Sunday, 30 September 2007

origami haga

Fionn and my weedding anniversary. We went into Dublin castle and visited gardens and library with kids.
Kids complimented on being very good in library. :)
And then we had food in the Schoolhouse (after throwing sticks into the canal).
Fionn had gotten me some small origami paper.
I had some paper and an origami book on my bed-side locker pile a few months ago but it has been put way again.
Anyway I got out oftc (Origami For the Connoisseur - a lovely origami-fest).
And almost the first thing in it is Haga's theorem which I had passed over everytime before.
I looked at it this time and the diagram in oftc is not great.
It mentiones a third triangle and isn't very clear. Hmf!
So I filled up and A4 sheet with algebra and found by applying pythagoras about 5 times that yes it divides the side
in a third. Yay me.
So tomorrow I look it up and find of course with one application of pythagoras you can prove the same. :D
Still puzzled over the three triangles oftc talks about?

Simple Haga Theorem
Let a be length of side of square.
Crease square in half NOT along diagonal (vertically here) (so that one has a rectangle a x a/2) and unfold.
Fold corner of square (bottom right corner here) so that it touches the midpoint of an opposite side (top side here).
The intersection of the two edges which overlap is a third of the way up (the left side here).

This paper by Robert Lang goes into more detail
Origami and Geometric Constructions
Starting with binary division (i.e. folding in half!) and going on to general case of dividing paper into any integral fraction (look for Haga's construction).
Lang Origami Constructions paper

Geometry origami

Math on the Street, a magic pinwheel, very nice, remind me to try make it sometime:
magic pinwheel

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