I love circles. Learning about circles formally, however, was so obscure and opaque that I’ve put in some time trying to imagine visuals to clear up my confusion.

Here’s a picture I came up with to visualize the circumference/diameter relationship:

Okay, so does this make sense to anyone out there? Please let me know.

I put this together because I like to know what things look like. Telling me that circumference divided by diameter equals 3.14159…, or pi, conjures up absolutely no pictures at all. I’ve often confused radius with diameter, which is completely understandable considering that after being taught the circumference/diameter thing, forever afterwards all the formulas use radius so, you know how it goes? My wires got crossed and all of a sudden radius and diameter seemed somehow synonymous.

For those of you who know what I mean, but are still unsure about the difference between radius and diameter, I offer this: Diameter comes from the Greek: meter means measure, and dia means across, so diameter is the length that measures all the way across the circle. Now, think of radius like a ray from the sun: it starts in the center and travels out, so it’s half of a diameter.

By the way, I so much like the way that the image above visually explains the Pi relationship that I’ve put together a hands-on cut-and-paste activity to really drive the point home. It’s 19 photographs long. I think it will be a few days before I put it up.

And, just in case you’re wondering, this is still a bookmaking and paper works blog…see, I use circles in bookmaking, too!

ADDENDUM: 12/2016 Below are some links to some of my other Pi Pages

Pieces of Pi: Colored in examples of some Coloring Pages for Pi to help with remembering the different ways pi is expressed when doing calculations that need to yield a specific rational number.

Visual artist Paula Beardell Krieg has been teaching bookmaking to students in schools, to teachers and to other artists since the mid 1980's.
View all posts by Paula Beardell Krieg

Thanks for the feedback on the circle illustration!
The book that has the crinkle look on it used regular weight paper, maybe an Arches Text Laid, or something comparable. First I did the crayon drawing, then crumbled up the paper. Next, I apply a coat of acrylic paint, then wipe it off: the paint stays in the cracks.

What do you think…when I am done with Pi, should I do a post on this technique?

I’d be interested in the process you used for the bright circles one. Did you crinkle up tissue paper, glue it, then color it?

Also, I think the 3 radii wrapping around the circle is a REALLY good visual for kids in math to understand that concept – did for me.

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Thanks for the feedback on the circle illustration!

The book that has the crinkle look on it used regular weight paper, maybe an Arches Text Laid, or something comparable. First I did the crayon drawing, then crumbled up the paper. Next, I apply a coat of acrylic paint, then wipe it off: the paint stays in the cracks.

What do you think…when I am done with Pi, should I do a post on this technique?

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