Folding fractions

There's an easier way to do this by the way:

Fold an arbitrary length perpendicular to the axis you want, then fold that length again... To X folds. Fold diagonally from top corner to the last fold then fold at the the intersections.

   ___    ___    ___    _____
  |   |  |___|  |__/|  |_|_|/|
  |   |  |___|  |_/_|  |_|/|_|
  |   |  |___|  |/__|  |/|_|_|
  |   |  |   |  |   |  | | | |
  |   |  |   |  |   |  | | | |
  |   |  |   |  |   |  | | | |
  |   |  |   |  |   |  | | | |
  |___|  |___|  |___|  |_|_|_|

Folding a third is not nearly as impressive as angle trisection, which is impossible with a straight ruler and compass, but possible using origami.

http://en.wikipedia.org/wiki/Angle_trisection#Using_origami

This is really useful for origami, when you want to fold unusual splits into your paper.

You can also use it in the opposite direction, so instead of bringing the point up to a specific mark on the top edge going from left to right (e.g. 1/2 on top gets you 2/3 on the right that you divide in two to get 1/3), you plan it so that your right edge get's crossed at 2/n (e.g. fold the paper so that the y length is 1/2, then your point will hit the 1/3 mark at the top of the paper). This is useful when you want to go from an easy fraction like 1/8 to 1/7, as opposed to going from 1/4 through 1/5 and 1/6 to get to 1/7.

I love using doing things like this.

Possibly somewhat off-topic, but the proof for the equation sin(A + B) = sin A.cos B + cos B.sin X is quite a nifty diagram that can be found here:

http://en.wikipedia.org/wiki/List_of_trigonometric_identitie...

It seems like the link to the book is broken.

Origamics: Mathematical Explorations Through Paper Folding https://books.google.com/books?id=zJR2Rr_wuFQC

This is one of those interesting items that is truly deserving of the headline "Neat Trick."

It reminds me of a card trick that I learned as a child that appeared to work by magic, but instead worked every time because it involved something complex going on involving math.

The is a delightfully entertaining article! Does anyone have a recommendation on the Kazuo Haga book, "Origamics"? vs David Mitchell's "Paper Crystals"? Origamics is a bit pricey... worth it?

Always wondered how to do this and never figured out how. My solution was to roll up the paper into a circle and slowly crease at the right roll amount. Reminds me of my old compass and straight edge lessons...

Interesting. But, it must be said that he was just lucky that the x^2 terms canceled :)