Shining a light on how we see numbers

fullsizerenderI love numbers–especially their visual representations.  So when I read this week’s Table Talk Math newsletter that was all about different ways to “see” numbers my mind started thinking about all the great conversations I get to have with students about numbers, and their representations with dice and ten frames and square numbers, cubic numbers and triangular numbers and Pascal’s Triangle and… well you get the picture.

So you can imagine my dismay when I was lying on my back, staring blankly at the ceiling, brain filled with mathy thoughts, and I notice the new LED light bulb I recently installed. And I had to count the number of LEDs that were in it.

I mean, I could see five, but knew there were six.  This got me thinking even more about my bias to visualise numbers like they’re on the square faces of dice. That’s where the five came from, yet the additional one in the middle makes for six.

dice

This led me to wonder what numbers would look like on circular faces.  And if that representations would even be helpful. What do you think?

Circular Numbers (1).png

As I started drawing numbers, one  through five made sense to me.  I really don’t like the lack of rotational symmetry in how I drew two, but I don’t think there’s anything that can be done about that.  After five, I was puzzled at what six should look like.  Should I add a center dot to five like in my LED light, or should  I double three, then add a dot for seven, double four for eight, then add a dot for nine, etc.? If I went with the LED model of six, then there’s a problem in imagining seven.

I’m confused at where the pattern should start, but mathematically that’s a fun place to be.  This has also led me to wonder what dice with round faces would look like too.  The number of faces on such a thing might have implications on the significance of this whole exercise, but that’s a puzzle for another day.

Tell me, where do you see the pattern repeating? Would you do anything differently? Feel free to make a copy of my Google Drawing to play with the numbers!

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