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Detalles de la revista
Formato
Revista
eISSN
2182-1976
Publicado por primera vez
16 Apr 2016
Periodo de publicación
2 veces al año
Idiomas
Inglés

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Volumen 5 (2018): Edición 10 (December 2018)

Detalles de la revista
Formato
Revista
eISSN
2182-1976
Publicado por primera vez
16 Apr 2016
Periodo de publicación
2 veces al año
Idiomas
Inglés

Buscar

3 Artículos
Acceso abierto

Mathematics of a Sudo-Kurve

Publicado en línea: 31 Dec 2018
Páginas: 5 - 28

Resumen

Abstract

We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.

Palabras clave

  • combinatorics
  • Sudoku
Acceso abierto

Ellipse, hyperbola and their conjunction

Publicado en línea: 31 Dec 2018
Páginas: 29 - 38

Resumen

Abstract

This article presents a simple analysis of cones which are used to generate a given conic curve by section by a plane. It was found that if the given curve is an ellipse, then the locus of vertices of the cones is a hyperbola. The hyperbola has foci which coincidence with the ellipse vertices. Similarly, if the given curve is the hyperbola, the locus of vertex of the cones is the ellipse. In the second case, the foci of the ellipse are located in the hyperbola’s vertices. These two relationships create a kind of conjunction between the ellipse and the hyperbola which originate from the cones used for generation of these curves. The presented conjunction of the ellipse and hyperbola is a perfect example of mathematical beauty which may be shown by the use of very simple geometry. As in the past the conic curves appear to be very interesting and fruitful mathematical beings.

Palabras clave

  • Geometry
  • conics
  • ellipse
  • hyperbola
Acceso abierto

Reflections on the n +k dragon kings problem

Publicado en línea: 31 Dec 2018
Páginas: 39 - 55

Resumen

Abstract

A dragon king is a shogi piece that moves any number of squares vertically or horizontally or one square diagonally but does not move through or jump over other pieces. We construct infinite families of solutions to the n + k dragon kings problem of placing k pawns and n + k mutually nonattacking dragon kings on an n×n board, including solutions symmetric with respect to quarter-turn or half-turn rotations, solutions symmetric with respect to one or two diagonal reections, and solutions not symmetric with respect to any nontrivial rotation or reection. We show that an n + k dragon kings solution exists whenever n > k + 5 and that, given some extra conditions, symmetric solutions exist for n > 2k + 5.

Palabras clave

  • shogi
  • combinatorics
  • symmetry
  • -queens problem
3 Artículos
Acceso abierto

Mathematics of a Sudo-Kurve

Publicado en línea: 31 Dec 2018
Páginas: 5 - 28

Resumen

Abstract

We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.

Palabras clave

  • combinatorics
  • Sudoku
Acceso abierto

Ellipse, hyperbola and their conjunction

Publicado en línea: 31 Dec 2018
Páginas: 29 - 38

Resumen

Abstract

This article presents a simple analysis of cones which are used to generate a given conic curve by section by a plane. It was found that if the given curve is an ellipse, then the locus of vertices of the cones is a hyperbola. The hyperbola has foci which coincidence with the ellipse vertices. Similarly, if the given curve is the hyperbola, the locus of vertex of the cones is the ellipse. In the second case, the foci of the ellipse are located in the hyperbola’s vertices. These two relationships create a kind of conjunction between the ellipse and the hyperbola which originate from the cones used for generation of these curves. The presented conjunction of the ellipse and hyperbola is a perfect example of mathematical beauty which may be shown by the use of very simple geometry. As in the past the conic curves appear to be very interesting and fruitful mathematical beings.

Palabras clave

  • Geometry
  • conics
  • ellipse
  • hyperbola
Acceso abierto

Reflections on the n +k dragon kings problem

Publicado en línea: 31 Dec 2018
Páginas: 39 - 55

Resumen

Abstract

A dragon king is a shogi piece that moves any number of squares vertically or horizontally or one square diagonally but does not move through or jump over other pieces. We construct infinite families of solutions to the n + k dragon kings problem of placing k pawns and n + k mutually nonattacking dragon kings on an n×n board, including solutions symmetric with respect to quarter-turn or half-turn rotations, solutions symmetric with respect to one or two diagonal reections, and solutions not symmetric with respect to any nontrivial rotation or reection. We show that an n + k dragon kings solution exists whenever n > k + 5 and that, given some extra conditions, symmetric solutions exist for n > 2k + 5.

Palabras clave

  • shogi
  • combinatorics
  • symmetry
  • -queens problem

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