Mathman! Mathman!

[rugbyLEAGUEfan]

I always was annoyed how the artistic subjects at school were by default considered the creative subjects . Now I love art , but can't draw a stick figure . I'm better at music but fairly mechanical .

But I loved maths at school . Calculus blew my mind . I felt I could be extremely creative in the maths classes when it came to solving problems . Its a shame that I would be utterly useless now through lack of practice .

 

[NinjaCow64]

Yay, maths.

I love mathematics, however I didn't post in any of the "ask a mathematician" because I'm still doing highschool mathematics, high end highschool mathematics, (Sequences and Diophatine Equations a-go-go) but highschool mathematics nevertheless. Honestly I don't think I could claim to be a mathematician and I didn't have any questions so I kept quiet. However, this thread seems to be more laid back so I am going to go ahead and bring some of my craziness.

There is one thing that annoys me about people when it comes to mathematics in general. Some people are like "oh, you must like maths because of it's relation to art/construction/science/whatever" and they don't understand that the best maths is maths for the sake of maths. Does anyone else get this?

Also, there was a silly test in English that wasn't worth any assessment and they asked for a metaphor for mathematics and I gave a positive one and I lost ten points for it and I was proud. VIVA LA RESISTANCE!

 

[azzaman333]

Why are the statistics kids so much cooler than the maths kids?

 

[Leoreth]

It's boring as hell, organic brains suck at it, and we have calculators and stuff now. Geometry, however, is awesome:

More geometry, less screwing around with numbers.

Haha, no. You can't do anything meaningful with geometry without "screwing with numbers" anyway.

 

[Mise]

Fair enough...

'Pooh', said the Wizard, 'is where we are now. The railway starts here and runs in a straight line via 39 intermediate and equally spaced stations to the terminus at Oz.

'Unfortunately, the railwaymen are on strike, so you'll have to go by bus. The bus goes along the Yellow Brick Road, which runs in a straight line from here to the outlying village of Bah, where it turns through a right-angle and goes in a straight line back to first railway station after Pooh. From there it goes in a straight line to the next outlying village, where it again turns through a right-angle and proceeds in a similar zig-zag fashion all the way to Oz, alternately calling at railway stations and outlying villages. Each of the 80 straight stretches of road is a different whole number of miles long. Rail distances are also whole numbers of miles.

'The fare is on ozzle per mile, but you needn't be alarmed, as all distances are as short as they can possibly be.'

I was alarmed, and it turned out I had good reason to be. My money was running short, for the Wizardry of Oz had been suffering from hyper-inflation recently.

Unfortunately the Wizard had vanished before I could ask him the vital question, HOW LONG IS THE Yellow Brick ROAD?

Someone solved this BTW (I think it was Truronian?)

Spoiler :

You just need a big old list of pythagorean triples, then add up the first 80 hypoteneuses. It will obviously be really god damn long...

I would download such a list from the internet.

 

[ShahJahanII]

What are your opinions on the Tau vs. Pi debate?

 

[NinjaCow64]

What are your opinions on the Tau vs. Pi debate?

'Tis stupid. Why change something that is so engrained in everyone's mind? I doubt there is an actual mathematical benefit to it as Wikipedia (which is a reliable source IMO) says, and I quote, "This proposition has been relayed in several news articles, but has not been echoed in scientific publications nor by any scientific authority."

If there is a benefit to using Tau in mathematics, why don't you just use 2(Pi)? Much better.

 

[ParadigmShifter]

Spoiler :

You just need a big old list of pythagorean triples, then add up the first 80 hypoteneuses. It will obviously be really god damn long...

I would download such a list from the internet.

No, you need to add up 40 Pythagorean triples, which are all different yet all sum to the same amount.

It's asking what is the smallest number that can be expressed as a sum of 2 squares in 40 different ways, then add up the lengths of the triangle edges (not including the hypotenuse).

Truronian's (correct) answer:

Spoiler :

http://forums.civfanatics.com/showpost.php?p=10399444&postcount=899

Sums of 2 squares is an interesting example of a use for factorisation of Gaussian Integers as well (a+ib, where a, b are integers and i = sqrt(-1)).

Because

(a+ib)(a-ib) = a^2 + b^2

 

[Mise]

Oh yeah, I forgot that the stations are equally spaced. That would be really god damn long.

EDIT: Apparently I read that exact same thing almost exactly a year ago, and still got the question wrong.

 

[ParadigmShifter]

If we acknowledge the existence of imaginary numbers, why are they still imaginary?

