Origami Pots

Angle trisection with Origami and related topics

“…The equivalence of (i) and (ii) follows from algebraization of the axioms, which shows that axioms (1)- (7) are equivalent to Origami-construct the roots of any irreducible polynomial of degree at most three with coefficients that are already Origami-constructable. For this see [20] or [1,19]. The equivalence of (ii) and (iii) follows as in the classical case (cf.…”

“…Axiom (6) however is equivalent to solve arbitrary cubic equations. In [20] this is deduced directly by studying the relevant algebraic equations. R. Alperin in [1] identified the pair given by a point and a line by a conic whose focus is the given point and directrix is the given line and uses some basic algebraic geometry.…”

“…They are called the Huzita-Hatori axioms for origametric geometry (sometimes the Huzita-Justin axioms). It was proved by Lang that these axioms completely describe all operations that can be performed by paper folding (see [20]) and therefore they are now the fundamentals of the mathematical theory of paper folding. We say that z ∈ R is Origami-constructable if the point (z, 0) is in N .…”

“…There are also other Origami constructions for 3 √ 2, e.g. based on solving the cubic equation X 3 − 2 = 0 (see [20]). Another classical question is which regular polygons can be constructed by compass and ruler.…”

An origami-inspired cargo drone

“…Origami structures have been shown to achieve high strength-to-weight ratios [10][11] and a significant size reduction by folding [12][13]. Among the possible origami designs [14][15] (Fig. 2A, 2B), the drone cage is inspired by the pattern used for foldable shelters [16] (Fig.…”