Zeitschriften und Ausgaben

Volumen 10 (2023): Heft 17 (January 2023)

Volumen 9 (2022): Heft 16 (June 2022)

Volumen 8 (2021): Heft 15 (November 2021)

Volumen 8 (2021): Heft 14 (October 2021)

Volumen 7 (2020): Heft 13 (November 2020)

Volumen 6 (2019): Heft 12 (December 2019)

Volumen 6 (2019): Heft 11 (September 2019)

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

Volumen 5 (2018): Heft 9 (September 2018)

Volumen 4 (2017): Heft 8 (December 2017)

Volumen 4 (2017): Heft 7 (May 2017)

Volumen 3 (2016): Heft 6 (December 2016)

Volumen 3 (2016): Heft 5 (March 2016)

Zeitschriftendaten
Format
Zeitschrift
eISSN
2182-1976
Erstveröffentlichung
16 Apr 2016
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch

Suche

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

Zeitschriftendaten
Format
Zeitschrift
eISSN
2182-1976
Erstveröffentlichung
16 Apr 2016
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch

Suche

3 Artikel
Uneingeschränkter Zugang

Mathematics of a Sudo-Kurve

Online veröffentlicht: 31 Dec 2018
Seitenbereich: 5 - 28

Zusammenfassung

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.

Schlüsselwörter

  • combinatorics
  • Sudoku
Uneingeschränkter Zugang

Ellipse, hyperbola and their conjunction

Online veröffentlicht: 31 Dec 2018
Seitenbereich: 29 - 38

Zusammenfassung

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.

Schlüsselwörter

  • Geometry
  • conics
  • ellipse
  • hyperbola
Uneingeschränkter Zugang

Reflections on the n +k dragon kings problem

Online veröffentlicht: 31 Dec 2018
Seitenbereich: 39 - 55

Zusammenfassung

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.

Schlüsselwörter

  • shogi
  • combinatorics
  • symmetry
  • -queens problem
3 Artikel
Uneingeschränkter Zugang

Mathematics of a Sudo-Kurve

Online veröffentlicht: 31 Dec 2018
Seitenbereich: 5 - 28

Zusammenfassung

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.

Schlüsselwörter

  • combinatorics
  • Sudoku
Uneingeschränkter Zugang

Ellipse, hyperbola and their conjunction

Online veröffentlicht: 31 Dec 2018
Seitenbereich: 29 - 38

Zusammenfassung

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.

Schlüsselwörter

  • Geometry
  • conics
  • ellipse
  • hyperbola
Uneingeschränkter Zugang

Reflections on the n +k dragon kings problem

Online veröffentlicht: 31 Dec 2018
Seitenbereich: 39 - 55

Zusammenfassung

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.

Schlüsselwörter

  • shogi
  • combinatorics
  • symmetry
  • -queens problem

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