Now that I think about it, the number of ways I use math just in playing games is kind of surprising.
[ul]
[li]I use statistics to examine how my character performs in a game.[/li]
[li]I use probability calculations to determine how much chance of success a particular strategy has, which tells me whether or not I need to come up with another plan. (I have spreadsheets full of probability tables for my Shadowrun characters that help me decide how many dice I need to roll to have a reasonable chance of success at various things.)[/li]
[li]I use algebra to come up with formulas to help decide which build choice is optimal.[/li]
[li]I use geometry and trig in building props for live-action games.[/li][li]I use algebra (among other things) to develop pricing models for in-game economies.[/li][/ul]
That’s without getting into all the ways I use math at work–I’m a software engineer, among other hats. I sometimes have to do math that most people have never even heard of.
I don’t use math. It makes you paranoid and rots your teeth.
I’m a software engineer. I took a lot of math in college because I enjoyed it, but I’ve rarely used any of the advanced knowledge since then (stats/trig/calc/difeq). Rarely I have used basic algebra. Mostly just basic arithmatic.
In most of the situations where I could use advanced math (how much water is in this curved pool which has a curved floor) it’s just for curiosity. I can just estimate by imagining the sides are straight and sloped and come up with a pretty good guess.
However, I still feel it’s useful for students to learn advanced math because they may eventually go into fields which require it. Plus, it gives them a deeper understanding on how the world works. Even if they never have to figure out the area underneath a curve, I feel it’s still beneficial that they know there is a technique to figure it out.
I’m also a software engineer. I DO use trig quite a lot, also geometry, and algebra once in a while. That’s because I work with mapping and navigation software. Most of the basic equations regarding distance between points on a sphere involve a cosine.
I don’t know if this counts, but it’s the most complicated math I’ve done in awhile.
Last year, on (I think) October 23, I attended a math professional development for second-grade teachers. The instructor for the program was trying to challenge us, so she put the date on the board as a four-digit number: 1023. She then asked us to find a subtraction equation with a difference equal to 1,023, that involved a perfect square.
Being the overachiever that I am, I mocked up a quick spreadsheet that helped me find a subtraction equation with a difference equal to 1,023, in which both the minuend and subtrahend were perfect squares. I said that I thought I’d found the only possible answer to the problem that met those criteria.
But then I thought about it more on the car ride home, and I realized that I’d made a faulty assumption; so, over the course of the next few car rides, I figured out in my head all the other possible equations matching that criteria.
Anything more advanced than multiplication generally enters my life as a puzzle: something fun to chew over, but not something that has any real practical effect on my life.
I like this problem! Even though it doesn’t really count as “real world.” (I think the real world is overrated, anyway.)
Unless I’m missing something, there are four possibilities. My solution is below. If anyone’s interested, I can explain how I got it.512[sup]2[/sup] - 511[sup]2[/sup] = 1023
52[sup]2[/sup] - 41[sup]2[/sup] = 1023
32[sup]2[/sup] - 1[sup]2[/sup] = 1023
172[sup]2[/sup] - 169[sup]2[/sup] = 1023
I use all sorts of probabilities and stats for game playing (esp. bridge).
I also use advanced logic to find problems with our application at work (without testing a thing).
@Thudlow Boink: Yep, those are the only four, using positive integers. I imagine your reasoning was this: a^2 - b^2 = (a + b) * (a - b). And any two numbers of the same parity uniquely can be considered a + b and a - b for some a and b (specifically, their average and their distance from their average). So the solutions correspond to ways of expressing 1023 as a product of two factors of the same parity. 1023 is a product of three distinct primes (3, 11, 31), so it has 2^3 many factors, which pair off into 2^3/2 = 4 many ways of expressing it as a product of two factors (in each case, with the same parity, since they are all odd). Which yields the four possibilities you list.
I do research in biology, specifically on how the brain perceives body motion; so I do a lot of experiments which involve moving the subjects (sinusoidally, constant velocity, etc) and measuring various things. Analyzing them involves a fair deal of linear algebra, differential equations and statistics, and I make good use of the lessons that I took in college.
Yep, that’s it. (Thus yielding another “application” of the rule that was discussed in the other thread.)
