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 9 (2022): Heft 16 (June 2022)

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

Suche

5 Artikel
Uneingeschränkter Zugang

Flattening the Curve. . . of Spirographs

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 1 - 20

Zusammenfassung

Abstract

The Spirograph is an old and popular toy that produces aesthetically pleasing and fascinating spiral figures. But are spirals all it can make? In playing with a software implementation of the toy, the author chanced upon a variety of shapes that it can make that are different from its well-known repertoire of spirals, in particular, shapes that have a visible flatness and not the curved spiral geometry that we are accustomed to seeing from the Spirograph. This paper reports on these explorations by the author and his delightful discovery of very elegant and simple geometric relationships between the Spirograph’s structural parameters that enable those patterns.

Schlüsselwörter

  • Spirograph
  • polygon
  • polygram
  • geometry
  • gear
  • trochoid
  • cycloid
Uneingeschränkter Zugang

Dots-and-Polygons

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 21 - 42

Zusammenfassung

Abstract

Dots-and-Boxes is a popular children’s game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the same lattice game board structure as Dots-and-Boxes. The nature of these variations along with this lattice structure lends itself to applying Pick’s theorem to calculate claimed area. Several strategies similar to those studied in Dots-and-Boxes are used to analyze these new variations.

Uneingeschränkter Zugang

Arithmetic Billiards

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 43 - 54

Zusammenfassung

Abstract

Arithmetic billiards show a nice interplay between arithmetics and geometry. The billiard table is a rectangle with integer side lengths. A pointwise ball moves with constant speed along segments making a 45° angle with the sides and bounces on these. In the classical setting, the ball is shooted from a corner and lands in a corner. We allow the ball to start at any point with integer distances from the sides: either the ball lands in a corner or the trajectory is periodic. The length of the path and of certain segments in the path are precisely (up to the factor √2 or 2√2) the least common multiple and the greatest common divisor of the side lengths.

Uneingeschränkter Zugang

Lagrange was Wrong, Pascal was Right

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 55 - 64

Zusammenfassung

Abstract

In this paper we compare the efficiency of the decimal system to the efficiency of different mixed radix representations. We use as a starting point for our study the duodecimal systems suggested by Pascal and the Maya “Long Count” system. Using the quality index we experimentally show that two slight deviations from the duodecimal system are more efficient than the previous two systems and also than the decimal system.

Schlüsselwörter

  • numerical systems
  • mixed radix numbers
  • duodecimal system
Uneingeschränkter Zugang

Musical Modes, their Associated Chords and their Musicality

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 65 - 70

Zusammenfassung

Abstract

In this paper we present a mathematical way of defining musical modes and we define the musicality of a mode as a product of three diferent factors. We conclude by classyfing the modes which are most musical according to our definition.

5 Artikel
Uneingeschränkter Zugang

Flattening the Curve. . . of Spirographs

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 1 - 20

Zusammenfassung

Abstract

The Spirograph is an old and popular toy that produces aesthetically pleasing and fascinating spiral figures. But are spirals all it can make? In playing with a software implementation of the toy, the author chanced upon a variety of shapes that it can make that are different from its well-known repertoire of spirals, in particular, shapes that have a visible flatness and not the curved spiral geometry that we are accustomed to seeing from the Spirograph. This paper reports on these explorations by the author and his delightful discovery of very elegant and simple geometric relationships between the Spirograph’s structural parameters that enable those patterns.

Schlüsselwörter

  • Spirograph
  • polygon
  • polygram
  • geometry
  • gear
  • trochoid
  • cycloid
Uneingeschränkter Zugang

Dots-and-Polygons

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 21 - 42

Zusammenfassung

Abstract

Dots-and-Boxes is a popular children’s game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the same lattice game board structure as Dots-and-Boxes. The nature of these variations along with this lattice structure lends itself to applying Pick’s theorem to calculate claimed area. Several strategies similar to those studied in Dots-and-Boxes are used to analyze these new variations.

Uneingeschränkter Zugang

Arithmetic Billiards

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 43 - 54

Zusammenfassung

Abstract

Arithmetic billiards show a nice interplay between arithmetics and geometry. The billiard table is a rectangle with integer side lengths. A pointwise ball moves with constant speed along segments making a 45° angle with the sides and bounces on these. In the classical setting, the ball is shooted from a corner and lands in a corner. We allow the ball to start at any point with integer distances from the sides: either the ball lands in a corner or the trajectory is periodic. The length of the path and of certain segments in the path are precisely (up to the factor √2 or 2√2) the least common multiple and the greatest common divisor of the side lengths.

Uneingeschränkter Zugang

Lagrange was Wrong, Pascal was Right

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 55 - 64

Zusammenfassung

Abstract

In this paper we compare the efficiency of the decimal system to the efficiency of different mixed radix representations. We use as a starting point for our study the duodecimal systems suggested by Pascal and the Maya “Long Count” system. Using the quality index we experimentally show that two slight deviations from the duodecimal system are more efficient than the previous two systems and also than the decimal system.

Schlüsselwörter

  • numerical systems
  • mixed radix numbers
  • duodecimal system
Uneingeschränkter Zugang

Musical Modes, their Associated Chords and their Musicality

Online veröffentlicht: 14 Jun 2022
Seitenbereich: 65 - 70

Zusammenfassung

Abstract

In this paper we present a mathematical way of defining musical modes and we define the musicality of a mode as a product of three diferent factors. We conclude by classyfing the modes which are most musical according to our definition.

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