Jun Maekawa Origami May 2026

Author: [Your Name/Institution] Date: April 13, 2026 Abstract Jun Maekawa is a pivotal figure in modern origami, distinct from both the traditional Japanese school and the later hyper-complex "super-complex" origami movement. This paper examines Maekawa’s dual legacy as a physicist and artist, focusing on his development of the Maekawa Theorem (concerning the parity of mountain and valley folds at a vertex) and his philosophy of "simple but elegant" geometric design. By analyzing his seminal works—such as the Devil , Cicada , and Pegasus —this paper argues that Maekawa’s origami represents a unique synthesis of rigorous mathematical constraint and expressive, minimalist aesthetics. 1. Introduction Origami, the art of paper folding, underwent a revolution in the 20th century. While Akira Yoshizawa elevated origami to an art form through wet-folding and organic shaping, and Robert Lang applied computational algorithms to create hyper-realistic insects with hundreds of folds, Jun Maekawa (b. 1958) occupies a critical middle ground. A former researcher at NTT (Nippon Telegraph and Telephone) and later a professor of information science, Maekawa brought the mindset of a physicist to the folding table. His work is characterized by crisp, polyhedral forms, a reliance on flat-foldable bases, and an obsessive economy of creases.

This paper will first explicate Maekawa’s most famous theorem, then trace its application in his design methodology, and finally assess his influence on contemporary origami education. Before Maekawa’s formal analysis, origami designers relied on intuition and trial-and-error. Maekawa’s most significant theoretical contribution is now known as the Maekawa Theorem , a necessary condition for a flat-foldable vertex. Theorem: For any vertex in a flat-foldable crease pattern, the difference between the number of mountain folds (M) and valley folds (V) is exactly 2. That is, |M – V| = 2. 2.1 Derivation and Implication Consider a single vertex where multiple creases intersect. For the paper to lie flat without self-intersecting, the sum of alternating angles must equal 180 degrees. By analyzing the angular order around the vertex, Maekawa proved that the total number of creases n must be even, and the parity constraint (M – V = ±2) must hold. jun maekawa origami

Fold a simple reverse fold (e.g., a rabbit ear). Count the mountain and valley folds around the central vertex. You will find: 2 mountains, 0 valleys (or vice versa), difference = 2. Try a waterbomb base vertex: 4 mountains, 2 valleys (difference = 2). 1958) occupies a critical middle ground