Math Tales

I could spend all day watching this channel .

Note: While some of these are better suited to older kids (if you actually expect them to under the concepts behind them) they do have plenty of younger kid appeal to those in to drawing.

A Möbius strip story:




Fractal Doodles!! X2  (Yes, someday I'll get over fractals, I promise. )






In truth, I obsess over these things, because I love mathematics but I hate arithmetic.  And the fact that we don't commonly know the difference is the tragedy of math curriculum.

Theme for the Day: Fractals

Remember my earlier post on fractals?   Well, I'm truly hopeless at this point, so I need to share my obsession.

So what are fractals anyway?

Wiki says:  a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.

Well (for the non math people like me) that basically that means layers of repeated shapes that can be calculated by a formula.  But you don't need a formula to enjoy them.  Check these out:

• Fractals in nature and even in the garden 
• Fractal art gallery on Cool Math
• Also check out the wiki link for some lovely examples

Ready to make your own?  Try these cool (free!) online generators:

• "Snowflake" style - design your fractal with five straight lines
• Cool Math has five
• Easy Fractal Generator lets you draw a Julia or Mandelbrot set (or a custom one if you are mathematically inclined) and lets you export your finished work to a file for printing.  Nice.
• This generator is similar to the snowflake one above but lets you overlap fractals and export the finished work
• Sierpinski Triangle

Hands on and fun links for the younger kids:

• this pbskids.org    project 
• The fractal foundation project
• Sierpinski Triangle color page
• Sierpinski carpet (cubes) color page
• Sierpinski gear (circles) color page
• A youtube.com search for "fractals" will give hundreds of results
• Fractal your dinner with the unusual  Romanesco cauliflower (see the details here - scroll down)
• Fractal cookies!  (Okay - a brave parent will have to help with this)
• Fractals in clay  (again better to stick with fewer iterations- repeats- with the little ones)

For the older kids and the lesson planners:

• pbs.org has a wonderful fractal lesson from Nova episodes including:
• A generator
• An article on Benoit Mandlebrot
• A fractal lesson that includes an interactive and a   discussion of fractals 
• A working video link to an interesting story about fractal analysis of tapestries
• You might notice the link to the Nova episode Hunting the Hidden Dimensions which is no longer available on PBS.org.  It is available for free on Hulu however. 

• Hoagies has some recc'd some interesting sites also.

Downloads

• A caltech worksheet for the Sierpenski Triangle. Notice! This is a word doc that will want to immediately download.
• A PDF worksheet on fractal math from fractalmath.com, advanced HighSchool+
• A PDF worksheet from Randoff College for grades 5-8
• Open Source software to download. Note: I have not trialed, so use at your own risk.
• A trial copy of (not-free) fractal software. Note:  I have not trialed, so use at your own risk.

Fractals Have Taken Over

What started out as an attempt to combine art with math for a fabulous home school assignment, ended up a little bonkers. It was innocent enough at first with paper and scissors and colored in Sierpinski Triangles.

Then I found this site.  (Also check out the enlargements of those beautiful models shown mid-way down and then scroll all the way to the bottom of the page and look at those too.  Wow!) My first thought was wow, soda cans! My second thought was er, soda cans? Mathematicians are sorta scary.

And yet, I figured, we could do that. (Maybe not with soda cans though.)  At first, I thought of cut up drinking straws.  I cut three of them into little pieces and realized that was way too much work.  Then I thought, melty beads! Someone had donated a ginormous pack and the associated hardware to the scouts. Hmmmmm.

Yeah, well, I'll spare you the rest of the thought process and skip to the end.

Ta Da!

Not perfect, I know, but the little points don't quite line up right.  Might try the square frame with a Sierpinski carpet next.  Yeah, clearly homeschooling is sending me over the edge.


ETA:  Eliminating bottom-most row of clear beads and putting the aqua frame beads in their place seemed to fix the problem.  I'm sure a mathematician could tell me why this is but I don't think I want to know. ;-)

(Sorry, the treehouse should be continued tomorrow.  I didn't have time to get all my photos together for today's post)