11:7 Rectangles

When I made the Valentine's Day heart last week, I stumbled into a rectangle of paper that was 11:7. That size rectangle works perfectly for the model. It was unintentional, not a simple matter of altering an 8.5 x 11inch sheet of paper. What I actually came up with was a sheet that was 9 x 5+13/16 inch and scaled it up so that one side would be 11 inches and it could be nicely made from an 8.5x11 sheet without too much hassle. After scaling, I realized the ratio would be 11:7. I know how to make a lot of rectangles from any given sheet, but 11:7 is an odd one. So I have been searching for a shortcut so that I don't have to measure it with a ruler.

I have two shortcuts. The first is from a sheet that is 8.5 inches by 11 inches. The second is from a square.

==( 1 )==

This shortcut works only because I already know the dimensions of the starting sheet (8.5x11). If you're using A4 or some other such paper, this wont be much of a help.

To get 7 inches from 8.5 we must subtract 1.5 inches (duh). The diagonal crease from the corner and the vertical crease from the center intersect at the corner of a 5.5x5.5 inch square. Which means it's 3 inches from the bottom and half of that is 1.5 inches. 

You do not necessarily need to remove the bottom section, but just know that it is superfluous and will need to be hidden inside the model.

==( 2 )==

 This shortcut is more complicated. Also, it is not as easy to memorize as the one above. Also, it does not arrive at a perfect 11:7, but instead arrives at a 11:7.046875. I suspect, though, that is plenty close enough for most models.

The diagram below indicates the creases that need to be made, the first ones on the left and then moving to the right. The first five creases are just to find the point on the sheet that is roughly 3/11ths from the bottom. The top section will be 8/11ths, so fold that in half and you get 4/11ths. cut off the 4/11ths and you get a rectangle that is 11:7.

I don't know what other projects require an 11:7 rectangle, but if you know of any, let me know!

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