The fascination of Maths thread

[Gonzo]

Ah from 20 year old memory that's complex numbers, Argand diagrams and the like. You're missing the beauty of it - an imaginary number can make perfect logical sense in the bigger scheme of things. The universe/god/some higher intelligence trying to tell you that not everything is black and white.

In my book that is just making things up for the sake of it. I stopped doing economics at university for the same reason.

[sasguru]

In my book that is just making things up for the sake of it. I stopped doing economics at university for the same reason.

Ah economics is a whole other ball game. It's a pseudo/soft science dressed up in mathematical garb. No wonder you're confused.
Maths on the other hand is how the universe "thinks".

[Diver]

Solve the following inequality for positive x:

x (8 (1-x)(1/2) + (1+x)(1/2)) ≤ 11 (1+x)(1/2) - 16 (1-x)(1/2).

[AtW]

Solve the following inequality for positive x:

No. Next!

[Diver]

Solve the inequality 2sin x + 2cos x ≥ 2(1-1/( 21/2)).

[BrilloPad]

Diver just reminded me of an A level task I was set - find the circumference of an ellipse as an exact formula.

[NotAllThere]

Once I was taught that the square root of -1 does not exist, but pretend that it does and we will call it "i", that was the point that I gave up on maths.

You shouldn't believe everything you are taught - what are you? A labour voter? The square root of one does exist. It is represented by the letter i. ( Or possibly j if you're an engineer or physicist ).

It is in fact considerably easier to derive the complex numbers from the reals, than it is to derive the reals from the rationals. And once you've defined the square root of -1, you get all the richness of all the complex numbers for free - you don't have to derive any more. The existence of the square root of -1 leads to a fully consistent* mathematics.

You know how there's a general solution for quadratic equations (involving x-squared)? There's a similar general solution for cubic equations (involving x-cubed). There's a set of these equations that have real answers, but to calculate those using the general solution, requires working with complex numbers.

Most maths is "just made up for the sake of it". But generally, any new mathematics eventually finds a real world application. Consider this: all the mathematics used to design and construct any electrical device will have involved complex numbers at some point. When the physicists and engineers needed some tools to do their calculations, mathematics had already developed them. This has been shown time and time again.

* Godel notwithstanding.

[NotAllThere]

Diver just reminded me of an A level task I was set - find the circumference of an ellipse as an exact formula.

There isn't one. There's four power series that give exact answers.

[Churchill]

There isn't one. There's four power series that give exact answers.

Ok clever clogs, square a circle.

[NotAllThere]

The full problem is "Create a square with exactly the same area as a circle, using only compass and ruler". Can't be done. The answer is as easy as π as any fule kno'.