You do realize that your proposed solution involves two perfect squares, right? i.e., one more than was required?
As I said, I’m sometimes an overachiever and braggart. In this case, the problem was too simple, and I wanted to see if I could find a cooler solution, so I went for two perfect squares. Also, the number was 1020, not 1023, which is a bit of a reason for looking for a cool method to solve it.
Out of curiosity, is -4 the perfect square of 2i, or can you not use imaginary numbers when making perfect squares?
Honestly, I can’t think of any occasion where I’ve needed to use advanced maths. Which is probably a good thing, since I’ve never studied it; perhaps if I had, I’d choose to use it (I would actually like to study it some more).
I do use arithmetic, basic algebra, basic stats and geometry pretty frequently, but nothing that the average British 15-year-old wouldn’t recognise - it doesn’t count as advanced.
But you only said ‘a perfect square,’ not ‘one perfect square and no more.’
While I agree that it would be useful if they offered more everyday math, I don’t think it’s a waste of time to learn advanced math. Many things you learn in school have no direct benefit to your later life. Think of all the history, language, biology, etc that you have forgotten. However, learning those things expanded your mind in a way that allowed you to think of new things. It’s a beneficial brain exercise that makes you an overall smarter person who is more confident to solve new and unique problems.
With no further context, “perfect squares” usually means the square of an integer, but with different context, it can mean squares of different kinds of things. (But, everything is someone’s square in some context, so the idea of distinguishing the “perfect squares” is only useful when you fix some particular domain of things you’re considering the squares of.)
Never, really, except for fixing electronic gear (when I can be bothered) and might have to calculate some correct values to make a little mod. Not my favorite.
It’s fun as a little crossword puzzle, though – I don’t mean sudoku or other nonsense, but working proofs. The reason most literature people have a bad reputation is that they never decided, for Christ, to bother to read what used to be called “technical philosophy,” which requires a fair amount of acumen and yields (or could – not one of my peers, at my school or anywhere else, AFAIK, either even bothered to read Ingarden’s main book, "The Controversy over the Existence of the World) interesting results of not-insignificant application to work in the ontology of fictional objects, to name one small idea, or consider even core concepts in metamathetics, proof theory, and so forth, in order to acquire powerful tools with which they may have attacked somewhat more serious problems than those to be found in the History of Philosophy – at least in the perversion to which it’s been subjected at the hands of literary critics.
True, which is why my showoffy solution was correct also. I was just tweaking him(?) because it looked like (and he confirmed) that he thought his 1024-1 used only one perfect square.
During the last Summer Olympics we were watching the 10m platform diving at work. Someone idly wondered how fast they were probably going when they hit the water. I knew 9.8m/s per second and my watch had a stopwatch on it. After I finished the calculation and conversion to MPH the announcer mentioned a nearly identical number. They looked at me like I just preformed witchcraft.
It’s nowhere near everyday life, but I do have an example.
I kinda did a :dubious: back in school, in the career counseling lectures. They’d bring in working engineers. Said engineers fell back on the old hoary ice-breaker of “You know, I never use calculus! LOL!” about 50% of the time.
But I have used calculus as an engineer. And I’m not even that advanced.
We had received a newer organic peroxide from a peroxide supplier. Half of our customers loved it. The other half said - it doesn’t work it all.
“Hmm,” thinks GameHat. "I wonder what its SADT (self-accelerating decomposition temperature) really is (supplier was being all coy)
So I initiated a sample using 50% known peroxide, 50% new peroxide. Stuck a thermocouple probe in the center of the mass.
I recorded the temperature of the sample as it cured with a data logger that read the thermocouple.
I dumped that data in Excel, then did a rough numerical derivative and second derivative on the data (still just basic excel)
Bingo - there was a step change at around 160 F. So now I can tell all my customers - if you want to use this peroxide, you need to achieve a curing exotherm of at least around 160 F for this thing to take off. It’s worked for many, many customers.
I see what you’re saying, but think the time spent teaching (IMHO utterly useless) advanced maths to most students would be better employed teaching spelling, computer skills, and other things that might help them in their everyday lives. It’s hard enough getting teenagers to learn as it is, so removing obstacles to that (subjects that are likely useless to them), IMHO, outweighs the “well rounded person” argument in that respect.
Absolutely. Lack of understanding of the basic (first week of class) fundamentals of probability makes people astonishingly easy to manipulate. Look how many people don’t know the odds of a fair coin coming up heads on the next flip when it has just been heads five times in a row. Or how many people don’t grasp the odds at a lottery. Or elections. Or what fatality rates mean for diseases. This kind of stuff is how frauds and charlatans take people’s money.
Read the book Innumeracy. I think it should be required reading for every high school student.
I’m 40. I don’t think I’ve had to use anything beyond basic math since high school. Pretty sure I wouldn’t remember how if I needed to. Hasn’t effected my life.
In the flying biz we do a lot of real-time mental 4-function arithmetic. The good news is we rarely need more than 2 sigfigs, so we can round & shortcut a bunch.
There’s also a bunch of angular calculations whose underlying reality is applying the trig functions sin & cos; as a practical matter we have rules of thumb for the range of angles we commonly encounter and that reduces the problems to simple multiplications by known ballpark factors.
As a software guy I’ve used a lot of logical decomposition. Thinking rigorously like a mathematician or physicist would. But I’ve had very little need for math as such beyond Algebra 200.
You do realize that your proposed solution involves two perfect squares, right? i.e., one more than was required?