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#176 Re: Help Me ! » Complex numbers in geometry » 2008-03-14 09:13:16
Or are you talking about vectors, where i or j is the y-component upward?
What I want is the basics and simple tips/facts that may help when attempting a geometric proof in the plane using complex numbers.
#177 Re: Help Me ! » Complex numbers in geometry » 2008-03-14 05:36:19
Please, cant anyone give any tips?? I really need to learn this...
#178 Help Me ! » Complex numbers in geometry » 2008-03-10 07:03:03
- Kurre
- Replies: 3
I have so far in school only learnt the pure basics of complex numbers (how to display them i the plane, addition/multiplication/division/exponents, trig-form, exp-form etc), but now i have stumbled upon problems in a math competition course were they use complex numbers as solutions to geometric problems. And i must admit, im totally lost! It just got too complicatet way too quick, and i cant really get the hang of it. So if anyone have any really simple problems, examples or guides dealing with really easy geometric applications of complex numbers that are just a little more advanced than the basics, I would be very grateful! I have loads of examples and solutions for more advanced problems, but to be able to understand them, I really need to take it from the beginning and work my way up from there to the more advanced level...
Thanks!
#179 Help Me ! » Math vs Physics » 2008-03-06 03:00:54
- Kurre
- Replies: 2
Okey, I have this dilemma that I dont know which one to focus on in my university studies. So please come with arguments why i should choose math, or why i should choose physics (i think im most into physics, but im still not 100% sure). I find the subjects equally fun and interesting, but in different ways (mathematics have very fascinating and elegant solutions/problems and proofs, but physics are dealing with the real world and therefor are interesting in its own way). So convince me! 
#180 Re: Help Me ! » Implicit differentiation » 2008-02-22 08:31:25
Then how come if you have y = 2, then you can differentiate to get dy/dx = 0 with no problems?
y depends on x, such that y=2 for all x, it doesnt change, so the derivative in respect to x is 0. But in the previous example we had x=5, and thus we cant have any values on y. in your example the single variable (y) is a function, while we didnt treat x as a function in the example x=5. lets say we make x dependant on y, then we will get dx/dy=0, which makes sense....
i think...:o
#181 Re: Exercises » Janes exercises » 2008-02-22 03:44:32
a more powerful result of 15:
which is two consecutive even integers, thus one can be written on the form 4k, and one on the form 4k+2, and thus k^{2n}-1 is divisible by 8, ie k^{2n} gives rest 1 when divided by 8.
#182 Re: Exercises » Janes exercises II » 2008-02-22 03:08:17
5#
There is probably noone looking here, but anyway:P:
lets call the requested coefficient t.
according to vietes identity:
we have that p=a+b+c, q=ab+bc+ac, r=abc, so that gives:
if we take (a+b+c)^3 we get:
therefor
thus
#183 Re: Help Me ! » Implicit differentiation » 2008-02-21 06:01:32
What if you had something like 2x = 10? If you differentiated both sides you would end up with 2 = 0?
2x=10 -> x=5, which is not a function and therefor cant be differentiatet..?
#184 Re: Jai Ganesh's Puzzles » General Quiz » 2008-02-19 07:46:48
also seen it before several times, heres a solution:
#185 Re: Help Me ! » What is another way of expressing... » 2008-02-17 01:37:29
mathsy, i just wonder, how did you get to the formula in the first place? just guessing?
#186 Re: Help Me ! » Trig Identities HELP! » 2008-02-17 00:55:50
just multiply the denominator and numerator with sin^2x.
#187 Re: Help Me ! » Lines Passing through a Circle... » 2008-02-16 02:47:04
Should be possible with induction. It is true for x=1.
If you add one line, it can max pass through each line one time each. when the line intersects two lines in a row, it splits the area in between into two pieces. When you include the circle, the line will intersect x+2 times, ie dividing x+1 areas into two pieces each, which means an increase with x+1 areas.
also, consider a line AB which intersects all other lines in points p1,p2...pn. If you add one line CD and let it intersect line AB in a point different from p1,p2...pn and let its intersections with the circle be closer to ABs intersections with the circle than any other line, the line CD must pass through all lines (easy to vizualize or show with a figure). this shows that it is always possible to add a line that intersects all the other lines.
assume the formula holds for any x. then, replacing x with x+1, we get:
ie an increase of x+1 areas, and by the the induction principle, this holds for all x.
#188 Re: Puzzles and Games » Integer parts and trigonometry » 2008-02-14 03:52:06
good work! :)
#189 Puzzles and Games » Integer parts and trigonometry » 2008-02-13 20:45:32
- Kurre
- Replies: 2
Solve the following system of equations in real x and y, where angles are measured in radians and [a] means the greatest integer less or equal to a:
#190 Re: This is Cool » Multiply by 12 Shortcut » 2008-02-09 21:44:23
But that is just that the normal way you proceed when multiplying any numbers with each other...where is the "shortcut"??
#191 Re: Exercises » IIT level questions - 1 » 2008-02-02 23:15:57
2:
the roots x1 and x2 can be written as:
for a constant k
According to Viètes identity:
i.e.
substituting b and c in the original equation yields:
#192 Puzzles and Games » 2 Juggling problems » 2008-01-23 06:52:15
- Kurre
- Replies: 0
A while ago I created and posted a lot of juggling riddles and math problems on a juggling forum. These two were the only ones that no one solved (at least not until the whole section got locked 
):
Some basic info on juggling: http://en.wikipedia.org/wiki/Juggling
just a few videos so you know how it looks like:
http://www.youtube.com/watch?v=ZNU96CJMdy4
http://www.youtube.com/watch?v=2o9nnHK1YG8
http://www.youtube.com/watch?v=pU7uobOMVyU&feature=related
(in basic patterns, odd numbers cross(cascade), even dont(fountain) i.e dont switch hands)
1: A juggler juggles 7 rings that are black on one side and white on the other side. When he begins, all rings has the white side turned to the audience. The juggler starts counting on the first catch and turns a ring if he counts a prime number. Show that after the second catch it will never occur again that all rings has their white side turned to the audience at the same time.
2: N objects are juggled in the basic patterns (fountain/cascade). Let S(x) be the sum of all heights of the objects at any moment x. Is S(x) constant? otherwise, when does maximum occur?
(we approximate the switch of objects in the hands, so when one object is thrown and one caught they just switch places instantly with no lost time and no empty hands. Also the hands dont move while throwing, so when the hands hold a ball, we think of the height as constant)
enjoy!
#193 Re: Jai Ganesh's Puzzles » 10 second questions » 2007-12-19 03:29:43
#195 Re: Jai Ganesh's Puzzles » 10 second questions » 2007-12-12 02:02:14
#196 Re: Exercises » Kurres exercises » 2007-11-24 22:05:40
5. Approximate
6. Which number is greater?
or
#197 Re: Exercises » Kurres exercises » 2007-11-21 07:24:14
Actually i wasnt sure about the mathematics invloved in nr 4, it may need the condition |x|>1 (or |x|>p where p is somewhere between 1 and 2), but I decided to not post it at first because i wasnt sure
#198 Re: Jai Ganesh's Puzzles » 10 second questions » 2007-11-20 04:07:29
#199 Exercises » Kurres exercises » 2007-11-19 10:28:13
- Kurre
- Replies: 4
Okey so here are my random exercises:
Solve the equations:
1.
2.
3. Give all solutions for x
where k is any integer
4.Find a function that satisfies
enjoy!
#200 Re: Exercises » Janes exercises II » 2007-11-19 09:57:40
edit: forgot to hide it 