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azerbajdzan
Veteran poster

Post Number: 790
 Posted on Sunday, 13 February, 2011 - 07:42 pm:

those of you, who do not like tomorrow's Valentine's Day like I do, can spend that day by thinking why I called f(z) the Valentine's Day's function... ;-)

$$f(z)=\frac{(z-6)^2 (z+16)^2 \left(z^2-24 z+180\right) \left(z^2-18 z+277\right) \left(z^2+2 z+197\right) \left(z^2+20 z+136\right)}{(z-5) (z+17) \left(z^2-24 z+244\right) \left(z^2-18 z+85\right) \left(z^2-8 z+272\right) \left(z^2+12 z+136\right) \left(z^2+26 z+173\right)}$$

On the other hand if you like Valentine's Day and forgot to buy something for your friend/partner then feel free to use this function as a gift ;-)
Jewbinson
Veteran poster

Post Number: 453
 Posted on Sunday, 13 February, 2011 - 07:53 pm:

Is z complex or real or what?
azerbajdzan
Veteran poster

Post Number: 791
 Posted on Sunday, 13 February, 2011 - 08:26 pm:

z is real or complex or whatever... but further extensions of complex numbers are beyond me... :-)
MathsFan
Prolific poster

Post Number: 255
 Posted on Sunday, 13 February, 2011 - 08:44 pm:

I don't understand it...
Jewbinson
Veteran poster

Post Number: 454
 Posted on Sunday, 13 February, 2011 - 09:16 pm:

It could be anything...
azerbajdzan
Veteran poster

Post Number: 792
 Posted on Sunday, 13 February, 2011 - 09:29 pm:

stay tuned for tomorrow revelation :-)
Sam Cappleman-Lynes
Prolific poster

Post Number: 219
 Posted on Sunday, 13 February, 2011 - 09:46 pm:

Plot the roots on an Argand Diagram ;)

You should get something nice.
Jewbinson
Veteran poster

Post Number: 455
 Posted on Sunday, 13 February, 2011 - 10:10 pm:

Ok... so what of the denominator?
Sam Cappleman-Lynes
Prolific poster

Post Number: 220
 Posted on Sunday, 13 February, 2011 - 10:14 pm:

It's just there for confusion, I guess...
azerbajdzan
Veteran poster

Post Number: 794
 Posted on Monday, 14 February, 2011 - 11:41 am:

Here is a graph of f(z)

isn't it nice? ;-)
James Cranch
Veteran poster

Post Number: 1927
 Posted on Monday, 14 February, 2011 - 12:46 pm:

quote:

It's just there for confusion, I guess...

Guess again.
azerbajdzan
Veteran poster

Post Number: 795
 Posted on Monday, 14 February, 2011 - 01:27 pm:

sometimes ordinary things (such as rational function) may look very different when we look at them from other point of view...
first example is view "from the side" and the following is "from above"

vertical axis is real and horizontal is imaginary... (they are swapped compared to usual usage letting the shape to be in upright position)

...so that's the shape of my heart :-)

just to support the romantic atmosphere here are some nice lyrics...
Sting - Shape Of My Heart
Sting - Shape Of My Heart 2

not to be completely out of topics of this forum try to think about mathematical explanation why this function looks exactly as it looks...

(hue represents argument of f(z), luminance represents absolute value of f(z))
Daniel Fretwell
Veteran poster

Post Number: 1108
 Posted on Monday, 14 February, 2011 - 06:48 pm:

I wondered why some of the things in the denominator were 1 more than some of the things in the numerator, now it makes sense.

Poles and roots make for nice pictures :p
Balakrishnan V
Veteran poster

Post Number: 818
 Posted on Monday, 14 February, 2011 - 11:53 pm:

Alternatively
elvinc
Veteran poster

Post Number: 466
 Posted on Tuesday, 15 February, 2011 - 10:16 pm:

very clever. Well done
Steve Hewson
Frequent poster

Post Number: 165
 Posted on Wednesday, 16 February, 2011 - 08:23 am:

That is fab!

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