‘Wish I was Jamie*
8. november 2008 ob 7:13 | Borut Levart |Saj ne vem, ali se že sme naslavljati angleško, Marka Crnkoviča in Dnevnik je stalo lep znesek, ker kolumnist ni “čutil politike” po naše, zato takoj pojasnjujem: Želim si, da bi bil Jamie, pa čeprav je ime angleško in četudi ga že nekaj let dajejo tudi puncam, saj kot bomo videli, ima vsak, ki mu je ime Jamie, čisto svojo funkcijo, ki ima takšen graf, ki se torej izriše tako, kot se pisano napiše Jamie. Ker je funkcija parametrične sorte, se hitro spomnimo, kaj je parametrična funkcija.
Zato smo narisali grafe štirih funkcij, podanih parametrično. Od leve proti desni in navzdol imamo najprej krožnico, lušten zgled parametričnosti. Smo v pravokotnem koordinatnem sistemu, funkcija ima koordinato x in koordinato y, ki se spreminjata kot kosinus in sinus t, pri čemer je t parameter ali neodvisna spremenljivka in ko gre t od 0 do dva pi (ravno perioda obeh funkcij), pride točka, sestavljena iz obeh koordinat, naokoli. Živele krožne funkcije! Sploh imamo lepše ime kot Angleži, angl. trigonometric functions. Kaj je to “tri”, “trigon”, kakšno vezo ima sinus s trikotnikom?! Ne bi ugovarjal, če bi rekli “nasus”, “nasal functions”, tako pa sem.
Sledi “ležeča osmica” (ali znak za neskončnost), ki se od krožnice loči le po podvojeni frekvenci koordinate y oziroma dvakrat hitrejšemu nihanju v navpični smeri. (Tu spelje pot k Lissajoujevim figuram.) Na desni je potlačena Arhimedova spirala, ki jo dobimo iz krožnice tako, da obe koordinati pomnožimo s parametrom, x s t, y pa z 0.75 t (graf stisne ta, 75-odstotni faktor). Velika slika kaže graf funkcije metuljčka cekinčka, tistega potepinčka, ki ima že kar zapleten predpis (zanimiva kombinacija eksponentne in krožnih funkcij), v čemer spomni na Jamijevo funkcijo, kateri se bomo posvetili takoj zdaj:
Njen parametrični zapis:
To ni kisla šala, to sta enačbi funkcije. Izumil jo je čeden izumitelj Jamie Kawabata (narcis), sam pa zdajle mislim, da čeprav se enačba zdi zapletena, se niti ne bi bilo težko spomniti takšne za poljubno ime. Koordinata y se itak ne spreminja drugače, kot da niha gor in dol, a poglejmo enačbo za x, sestavljena je iz enakih členov, ulomkov s kvadratno funkcijo v imenovalcu, graf takšnega ulomka je zvonasta krivulja, ki je skoraj povsod blizu 0, le pri določeni vrednosti naraste, nakar začne spet padati. (Zelo podobno kot Gaussova krivulja.) Zato se ne splača več izgubljati besed, ampak se splača matematizirati lastno ime, nakar naslov, Rad bi bil Jamie, ne bo več pomemben, ker potem bomo lahko vsi Jamiji.
Ko gre parameter t od 0 do 8, se Jamie izriše takole:
Hm, pa pika na i, kdo bo dal, kaj bi dalo piko na i?
*Želim, da bi bil Jamie
8. november, 2008 ob 10:06
Luštkano :)
Pika na i? (5.5; 1.5) ali raje (5.5 + 0.1 cos t; 1.5 + 0.1 sin t) ?
8. november, 2008 ob 11:17
Ja, tako že. :)
Kar pa pomeni dodatno funkcijo ob prvi. Ampak da bi vse naredil samo z eno? Za piko bi se moral na koncu po e prestaviti na i in nekaj narediti. Rabil bi neko singularnost, se mi zdi.
8. november, 2008 ob 12:49
Takšna singularnost je gotovo možna, vprašanje pa je, v kolikšni meri je določljiva v okviru dane funkcije za Jamie.
