Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [2 of 3]

[pokerfan]

This is a fun series...

Stay tuned for part 3, where we solve ALL the mysteries. Well, sort of. Coming soon! (2 weeks?)

Note: Beautiful spirally non-Fibonacci pinecones are very rare! If you find one, keep it.

[chervilant]

1. OMG!!

This is GREAT! I can't wait to show this to my math students!!!!!!!!

[chervilant]

2. Sigh...

I bet hardly anyone will view or comment on this great video... I will be coming back to check. If I am right, I will be adding more comments, hoping to motivate the mathemati-phobes to take a peek...

[pokerfan]

3. I posted part one here a couple of weeks ago

and it received no comments.

http://www.democraticunderground.com/1228592

[chervilant]

10. Wow.

I spent almost two hours on utube last night, watching Vi's other videos. That child is amazing!!! As a math teacher, I am constantly seeking effective ways to captivate my students' imaginations, AND promote a sincere love of math. I think Vi is the greatest math educator I've ever witnessed! I will be having my students watch her videos and get just as creative with their math projects.

[Jim__]

4. That raises so many questions.

For instance, at the beginning of the video she tries spacing the leaves at 180 degrees, so the second leaf is on the opposite side of the stem, then the third leaf is over the first leaf, but in the drawing, there is a lot of vertical space between the leaves and given the varying height of the sun across a day, this arrangement might give each leaf more sunlight across a day rather than an arrangement where a leaf gets sunlight, say, only in the morning. Does this spiral arrangement actually maximize the amount of sunlight each leaf gets across a period of a day? Would the optimal arrangement of leaves depend upon the latitude that the plant grows in? Is the spiral arrangement optimal given a random latitude for the plant?

According to wikipedia ( http://en.wikipedia.org/wiki/Phyllotaxis ) the arrangement of leaves is largely dependent upon the distribution of auxin:

The pattern of leaves on a plant is ultimately controlled by the local depletion of the plant hormone auxin in certain areas of the meristem.[3] Leaves become initiated in localized areas where auxin is absent. When a leaf is initiated and begins development, auxin begins to flow towards it, thus depleting auxin from another area on the meristem where a new leaf is to be initiated. This gives rise to a self-propagating system that is ultimately controlled by the ebb and flow of auxin in different regions of the meristematic topography.[4]

Why would that lead to a spiral pattern of leaves? That seems more likely to lead to the 180 degree pattern.

Interesting video. I wish I had time to look into this a little bit more.

[pokerfan]

6. Did you watch the first video in the series?

There's also more here on Wolfram Mathworld. Not so much the article itself but a whole bunch of references: http://mathworld.wolfram.com/Phyllotaxis.html

I don't think it's so much a matter of it having to be this way because, as you noted, a 180 degree spacing could work more or less as the third leaf doesn't completely shade the first lead as it's further up the stem. It's just that some arrangements are more efficient than others and natural selection has a way of rewarding the most successful.

It's not entirely unlike the life cycle of the Cicada (http://en.wikipedia.org/wiki/Cicada#Life_cycle) being on 13 or 17 year cycles, both prime numbers. A sort of natural Archimedes sieve which generates prime numbers.

[SemperEadem]

5. wow... my head hurts

I'm glad nature got this figured out a long time ago.

[ensho]

7. neat! thanks for posting

nt

[Little Star]

8. This is so neat! k&r

[JDPriestly]

9. Fascinating. She talks too fast for me so I will have to watch it again.

But since I love plants, it really holds my interest.

Math was not taught like that when I was a kid. This is much more interesting than what I learned.

Is there a link for this?

[pokerfan]

13. Links

Vi Hart's social links:

YouTube channel: http://www.youtube.com/user/Vihart
Blog: http://vihart.com/
Facebook: http://www.facebook.com/pages/Vi-Hart/154711904574944

And more reading on the fibonacci series and the golden ratio:
http://science.howstuffworks.com/environmental/life/evolution/fibonacci-nature1.htm
http://www.environmentalgraffiti.com/news-natural-patterns-and-their-perfection
http://photoinf.com/Golden_Mean/Stuart_Low/The_Golden_Mean.htm
http://en.wikipedia.org/wiki/Golden_ratio

[chervilant]

11. Yipeeeeeeeee, pokerfan!!!

So thrilled to see more responses to this creative genius' work! Thank you so very much for posting these vids. Can't WAIT for the third installment!

[tclambert]

12. Slug cats?

[BlancheSplanchnik]

14. saving

this

Thanks!

[Richardo]

15. Vi Hart is a big favorite of mine

My brother teaches middle school math and he introduced me to these videos.

[shireen]

16. thanks for posting

those two videos were a lot of fun!

[UnrepentantLiberal]

17. That was great.

Very original.