Related papers: Play Ground for Victor's Magic Squares
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
In this expository paper, we show how to use the Douglas-Rachford algorithm as a successful heuristic for finding magic squares. The Douglas-Rachford algorithm is an iterative projection method for solving feasibility problems. Although its…
We introduce Magic Gems, a geometric representation of magic squares as three-dimensional polyhedra. By mapping an n times n magic square onto a centered coordinate grid with cell values as vertical displacements, we construct a point cloud…
Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes.
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
Magic squares are a fascinating mathematical challenge that has intrigued mathematicians for centuries. Given a positive (and possibly large) integer \( n \), one of the main challenges that still remains is to find, within a computational…
In recreational mathematics, a normal magic square is an $n \times n$ square matrix whose entries are distinctly the integers $1 \ldots n^2$, such that each row, column, and major and minor traces sum to one constant $\mu$. It has been…
This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some…
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…
In this paper, we continue the study of almost squares and extend the result of the author's fourth paper of the series to almost squares with closer factors.
Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement…
A novel kind of self-referential square matrix is introduced. A certain subset of the matrix entries record the frequencies of occurrence of each distinct number appearing within the entire matrix. Such squares are necessarily elusive. Our…
In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…
The purpose of this paper is to show the magic of physics by showing the physics of magic. What usually makes magic tricks interesting is that something unexpected occurs. Similarly, demonstrations are interesting inasmuch as they produce…
Simple constructions are given for finite semifields that include as special cases both old semifields and recently constructed semifields.
We show a new construction for square packing, and prove that it is more efficient than previous results.
Benjamin Franklin constructed three squares which have amazing properties, and his method of construction has been a mystery to date. In this article, we divulge his secret and show how to construct such squares for any order.
Placement games are a subclass of combinatorial games which are played on graphs. We will demonstrate that one can construct simplicial complexes corresponding to a placement game, and this game could be considered as a game played on these…
In this Paper we defined the improved concept of fuzzy magic Graph as the set of two injective functions defined on [0; 1] such that sum of the labeled defined on vertices greater than respective edge label while sum of two vertices and…
This is a survey article on distance-squared mappings and related topics.