ATAR Notes: Forum

VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: fagsu on June 19, 2010, 10:56:01 pm

Title: Surds
Post by: fagsu on June 19, 2010, 10:56:01 pm: wtf

Are surds even math? :o ???
Title: Re: Surds
Post by: Hutchoo on June 19, 2010, 10:59:27 pm: Surds are a pain in the @55.
At the beginning anyway.
Ask Ms.Chen.
Title: Re: Surds
Post by: fagsu on June 19, 2010, 11:00:32 pm: Ms. Chen calls me stupid
Title: Re: Surds
Post by: QuantumJG on June 22, 2010, 11:34:43 pm: This is the first time I have heard of surds since high school. Really cherylim23 explans this perfectly. It's usefull to learn how to manipulate them to extend your knowledge of arithemetic.

We learn arithmetic of natural numbers in early primary school and the rational numbers in later primary school to our early years of high school. But what about arithmetic of irrational numbers (for example $\sqrt{2}$ ).

So we know:

1+2=3, since 3:=1+1+1 & 2:=1+1

But what about:

$\sqrt{2}$ + $\sqrt{3}$ = ?
Title: Re: Surds
Post by: Ilovemathsmeth on June 23, 2010, 01:48:31 am: I never really disliked surds ... :S
Title: Re: Surds
Post by: kamil9876 on June 23, 2010, 04:40:34 pm: I like the point Quantum made, I disliked the vague notion of real numbers we were always taught so I didn't like that about surds until I read this

That aside, surds have an interesting history, the Pythagoreans drowned people for figuring out that the $\sqrt{2}$ cannot be written as a fraction of two integers (they thought all numbers could). And also the question of whether every solution to a polynomial with integer coefficients is always a combination of surds lead to some amazing math :)

(http://rlv.zcache.com/galois_theory_tshirt-p235665124638439879trlf_400.jpg)
Title: Re: Surds
Post by: Ilovemathsmeth on June 23, 2010, 06:54:52 pm: I like the T-shirt :P
Title: Re: Surds
Post by: humph on June 23, 2010, 11:06:01 pm: Hint: Eisenstein's criterion.
Title: Re: Surds
Post by: TrueTears on June 23, 2010, 11:07:15 pm: Quote from: humph on June 23, 2010, 11:06:01 pm
Hint: Eisenstein's criterion.
lol this was like one of the first theorems i learnt.
Title: Re: Surds
Post by: kamil9876 on June 24, 2010, 05:07:21 pm: Is it solvable in radicals though? after all this is a topic about surds ;D
Title: Re: Surds
Post by: Hutchoo on June 25, 2010, 03:21:21 pm: Surds are turds.