It's an unfortunate term. Complex number (i.e. a+ib, a, b real, i = sqrt(-1)) is better, an imaginary number has real part 0.

It would be bad if there was no solution to x^2 + 1 = 0, so we invented a new kind of number. Then Gauss proved (9 different ways!) that all polynomials with coefficients in the complex field have roots in the complex field, so we don't need any more new numbers to solve those types of equations.

 

[SS-18 ICBM]

I'd like an opinion on the duodecimal system, if it's not too much trouble.

 

[ParadigmShifter]

It's OK. Good enough for time anyway I don't think we are going to change. UK money used to be based on 240 pence in a pound (12d per shilling, and 20s per pound), it didn't make things easier.

 

[SS-18 ICBM]

But you have more divisors. That should make fractions much easier. Although I see it might be too late to change now.

 

[ParadigmShifter]

Fractions are easy anyway. What's 1/3 of 10? 10/3 Decimals are a bit harder, of course.

Unless you use a base that is a product of loads of prime divisors, you are going to end up with some divisor that isn't nice (dividing by 5 isn't nice in base 12). And there's a practical limit to how many symbols we can work with easily, so huge base values aren't good for calculation.

 

[IdiotsOpposite]

Is it any surprise that I'm subscribing to this thread?

EDIT: Srs question.

 

[SS-18 ICBM]

Unless you use a base that is a product of loads of prime divisors, you are going to end up with some divisor that isn't nice (dividing by 5 isn't nice in base 12). And there's a practical limit to how many symbols we can work with easily, so huge base values aren't good for calculation.

We only use 5 a lot since it's a divisor of 10. And 2 extra symbols isn't that unwieldy.

 

[Truronian]

Some cool videos I've encountered in my my first year of teaching:

Quicksort folk dancing:


Link to video.

Powers of ten (I use it to introduce standard form):


Link to video.

Philip Glass and Sesame Street team up to bring us cool circle geometry:


Link to video.

I'll post a problem in a minute if I can find it.

 

[Borachio]

Excellent thread. Why do Americans always use that typo math? I don't get it. But there's loads of other words they can't spell too. Color, humor,...er...well two anyway. (only joking)

Okay, not related to maths (I'm supporting the Brits on this one ) itself, but why do you think it's such an unpopular subject among students? Does the majority of people just don't "get" maths? Is it too abstract to catch their interest? Or is it just taught poorly?

And if so, what would you improve in the way it is taught?

I go with poorly taught. Don't know what the answer is.

I find I generally prefer the more abstract stuff to the extent I tolerate math at all. Screw spatial reasoning.

I love topology. But it is oh-so hard. Very abstract, and spatial. Does that make sense?

Actually I love maths when I can do it. When I can't I hate it vehemently.

If we acknowledge the existence of imaginary numbers, why are they still imaginary?

Aren't real numbers imaginary too? (in some sense of the word)

Yay, maths.

I love mathematics, however I didn't post in any of the "ask a mathematician" because I'm still doing highschool mathematics, high end highschool mathematics, (Sequences and Diophatine Equations a-go-go) but highschool mathematics nevertheless. Honestly I don't think I could claim to be a mathematician and I didn't have any questions so I kept quiet. However, this thread seems to be more laid back so I am going to go ahead and bring some of my craziness.

There is one thing that annoys me about people when it comes to mathematics in general. Some people are like "oh, you must like maths because of it's relation to art/construction/science/whatever" and they don't understand that the best maths is maths for the sake of maths. Does anyone else get this?

Also, there was a silly test in English that wasn't worth any assessment and they asked for a metaphor for mathematics and I gave a positive one and I lost ten points for it and I was proud. VIVA LA RESISTANCE!

Maths, pure maths especially is definitely maths for the sake of maths.
What's a positive metaphor for maths? I'm intrigued.

@SS 18 duodecimal came in really handy for packing problems. If you ever get into Logistics (Transport and Warehousing) you quickly discover that decimal is crap when it comes to goods handling. (though I'm by no means an expert on the problem - and have already exhausted my knowledge of the subject, largely)

 

[SS-18 ICBM]

Which maths are the most useful for killing people?

 

[Truronian]

Aforementioned Maths puzzle:

What fraction of this regular octagon is shaded? Just in case it's not clear from the image: The four sets of parallel lines hit the edges of the octagon at the trisection points.

EDIT: Incidentally, it had better take you guys bloody ages to work this out because it took me about 15 minutes to construct this in geogebra.