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Friday, January 20, 2017

Intersecting Curves

 
One morning earlier this week it was frosty outside and I thought this was an intriguing pattern. Notice how all three lines intersect at the same point in the lower corners.

intersecting curves

Have you figured out what this is?

If you have, your mind correctly interpreted that although the lines appear to touch and be in the same plane, it really has three dimensions.

It's my ordinary old-fashioned clothesline. The lines don't really intersect because we know there is a third dimension. If we move to a different location in that third dimension, depth, the lines are actually pretty much parallel (and not nearly so interesting).

clothesline

Gives a person something to think about, eh? We live in three dimensions and are sure we know what things look like. But what if there is a fourth spatial dimension that we don't know about? If we could move just one step in that direction things might be quite different. Maybe we shouldn't be so sure we know it all.

By the way... if you are wondering why those corners in the first picture line up so nicely, it's not a trick of where I was standing. It's math. X^2 - y^2 = -1 to be exact. Some of you will understand.

See Fluid Geometry
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1 comments:

Ann said...

I don't have a mathematical mind. A calculator does my math for me. I do like that first picture though and it's always amazing to me how a different perspective can give something a whole different look

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