MATH IS FOR THE BIRDS! Part 1

Black Capped Chickadee

An Invitation to 
Urban Birdwatching

********************************

Sitting on the back steps of my home in East Vancouver earlier this week, I was visited by four different kinds of birds. I identified them using a guide to birds in Vancouver.

European Starling

Bushtit

House Finches

The house finches appear in a pair. The male has salmon coloured feathers. The female is mainly brown and grey to help her go unseen when she sits on a nest. The two of them like to sit and feed on the top of my kale plants that are going to seed. 

I listen to the birds sing and call and when I see them. I want to try to identify them by their sounds even when I can’t see them.

ACTIVITY: START A BIRD JOURNAL

Start with three or four birds that you can see from your home or on walks close to your home. Using drawings and writing, record what you notice. 

Which birds do you see?

What do they look like?

Are the male and female different?

Identify them by name? 

What do you notice them eating?

What calls and songs do you hear?
Do they move about alone, in pairs, in groups?


Start a routine of recording when you see or hear these birds. How will you record over time?

Identify and describe more birds as you notice them.

Fractals 2 of 5: Drawing Fractals

We can draw fractals!

https://www.youtube.com/watch?v=PU1dwwB_Im0

Try drawing these... then, see if you can come up with your own fractal 'seeds' and draw them out to make your own original fractals... and share them with us in the comments!

www.study.com

   

https://en.wikipedia.org/wiki/Pythagoras_tree_(fractal)

Can you find some fractals outside? Or maybe even inside your fridge?

More references:

https://www.wikihow.com/Draw-the-Koch-Snowflake
https://www.es.com/Shows/FantasticFractals/FantasticFractals_EducatorsGuide.pdf

Fractals 3 of 5: Fractals in plants

I went outside fractal-hunting today. I was looking at plants, and here are a few of my findings:

A red cedar branch. It's Y's all the way down!

A camelia flower, its petals going round and round.

Each branch of this shrub comes from another (thicker) branch and so on until the trunk. Below ground, its root system is like a branch system that we could draw as a fractal.

Look at this really cool photograph (done by an artist) of an autumn leaf CLOSE UP:

PAUL OOMEN / FINEARTAMERICA.COM

Are there fractals in the plants around where you live, too? 

I wonder why plants grow with repeating patterns like this...does Nature just find fractals pretty or is there more to it? What do you think?

Fractals 4 of 5: What is the shape of a cloud?

Cloud photo credits: Susan Gerofsky

 Here's a lovely thing to do together, especially on a day when the sky is blue and those fluffy cumulus clouds are moving around in the wind. Try looking up (or better yet, lying on your back in the grass) and watching the clouds.

You might try photographing or drawing them, as I've done here. But how to draw a cloud? What shape is a cloud?

We have learned the names of shapes with straight-line edges like triangles, rectangles and octagons, and curved shapes with continuous line edges like circles, ellipses and parabolas. But none of these really describes the ragged-edged (and ever-changing) shapes of clouds.

You might notice that some clouds look a lot like the maps of islands, continents and shorelines. (The bottom photo here reminds me of a map of Europe and the Mediterranean...) Shorelines are also ragged-edged and changing, more slowly, because of forces of erosion and tectonic shift. So if we can figure out what shape clouds are, we might also figure out what shape islands, continents and shorelines are!

Try looking at a small bit of a cloud you have photographed. Is there a small section of the cloud that looks almost like a miniature version of the whole cloud? If so, then you may have discovered a fractal 'seed' that can be copied bigger and bigger (and/or smaller and smaller...) to create the shape of the whole cloud! That is what is meant by a fractal: a shape that repeats itself in more or less the same way on different scales ( really tiny, small, medium, large, really large...) to create a ragged-edged and evolving shape without straight-edged boundaries.

Here is a good explanation by a meteorologist at the University of Bonn, Germany about the ways that clouds are at least partly fractals (and not always completely so, as the big central parts of clouds are not as affected by wind turbulence as the edges).

 And here is a very nice film about natural fractals, featuring the mathematician who 'discovered' fractal geometry, the late Benoît Mandelbrot!

Try drawing the shape of bumpy or ragged edge of a cloud. It might be easiest to draw it fairly large on your page. Then, on each of the 'bumps' try drawing smaller bumps that have the same shape only smaller. Do that again, three or four times. Are you getting a shape that looks a bit like the edge of a cloud -- or a shoreline?