quadratic equations (white flag goes up)

[Martin]

Doesn't seem to work.

It does.

slightly edited:

y= 12 + 11x  + 3x² is the equation of a quadratic curve, and if you insert the discrete points n = 0, 1, 2 etc you get the series that Martin gave us.

yebbut if you were to enter that as the solution in MyMaths you would get a big fat 0

[andyoxon]

3n^2 - 7n + 6 ...?

nope

This was the source of my 'efforts'...    perhaps it is wrong though...
id:A027599 - OEIS Search Results

[Frenchie]

the problem I have with all this is that it it just maths for maths sake; nobody is ever ever going to need this apart from maths teachers

or anyone who does a Physics degree or a PhD....

My PhD had some practical applications; most of the PhD students I am involved with will eventually compute solutions to say engine or oil industry or sportswear  problems, possibly idealised at first but quite applicable next. The math and physics are just a way to formulate a solution to a "complex" problem.

[citoyen]

the problem I have with all this is that it it just maths for maths sake; nobody is ever ever going to need this apart from maths teachers

I love maths, so I find quadratic equations fun for their own sake. And I'm sure that the mental exercise is beneficial in the same way that being forced to do ten mile cross country runs in the freezing rain was beneficial for the physical health, even if they didn't have any practical real-world applications.

However, if you want to know just what is the point of quadratic equations, read these fascinating articles:
101 uses of a quadratic equation
101 uses of a quadratic equation: Part II

d.

[border-rider]

Doesn't seem to work.

It does.

slightly edited:

y= 12 + 11x  + 3x² is the equation of a quadratic curve, and if you insert the discrete points n = 0, 1, 2 etc you get the series that Martin gave us.

yebbut if you were to enter that as the solution in MyMaths you would get a big fat 0

Why ? What form do they need it in ?

[rower40]

3n² + 5n + 4
Seems to work; it gets 12 for n=1, 26 for n=2 etc.

[Frenchie]

Nice link Smutchin! Didn't know this mag'.

That (below) what I do for a living...   (except that the NS equations describe other fluids than air and that these eqns have very few analytical solutions, esp not in the case below! A bit approximative for a mathematical mag'   )

The team instead turned to the Navier-Stokes equations, a set of complex differential equations which describe air flow. In most real-life situations, as in this one, it's impossible to solve these equations analytically. But with the help of powerful computers, you can employ some educated guesswork to come up with approximate solutions that tell you just how the air will behave. The branch of maths that develops the computer algorithms for this task is called computational fluid dynamics. It requires massive amounts of computing power, but comes up with effective results.

Source: Career interview: The fastest mathematician on Earth (latest issue, 52, of +plus)

[Frenchie]

Doesn't seem to work.

It does.

slightly edited:

y= 12 + 11x  + 3x² is the equation of a quadratic curve, and if you insert the discrete points n = 0, 1, 2 etc you get the series that Martin gave us.

yebbut if you were to enter that as the solution in MyMaths you would get a big fat 0

Why ? What form do they need it in ?

n = [1 ... n] I think

[border-rider]

Aha! I started at n = 1

In which case you'd need to transform it from n to n-1.  That'd give you 3n² +5n +4

[Frenchie]

Aha! I started at n = 1

In which case you'd need to transform it from n to n-1.  That'd give you 3n² +5n +4

Yep. Viz Rower40 above as well.

[border-rider]

Why ? What form do they need it in ?

n = [1 ... n] I think

But they want the formula for the n^th term.  That's what we've derived.

[Frenchie]

Why ? What form do they need it in ?

n = [1 ... n] I think

But they want the formula for the n^th term.  That's what we've derived.

Je ne parle pas l'anglais. 

[Wowbagger]

I had a look at Smutchin's link as well. My problem is that the moment letters are used to represent numbers, I have to turn them back into example numbers again and do the arithmetic before I can work out what is going on. By the second example the frustration starts to well up and I do something else instead.

So my WFT (White Flag Threshold) is a good deal lower than most people's.

[border-rider]

My problem is that the moment letters are used to represent numbers, I have to turn them back into example numbers again and do the arithmetic before I can work out what is going on. By the second example the frustration starts to well up and I do something else instead.

You're algebraphobic

[Frenchie]

Wow, I thought you enjoyed chess? Surely you can link letters to a strategy (e4 x...) and solve a problem (you do iwith chess, don't you?)!

