Reflection - Class FIVE

Pure mathematics is, in its way, the poetry of logical ideas.
- Albert Einstein

I was sort of lost while going through the division of fractions, so I ended up working on an origami crane. But there was a sudden thought-provoking moment that got me thinking whether there was any mathematical sense in origami. So this was what I found:

Some classical construction problems of geometry — namely trisecting an arbitrary angle, or doubling the cube — are proven to be unsolvable using compass and straightedge, but can be solved using only a few paper folds. Paper fold strips can be constructed to solve equations up to degree 4. (The Huzita–Hatori axioms are one important contribution to this field of study.) Link: Origami & Geometric Construction

And then I further read on about Pick's Theorem that provides a method to calculate the area of simple polygons whose vertices lie on lattice points—points with integer coordinates in the x-y plane. The word “simple” in “simple polygon” only means that the polygon has no holes, and that its edges do not intersect. Refer to this article: [Pick's Theorem].

The 4 content goals for geometry, p.400:

1. Shapes and Properties
2. Transformation
3. Location
4. Visualization

Wow! So much for mere shapes of circle, triangle, rectangle and square. =\