

Mathematical Paper Folding Exhibit (2005) - Mz
http://theiff.org/oexhibits/paper02.html

======
mturmon
The IFF also does some wonderful workshops on "modular origami," which is
building shapes out of, typically, cubes made of business cards.

The basic directions are pretty simple
([http://theiff.org/images/menger/sponge%20cube%20instructions...](http://theiff.org/images/menger/sponge%20cube%20instructions.pdf)),
and you can make the "level 1" Menger cube shown there in a couple of hours.
It's a fun diversion in restaurants to make a cube or two from postcards or
business cards that they might have laying around.

The IFF sponsored a very large Menger sponge
([http://theiff.org/oexhibits/menger02.html](http://theiff.org/oexhibits/menger02.html)),
which was shown around various places in LA, including a library at USC.

Finally, they have branched out in other ways, using iterated construction
rules to make crocheted surfaces that expand everywhere ("hyperbolic
geometry") to mimic coral or other natural shapes
([http://theiff.org/exhibits/iff-e5.html](http://theiff.org/exhibits/iff-e5.html)).
There is one of these at the Museum of Math in NYC
([http://momath.org](http://momath.org)), and they have shown them
internationally ([http://crochetcoralreef.org/preorder-crochet-coral-reef-
book...](http://crochetcoralreef.org/preorder-crochet-coral-reef-book.html)).

------
hobolord
"Using straight edge and compass you can only solve equations with x to the
power of 2."

Why is that?

~~~
hypersoar
First, what does "solving" an equation mean in this context? Start with a pair
of points, defined to be distance one apart. To solve an equation for x is to
construct a line segment of length x (i.e., a line segment of length x
multiplied by the length of that "unit" segment). For example, one can solve
the equation x^2 = 2 by constructing a unit square and then connecting the
opposite corners. With a compass and straightedge, you can make two things:
straight lines and circles, which are defined by linear and quadratic
polynomials, respectively. Any constructible length will then be a solution to
a bunch of equations made from various linear and quadratic polynomials. And
these are the _only_ lengths you can make. You can't make a cubic polynomial
by plugging linear and quadratic polynomials into each other (you can make it
by multiplying polynomials, but that's not what we're doing, here).

The reason "trisecting the angle" is impossible is because it involves solving
a cubic polynomial. One can, however, solve polynomials whose degree is a
power of two. The way to do this rigorously is with field extensions and
Galois theory.

------
dang
We changed the url from
[http://theiff.org/oexhibits/paper01.html](http://theiff.org/oexhibits/paper01.html)
to what seems to be the most substantive part of the series.