I am a stockbroker specializing in options. I use all the calculus and statistics I learned in college and I am going to study more math.
That’s a much more elegant solution than mine. I noticed at some point that perfect squares were separated by a series of odd numbers–1 and 4 are separate by 3, while 1 and 25 are separated by 3+5+7+9=24. So I found all the series of consecutive odd numbers that equaled 1023 and worked backwards from there.
The odd number separating two perfect squares equals twice the higher square’s root, minus 1.
For the first one, I divided 1023 by 3 to get 341, and figured that the squares separated by 339, 341, and 343 were the ones I was looking for. The highest square’s root therefore had to be 344/2, or 172, making the square 29584; three down from there would be the square of 169, or 28561.
Figuring out the others followed a similar process. However, now that I’m looking at the problem again, I realize that the session must’ve been on a different date–and looking back at my calendar, it was actually 10/20, so you’re looking for all the equations equalling 1,020. Meaning the first one must be the squares of two numbers with a difference of 2.
Like I said, mine is much less elegant, but it has that homegrown charm to it :).
Heh.
A[sup]2[/sup] + B[sup]2[/sup] = C[sup]2[/sup] helped me figure out how much lumber and where to cut for building the slanted roof on my greenhouse.
I concur with the 114 gallons estimate. (I got 114.119106351 gallons to the accuracy of my calculator.)
I’m a theatre technician and lighting designer. I use algebra up to and through squares and square roots to calculate light levels at distances from particular instruments through particular color filters and I use geometry to calculate angles to figure whether lights will do what I need them to without, you know, lighting the set instead of the actors. I’m not primarily a carpenter, but when I was I frequently used geometry to figure lengths of connecting set pieces, ensure that parallel lines remained parallel, and generally piece things together. The most math-intensive thing I ever did at work was calculating the necessary foci and length of string necessary to produce an ellipse of desired semi-major axes. I did this by failing for an hour, then getting my girlfriend (who is getting her doctorate in engineering) to explain it to me. I did learn that stuff in high school, I had just forgotten exactly how to work it.
Overall, I found my high school geometry to be extremely useful and subsequent math to be less useful.
I do use some search space algorithms for puzzle solving.
A while back I was sitting in a new car dealer, and the manager was trying to sell me a lease. I was able to compute the true cost and effective interest rate in my head, which kind of blew his mind.
And I recently used some graph theory at work - in fact it was so odd I posted a question about it in GQ. It was interesting in that the relation wasn’t transitive, so most of the published clique algorithms don’t work.
The short answer to the OP (taking the definition to mean “trigonometry, functions, complex algebra, integrals, and differentials” (I’m excluding probability and statistical analysis because they’re really not that hard to work out for everyday use), in my case, is “Absolutely Never”. (Journalism/Retail)
I’d further add that I absolutely agree advanced maths is an utter waste of time for most people, and the best thing schools could do is to stop teaching it to every student and make it available to “advanced” students, with the focus for “Normal Maths” being on useful things like working out change, time/distance, foreign exchange, weights & measures in everyday use for normal people, and so on.
When I was working in home restoration and repair, had to be able to figure out the volume of air in a given space, had to know the volume of air a single air mover would move in an hour, had to know how fast water evaporates at a given range of temperature and ppm level and if using a dehumidifier, had to know what volume of water it removed from the air at what rate. Had to use all those values to figure out the optimal number of air movers, heaters (crap forgot heater, had to know about those too) dehumidifiers etc, to dry carpet/drywall/hardwood flooring furniture in a given sized room at a certain exchange rate of air per hour etc etc etc. there was even a formula to tell you how to place the equipment for optimal drying and not anything complicated but it sure looks like it on paper
I use more “advanced math” than I do normal math because advanced math doesn’t require numbers. I’m frequently doing rough modeling and simulation in my head using calculus, statistics, trig functions, etc. It’s not so much knowing the nuts and bolts of it so much as having a sufficient grasp of the conceptual fundamentals so that they can be deployed in interesting ways.
Forgive me if I am terminally dense, I’d have said “1024 - 1 = 1023. Can we break for coffee?” But then I am an engineer. The elegant solutions upthread involve two perfect squares i.e. one more that was required.