8. november, 2008 ob 23:45
za pikico bi pač definirali parametrično, a odsekoma zvezno funkcijo in en določeni odsek bi bil pika na i. in to je po mojem vse.
9. november, 2008 ob 6:57
Ja, recimo kar je napisal Rober Q. in pa pogoj, ko t > 8 …, prej pa, kar že piše. Pogoj je lahko narejen z omega funkcijo (integralom delte) ali kakim njenim analitičnim približkom, tako da je vse “lepo”, no, brez kakega if stavka …
16. september, 2023 ob 12:53
Amazing! Its really amazing piece of writing, I have got much clear
idea regarding from this article.
18. oktober, 2023 ob 20:18
I’m not sure where you’re getting your info, but good topic.
I needs to spend some time learning much more or understanding more.
Thanks for excellent info I was looking for this info for
my mission.
23. december, 2023 ob 13:32
Howdy! I simply wish to give you a big thumbs up for your excellent information you’ve got right here on this post.
I am returning to your blog for more soon.
30. december, 2023 ob 3:56
I don’t even know how I ended up here, but I thought this post was good.
I don’t know who you are but definitely you’re going to a famous blogger if you aren’t already ;) Cheers!
30. december, 2023 ob 3:58
My brother suggested I might like this blog. He was totally right.
This post truly made my day. You can not imagine
simply how much time I had spent for this info! Thanks!
30. december, 2023 ob 3:59
Hi, this weekend is pleasant in support of
me, for the reason that this moment i am reading this impressive informative
post here at my house.
30. december, 2023 ob 4:01
Hello! This is my first visit to your blog! We are a collection of volunteers and
starting a new initiative in a community in the same niche.
Your blog provided us valuable information to work on. You
have done a extraordinary job!
30. december, 2023 ob 4:07
I blog frequently and I really appreciate your information.
This great article has truly peaked my interest.
I’m going to book mark your blog and keep checking for
new details about once a week. I subscribed to your Feed too.
30. december, 2023 ob 4:30
Highly descriptive post, I loved that a lot.
Will there be a part 2?
30. december, 2023 ob 4:39
whoah this weblog is magnificent i love studying your articles.
Keep up the great work! You recognize, a lot of
people are searching round for this info, you could help them greatly.
5. januar, 2024 ob 19:17
This post provides clear idea in support of the new visitors of blogging, that
in fact how to do blogging.
5. januar, 2024 ob 20:15
My spouse and I stumbled over here by a different web address and thought
I might check things out. I like what I see so now i am following you.
Look forward to finding out about your web page yet again.
6. januar, 2024 ob 17:11
If you wish for to get a great deal from this article then you have to apply these techniques
to your won blog.
6. januar, 2024 ob 17:40
Hi there! This article couldn’t be written much better!
Going through this post reminds me of my previous roommate!
He always kept preaching about this. I most certainly will send this information to him.
Pretty sure he will have a very good read. Many thanks for sharing!
6. januar, 2024 ob 19:36
Hello there, You have done an incredible job. I will certainly digg it
and personally suggest to my friends. I’m sure they will be benefited from this web site.
6. januar, 2024 ob 19:37
Hello would you mind stating which blog platform you’re working with?
I’m looking to start my own blog soon but I’m having a difficult time deciding
between BlogEngine/Wordpress/B2evolution and Drupal.
The reason I ask is because your design seems different then most blogs and
I’m looking for something completely unique.
P.S My apologies for being off-topic but I had to ask!
6. januar, 2024 ob 20:36
I was recommended this website by my cousin. I’m not sure whether this post is
written by him as nobody else know such detailed about my difficulty.
You are incredible! Thanks!
7. januar, 2024 ob 3:08
I do not even know how I ended up here, however I thought this submit used
to be good. I don’t recognize who you’re but definitely you’re going to a well-known blogger for those who aren’t
already. Cheers!
7. januar, 2024 ob 5:26
I was very happy to find this page. I want to to thank you for your time due to this fantastic read!!
I definitely appreciated every little bit of it and I
have you saved as a favorite to see new stuff on your
blog.
7. januar, 2024 ob 17:50
What’s up, this weekend is good for me, because this moment i am
reading this impressive informative post here at
my home.
