Origami, Geometry, and Math

Origami, Geometry, and Math have many shared concepts and uses.  Other subjects sometimes taught separately such as Algebra and its advanced topics blend right into Calculus.  Math in its many manifestations are representations of the same underlying concepts; for example, (a+b) squared, can be worked out with algebra, but it can also be represented in squares and rectangles of a square with a side of length (a+b). https://www.mathdoubts.com/a-plus-b-whole-square-geometric-proof/   Using either the geometry or the algebra, the answer turns out to be the same.  Why? it's the same underlying idea, we are looking at and solving the same problem through either an algebra viewing lens, or a geometry viewing lens.

Origami of course is closest to geometry in physical appearance. There are, however, things that can be easily done with origami that are hard to do with conventional tools of geometry (straightedge, compass), such as trisecting an arbitrary angle.  See https://plus.maths.org/content/trisecting-angle-origami for details. 

Starting with basic constructions, it is possible to arrive at either exact 30 and 60 degree angles, or usable approximations of a 72 degree angle (a whole 360 degree circle divided into fifths), and those useful approximations can be used in origami construction that are sometimes clumsy using a protractor and ruler.

Coming back to the original point, Origami, Geometry, Algebra, Calculus and other aspects of Mathematics are simply different viewing lenses, or windows with which we look at a set of concepts and principles.  Sometimes Origami can give us an angle that is useful and pleasing to look at.