[David Martin]

Wow, I thought you enjoyed chess? Surely you can link letters to a strategy (e4 x...) and solve a problem (you do iwith chess, don't you?)!

Chess isn't analytical, it is pattern recognition. That is why you learn all the standard moves..

..d

[Wowbagger]

I see no link whatever between quadratic equations (or any other maths for that matter) and chess problems. Although many of this country's best chess players have been mathematically very gifted (the "English Chess Explosion" of the 1980s was largely based upon some of the top Maths brains from Cambridge) there are plenty of examples of brilliant mathematicians who have been duffers at chess. Einstein himself, apparently, was a very weak player. Alan Turing also, although as I mentioned on one of the recent threads about him, Bletchley was crammed with top chess players.

[Martin]

3n² + 5n+4

(no I didn't deduce this it was a maths teacher)

[teethgrinder]

Why ? What form do they need it in ?

n = [1 ... n] I think

But they want the formula for the n^th term.  That's what we've derived.

Oh come on you lot.

It must surely be n+1

[Wowbagger]

Wow, I thought you enjoyed chess? Surely you can link letters to a strategy (e4 x...) and solve a problem (you do iwith chess, don't you?)!

Chess isn't analytical, it is pattern recognition. That is why you learn all the standard moves..

..d

Rote-learning the moves won't help you. You have to understand the underlying ideas. Matthew Sadler, who I think was World no. 7 at his peak, used to sit down after every game and explain it all to his mum (a Frenchwoman!  ) who so far as I know never played competitively. I watched him on a few occasions and it was amazing how much he saw, and in fact how good he was at explaining it.

Edit: whether we are talking about different things I don't know, but chess certainly is analytical. We talk about the "tree of analysis". Alexander Kotov, in his 1972 masterpiece "Think like a Grandmaster" goes into a lot of detail about this.

[citoyen]

3n² + 5n + 4

That looks good to me.

How did you arrive at that? Was it by trial and error? That's how I was trying to do it, and I might have got there eventually, but not for a while yet. Seems like a pretty tough task for this level of maths unless there's a specific technique that has been taught as a means of making it more straightforward.

My son is doing very similar number sequence stuff at the moment, but on sequences with much simpler rules (he's 11, ie year 7).

d.

[matthew]

What was your son's mathematical problem?

"write down an nth term formula for the original sequence
12 26 46 72 104 142"  

a Freddered gold 1 point star to the first (non maths teacher) who can come up with the correct answer  

At 13yo your child is probably only just being introduced to quadratics.

The first and second differences are precisely that:

The first difference being the difference between each consecutive number in the series.
The second difference being the differences between each of the first differences.

series: 12 26 46 72 104 142
1st diff:   14  20 26 32  38
2nd diff:       6   6   6    6  

The second diff being constant implies function including x^2

your son is therefore familiar with series and y=ax+b I expect this is to then build on this to reach y=ax^2+bx+c

For instance if you write the series x^2

1 4 9 16 25 36, the first differences are 3, 5, 7, 9, 11 ... the second differences are 2, 2, 2, 2, 2

therefore A in the term Ax^2 is the second differential /2

then write out the series 3x^2 and subtract from the original series to leave 9 14 19 24 29 34. This new series is of the form 5x +b as the first difference is 5, this is 5x+4. Therefore the final function is 3n^2 + 5n + 4

[Martin]

My son is doing very similar number sequence stuff at the moment, but on sequences with much simpler rules (he's 11, ie year 7).

best stop wasting your time going out on that bike and boning up for the next 2 years then  

BTW can anybody remember how we solved all this utter crap back in the '70s? it certainly didn't involve drawing chain link fences on pieces of paper.

[HTFB]

Oh, I'm late to this party.

In fact I'm late to this party because I've been trying to help the Beloved Stoker recover the formula used by the regulator to model a proposed incentive scheme, where the rate of the incentive payment and the value you're incentivised to hit are both dependent on the same thing.

So we've been doing exactly this---second differencing (approximate) data to try to get a plausible quadratic formula out.

It's a real-world problem!

[border-rider]

The first difference being the difference between each consecutive number in the series.
The second difference being the differences between each of the first differences.

series: 12 26 46 72 104 142
1st diff:   14  20 26 32  38
2nd diff:       6   6   6    6  

The second diff being constant implies function including x^2

your son is therefore familiar with series and y=ax+b I expect this is to then build on this to reach y=ax^2+bx+c

That was exactly how I did it.