7. januar, 2024 ob 18:15
It is in point of fact a great and useful piece of info.
I am satisfied that you shared this useful info with us.
Please stay us up to date like this. Thank you for sharing.
12. januar, 2024 ob 14:50
I know this web page gives quality depending content and
extra information, is there any other web site which provides these kinds of information in quality?
12. januar, 2024 ob 15:38
you are actually a excellent webmaster. The site loading velocity is
amazing. It seems that you’re doing any distinctive trick.
Moreover, The contents are masterpiece. you have done a wonderful
activity in this matter!
12. januar, 2024 ob 16:17
Hello! I just wanted to ask if you ever have
any trouble with hackers? My last blog (wordpress) was hacked and I
ended up losing many months of hard work due to no data backup.
Do you have any methods to stop hackers?
12. januar, 2024 ob 16:59
My family all the time say that I am wasting my time here at web, however I know I am
getting familiarity everyday by reading thes good
content.
13. januar, 2024 ob 18:11
Have you ever considered about including a little bit more than just your articles?
I mean, what you say is important and everything.
Nevertheless think about if you added some great graphics or
video clips to give your posts more, “pop”! Your content is excellent but with pics and clips, this website could definitely be one of the greatest in its
field. Excellent blog!
13. januar, 2024 ob 20:10
I like reading through an article that will make people think.
Also, many thanks for permitting me to comment!
13. januar, 2024 ob 21:52
Thank you for sharing your thoughts. I truly appreciate
your efforts and I will be waiting for your further post thanks once again.
13. januar, 2024 ob 22:11
I’m very pleased to find this website. I want to to thank you for ones time
due to this wonderful read!! I definitely liked every bit of it and i also have
you saved as a favorite to look at new stuff in your site.
14. januar, 2024 ob 1:10
whoah this blog is wonderful i like studying your posts.
Keep up the great work! You recognize, lots of persons
are searching around for this info, you can help them greatly.
21. januar, 2024 ob 13:51
Every weekend i used to visit this site, because i wish for enjoyment, since this
this site conations genuinely fastidious funny material too.
21. januar, 2024 ob 17:42
What’s up colleagues, good article and nice
urging commented here, I am truly enjoying by these.
21. januar, 2024 ob 18:12
Hi there, I discovered your web site by way of Google while looking for a comparable matter, your web site got
here up, it seems great. I have bookmarked it in my google bookmarks.
Hi there, simply became alert to your weblog
thru Google, and located that it is really informative.
I am gonna watch out for brussels. I will appreciate when you continue this in future.
Lots of other folks will be benefited from your writing.
Cheers!
21. januar, 2024 ob 21:52
Hi there! Someone in my Myspace group shared this site
with us so I came to give it a look. I’m definitely enjoying the information. I’m book-marking and will be tweeting this to my followers!
Exceptional blog and fantastic style and design.
21. januar, 2024 ob 22:54
Wow, that’s what I was searching for, what a stuff!
present here at this blog, thanks admin of this site.
21. januar, 2024 ob 22:58
Wonderful post however , I was wondering if you could write a litte more on this
subject? I’d be very grateful if you could elaborate a little bit more.
Thank you!
21. januar, 2024 ob 23:58
Undeniably believe that that you said. Your favorite reason seemed to be
on the web the simplest thing to take into account of.
I say to you, I certainly get annoyed while other
folks consider worries that they just don’t realize about. You managed
to hit the nail upon the top as neatly as defined
out the entire thing without having side effect , other people could take a
signal. Will likely be again to get more. Thanks
22. januar, 2024 ob 13:42
Asking questions are in fact nice thing if you are not understanding
something totally, however this article offers fastidious understanding
yet.
22. januar, 2024 ob 13:45
Do you have a spam issue on this website; I also am
a blogger, and I was wanting to know your situation; many of us have
developed some nice practices and we are looking to exchange solutions with
other folks, please shoot me an email if interested.
22. januar, 2024 ob 14:26
Hello, i think that i saw you visited my web site so i came to “return the favor”.I’m
attempting to find things to enhance my web site!I suppose its ok to use a few of your
ideas!!