#### Thesis Title

#### Date of Graduation

Summer 2013

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Kishor Shah

#### Keywords

straightedge and compass, origami, folding, conic-constructible points, intersecting conics

#### Subject Categories

Mathematics

#### Abstract

We study mathematical origami and conic-constructibility in this thesis. We explain how to construct cube roots, solve cubics and certain quartics, and trisect angles. Videla defines the set of conic-constructible points to be an infinite union of certain finite sets. We are able to establish a detailed multipart theorem involving these sets. Furthermore, we use mathematical induction to provide a clearer proof of Videla's theorem that gives a criterion to determine conic-constructible points. It is known that the field of origami numbers equals the field of conic-constructible numbers; we provide a proof of one inclusion using the aforementioned sets. In this thesis, a main reference for origami is Galois Theory by David Cox and for conic-constructibility, the paper in The Mathematical Intelligencer by Carlos Videla.

#### Copyright

© Sarah Kate Rodrigues

#### Recommended Citation

Rodrigues, Sarah Kate, "Mathematical Origami and Conic-Constructibility" (2013). *MSU Graduate Theses*. 1650.

https://bearworks.missouristate.edu/theses/1650