# Proof for triangle division into sevenths

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Basically, what's going on is that the division along the side of the triangle serves as the necessary references for a larger triangle. So this is an exact construction for division into any number 2n-1.

*edit* In case it isn't obvious, I put in a dotted line showing why it's 2n-1 and not some other number. My brother also pointed out that this will work for ANY triangle, not just an equilateral one. Following up on that, it seems that this triangle is an application of the Crossing Diagonals method on half a parallelogram.

daniel64, Ray Schamp, Gollinbursti, and 3 other people added this photo to their favorites.

1. Holy bejeezums!!!! You're on the edge of something, I just have no idea what/...
Could I understand this any less? Not complaining or anything, but either you are a rocket scientist or mayba I gotta go back to school....

2. This image could be used to demonstrate what I mentioned in my other comment about how slope-tricks work with triangle grids... Though you are using it to serve a different purpose (obtaining "awkward" divisions).

It seems that you have managed to stumble your way from a random curious case to a rediscovery of the crossing diagonals method. It's like finding you way back to civilization xD

3. Haha, it's like rocket science but I can't get a degree or a salaried job out of it :D Selfless sacrifice for the arts I guess, though that seems far too romanticized. Maybe just getting obsessively involved in my little hobby :D

Finding your way back to civilization is a good way to put it. I keep being surprised at how elegant and powerful the Crossing Diagonals construction is... Sometimes it seems like most of geometric origami comes from the application and generalization of a few basic concepts.

4. By the way, this method would have been PERFECT for this model of mine from 6 years ago: www.flickr.com/photos/8303956@N08/650685427/

As you can see, I had settled for the approximation technique, which is in every way less elegant than this.

5. And you're still wondering whether or not you should take more math classes??? Just do it! (And you could totally get a degree and a salaried job out of math! And if you choose to specialize in branches of math that are related to origami, then all the better!)

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