Related papers: Solving Sangaku: A Traditional Solution to a Ninet…
Between 17th and 19th centuries, mathematically orientated votive tablets appeared in Shinto shrines and Buddhist temples all over Japan. Known as sangaku, they contained problems of a largely geometrical nature. In the 17th century, the…
By combining theoretical and computational techniques from geometry, calculus, group theory, and Galois theory, we prove the nonexistence of a closed-form algebraic solution to a Japanese geometry problem first stated in the early…
Eighteenth century Japan was a time of isolation and peace, where education and the arts blossomed. Originally posted before 1749 by an unknown author, the sangaku (mathematical tablet) that became known as the Gion Shrine problem, has…
We give a new solution to the famous Gion shrine geometry problem from eighteenth-century Japan. Like the classical Japanese solution, ours is given in the form of a degree ten equation. However, our polynomial has the advantage of being…
This work presents for the first time a solution to the 1821 unsolved Sawa Masayoshi's problem, giving an explicit and algebraically exact solution for the symmetric case (particular case b = c, i.e., ABC \equiv right-angled isosceles…
We explore the capabilities of physical computing with Oscillatory Neural Networks (ONN) to solve combinatorial optimization problems. To solve Sudokus with ONNs, we define a novel mapping strategy that utilizes the unique characteristics…
In this article we discuss problem HI 028 of the Hirotaka files, a collection of sangakuproblems created by Hirotaka Ebisui.
This project undertakes the training and analysis of optical character recognition OCR methods applied to 10th century ancient Tamil inscriptions discovered on the walls of the Brihadeeswarar Temple.The chosen OCR methods include…
Let $\mu(r)$ denote the minimal side length of a square inscribed in the curvilinear triangular region formed by two tangent circles of radii $1$ and $r \ge 1$ together with their common tangent line. The problem of finding a closed-form…
This paper examines how the mathematicians and astronomers of the Kerala school tackled the problem of computing the values of the arcsin function. Four different approaches are discussed all of which are found in Nilakantha Somayaji's…
In 1943 from September to December Kiyoshi Oka wrote a series of papers numbered from VII to XI, as the research reports to Teiji Takagi (then, Professor of Tokyo Imperial University), in which he solved affirmatively the so-called Levi…
Details for known solutions of some geometric and algebraic problems with the help of origami are presented: two theorems of Haga, the general cubic equation, especially the heptagon equation, doubling the cube as well as the trisection of…
Origami is the art of paper folding, and it borrows its name from two Japanese words \emph{ori} and \emph{kami}. In Japanese, {ori} means folding, and the paper is called {kami}. While origami is just a hobby to most, there is a lot more to…
We give a hierarchial set of axioms for mathematical origami. The hierachy gives the fields of Pythagorean numbers, first discussed by Hilbert, the field of Euclidean constructible numbers which are obtained by the usual constructions of…
In this report we consider the set of the 16 possible convex tangrams that can be composed with the 7 so-called "Sei Shonagon Chie no Ita" (or Japanese) tans, see [10]. The set of these Japanese tans is slightly different from the…
This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and…
Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic curves that cannot be regularized by geometric methods. Starting from the same core idea…
We define a Tanaka's equation on an oriented graph with two edges and two vertices. This graph will be embedded in the unit circle. Extending this equation to flows of kernels, we show that the laws of the flows of kernels $K$ solution of…
Septoku is a Sudoku variant invented by Bruce Oberg, played on a hexagonal grid of 37 cells. We show that up to rotations, reflections, and symbol permutations, there are only six valid Septoku boards. In order to have a unique solution, we…
We develop a new discrete mathematical model which includes the classical Sudoku puzzle, Latin Squares and gerechte designs. This problem is described by integer equations and a special type of inequality constraint. We consider solutions…