(no subject)
May. 13th, 2005 09:22 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
which_chickAll of the geeky math friends that I have already know all about this. If you're one of them, please skim, nod, and smile.
The NON-geeky-math friends, lookit! Pinecones! Math!
Quite some time ago, I read that pinecones had something to do with number theory or impressive math or some such fucking thing. Today, while I was waiting for the ballot box to be delivered (we have primary elections on Tuesday, so they were delivering the ballot box this evening so's we could be ready. It's a metal box. For holding ballots. Paper ballots. Yes, we are in the stone ages here in BumFuck.) I took a few pictures of pinecones so that I could, with the help of t3h interw3b, examine the pinecones and see if people were slinging bullshit or if the business what with math and pinecones was for real.
Since the internet takes pity on fools like me, google has useful responses for "pinecone math" in the first three results, including the name Fibonacci. Thank you, Mr. Gore! Your invention is truly the eighth wonder of the ancient world!
Wikipedia has a nice article on the Fibonacci sequence, but you don't have to read that if you don't want to. You don't need that much to grasp the pinecone thing, but it's nice reading anyway. The people at Wikipedia generally write pretty solid entries.
To get the pinecone math thing, you need to know the following stuff...
1. The Fibonacci sequence you will need for the pinecone math thing is this one: 0,1,1,2,3,5,8,13,21,34,55 (etc). It's generated by N(i) = N(i-1) + N(i-2), if that helps.
2. Pinecones have spiraly organization wherein the number of rightward spirals is a Fibonacci number from the sequence above and wherein the number of leftward spirals is an ADJACENT Fibonacci number from the same sequence. This here is the interesting thing about pinecones and math, this thing with the number of rightward and leftward spirals and adjacent Fibonacci numbers from the sequence above. (Lots of other plants ALSO have this organization with spirals and the Fibonacci number thing going on, but people always mention pinecones so I'm doing pinecones. What can I say -- I'm trendy. I'm with it. I'm hip. I'm fucking happening!)
Let's look at some examples (with colored spirals I drew on the pinecones so's you can see what the hell I'm counting). I know you're as excited as I am to see if this really actually works with real, actual pine cones or if it's just math teacher bullshit.
Pinecone One: 5 and 8 are sequential Fibonacci numbers.
Pinecone Two: 8 and 13 are sequential Fibonacci numbers.
Pinecone Three: 8 and 13 again.
Conclusion: The pinecone thing probably isn't bullshit. It worked three for three. That's good enough for me.
The NON-geeky-math friends, lookit! Pinecones! Math!
Quite some time ago, I read that pinecones had something to do with number theory or impressive math or some such fucking thing. Today, while I was waiting for the ballot box to be delivered (we have primary elections on Tuesday, so they were delivering the ballot box this evening so's we could be ready. It's a metal box. For holding ballots. Paper ballots. Yes, we are in the stone ages here in BumFuck.) I took a few pictures of pinecones so that I could, with the help of t3h interw3b, examine the pinecones and see if people were slinging bullshit or if the business what with math and pinecones was for real.
Since the internet takes pity on fools like me, google has useful responses for "pinecone math" in the first three results, including the name Fibonacci. Thank you, Mr. Gore! Your invention is truly the eighth wonder of the ancient world!
Wikipedia has a nice article on the Fibonacci sequence, but you don't have to read that if you don't want to. You don't need that much to grasp the pinecone thing, but it's nice reading anyway. The people at Wikipedia generally write pretty solid entries.
To get the pinecone math thing, you need to know the following stuff...
1. The Fibonacci sequence you will need for the pinecone math thing is this one: 0,1,1,2,3,5,8,13,21,34,55 (etc). It's generated by N(i) = N(i-1) + N(i-2), if that helps.
2. Pinecones have spiraly organization wherein the number of rightward spirals is a Fibonacci number from the sequence above and wherein the number of leftward spirals is an ADJACENT Fibonacci number from the same sequence. This here is the interesting thing about pinecones and math, this thing with the number of rightward and leftward spirals and adjacent Fibonacci numbers from the sequence above. (Lots of other plants ALSO have this organization with spirals and the Fibonacci number thing going on, but people always mention pinecones so I'm doing pinecones. What can I say -- I'm trendy. I'm with it. I'm hip. I'm fucking happening!)
Let's look at some examples (with colored spirals I drew on the pinecones so's you can see what the hell I'm counting). I know you're as excited as I am to see if this really actually works with real, actual pine cones or if it's just math teacher bullshit.
Pinecone One: 5 and 8 are sequential Fibonacci numbers.
Pinecone Two: 8 and 13 are sequential Fibonacci numbers.
Pinecone Three: 8 and 13 again.
Conclusion: The pinecone thing probably isn't bullshit. It worked three for three. That's good enough for me.
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no subject
Date: 2005-05-14 12:58 pm (UTC)Thanks for doing this--the red and blue swirls were exactly what my tired eyes needed this morning.
no subject
Date: 2005-05-14 01:17 pm (UTC)What I am counting is the number of rightward (CLOCKWISE -- shown in red) swirls and the number of leftward (COUNTERCLOCKWISE -- shown in blue) swirls. The number of rightward swirls and the number of leftward swirls on a pinecone are *generally, but not always* adjacent Fibonacci sequence numbers, and that's the thing we're looking at here.
The reason pinecones (and other plant things) grow this way probably has something to do with efficient packing on a molecular level. You can read more about phyllotaxis in general and Fibonacci phyllotaxis in particular here:
http://maven.smith.edu/~phyllo/About/fibogolden.html (http://maven.smith.edu/~phyllo/About/fibogolden.html)
no subject
Date: 2005-05-14 01:36 pm (UTC)no subject
Date: 2005-05-14 05:02 pm (UTC)If you'd like more information, here's some nice content on Fibonacci and plants in general (including pinecones): http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#golden (http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#golden)
Some further information specifically on pinecones (with lovely pictures) can be found at the following page: http://www.math.ohio-state.edu/~goldstin/pinecones.html (http://www.math.ohio-state.edu/~goldstin/pinecones.html)
Hope that this helps.