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FLATLAND: A Romance of Many Dimensions

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Edwin A. Abbott was born on December 20 1838. Abbott was an English school headmaster and theologian who in 1884 wrote a very unusual book, Flatland: A Romance of many dimensions, under the pseudonym of “A square”. It predated Einstein’s ideas about the 4th dimension and is a social satire which tells the story of a world where there are only two dimensions, no third dimension that would give us height. Men are polygons, women are line segments and a circle is the perfect shape (an infinite polygon). A film was made about it in 2007.

The funny thing is that when Duffy and I first met way back in the late 1980s we discovered that we both had a copy of this unusual book. I know of only one other person who had a copy, my friend Bill Barry, a famous mathematics educator from Sydney in the 1960s through to the 1980s.

Perhaps thinking about the world as only 2D can help our primary students understand 3D better. Imagine as a girl you are a straight line. When you move you can move forwards or backwards and if you bump into anyone you would sort of bounce off them. However if you are a straight line and you move sideways, when you bump into someone you might hurt them as you would have a sharp point on either end.

Boys are polygons which mean they have at least 3 straight sides. So depending on how they move they might bounce off their 3 straight sides or hurt someone with their 3 sharp corners. And boys might also be a square or an oblong, or a pentagon and so on. They become more dangerous as the number of sides increase.

If you are a circle, no matter how you move you will bounce off other people in your area as long as their pointy ends or corners don’t stick into you. You can sort of move anywhere you like without worrying about who you might bump into but still trying to avoid those sharp points. But when you think about it, you would appear to be a straight line when viewed by a non-circle. Your centre would be closer to them and perhaps the outer parts of your “line” would be a little shadowy. It would be quite a subtle distinction. I think inhabitants would learn to tell the difference between encountering a circle or a non-circle and act accordingly.

So Flatland would be quite a scary place to live. It certainly gives you heaps to think about and discuss together with your students, especially with Stage 3.