any examples where a technological breakthrough wasn't possible until there was some sort of mathematical breakthrough? I've been told that Egyptians were able to forge ahead in geometry, which better allowed them to figure out the areas of their fields. I'm not exactly sure how useful this is, but this is the best example I can think of.<br>
<br>
I'm also somewhat familiar with Leibniz and Newton and calculus, but did either of them start with a problem to solve, "figure out" integral calculus and then use it to solve their problem?<br>
<br>
Did anyone else make a breakthrough once they figured out new mathematical techniques?tag:ask.metafilter.com,2011:site.182770Wed, 06 Apr 2011 13:16:19 -0800Brian PuccioMathematics help for 6yr old son
http://ask.metafilter.com/182692/Mathematics%2Dhelp%2Dfor%2D6yr%2Dold%2Dson
Help me help my 6yr old with maths. My son is in Year 1 (First grade) and is struggling with addition & subtraction, which are the basics. <br>
I'm not sure how to help him as I'm embarrassingly bad at explaining things.<br>
His father and I help him daily with his homework but I think all we're doing is confusing him with our own methods and he's already generally not very sure of himself unfortunately. <br>
I'm just looking for a simple and fun way to teach him. What effective method will stick? Counters, base ten or just using his fingers to count? Any suggestions will be appreciated.tag:ask.metafilter.com,2011:site.182692Tue, 05 Apr 2011 17:55:19 -0800sammyabduIs not the headbutt somewhat pyrrhic?
http://ask.metafilter.com/179309/Is%2Dnot%2Dthe%2Dheadbutt%2Dsomewhat%2Dpyrrhic
Help me understand the efficacy of a headbutt as an offensive opening gambit in a bout of fisticuffs... I've been thinking it over, and it seems to me to be a problem of the conservation of momentum. That is to say, m1v1 = m2v2. From a purely mathematical standpoint I imagine that one would do as much harm to oneself as to one's opponent (all heads being of equal mass). Am I missing some key element? Please, I find myself a rather confused man.tag:ask.metafilter.com,2011:site.179309Thu, 24 Feb 2011 16:32:23 -0800dougrayrankin