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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 6 (2019): Edición 12 (December 2019)

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

4 Artículos
Acceso abierto

Yes, Gauss’s Answer is Indeed Correct!

Publicado en línea: 07 Feb 2020
Páginas: 5 - 8

Resumen

Abstract

A meaning of three dots (. . . ) and the Gauss’s sum.

Palabras clave

  • three dots
  • Gauss sum
Acceso abierto

It’s Common Knowledge

Publicado en línea: 07 Feb 2020
Páginas: 9 - 32

Resumen

Abstract

We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.

Palabras clave

  • logic puzzles
Acceso abierto

Crazy Sequential Representations of Numbers for Small Bases

Publicado en línea: 07 Feb 2020
Páginas: 33 - 48

Resumen

Abstract

Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers− equations made of sequences of one through nine (or nine through one) that evaluate to a number. All previous work on this type of puzzle has focused only on base ten numbers and whether a solution existed. We generalize this concept and examine how this extends to arbitrary bases, the ranges of possible numbers, the combinatorial challenge of finding the numbers, efficient algorithms, and some interesting patterns across any base. For the analysis, we focus on bases three through ten. Further, we outline several interesting mathematical and algorithmic complexity problems related to this area that have yet to be considered.

Palabras clave

  • representations
  • algorithms
Acceso abierto

Infinite Tiles of Regular rep-tiles

Publicado en línea: 07 Feb 2020
Páginas: 49 - 105

Resumen

Abstract

Here I describe an infinite number of fractal tiles of regular rep-tiles in all dimensions above 1. Each rep-tile’s set of tiles can be divided into subsets based on certain visual characteristics. As fractals, they can be programmed and rendered in any size. They can be arranged in groups according to their aesthetic properties; used as an unending visual and pattern-recognition training ground for AI; and even animated as increments from one to the next.

Palabras clave

  • rep-tiles
  • fractal
  • tiles
  • square
  • triangle
4 Artículos
Acceso abierto

Yes, Gauss’s Answer is Indeed Correct!

Publicado en línea: 07 Feb 2020
Páginas: 5 - 8

Resumen

Abstract

A meaning of three dots (. . . ) and the Gauss’s sum.

Palabras clave

  • three dots
  • Gauss sum
Acceso abierto

It’s Common Knowledge

Publicado en línea: 07 Feb 2020
Páginas: 9 - 32

Resumen

Abstract

We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.

Palabras clave

  • logic puzzles
Acceso abierto

Crazy Sequential Representations of Numbers for Small Bases

Publicado en línea: 07 Feb 2020
Páginas: 33 - 48

Resumen

Abstract

Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers− equations made of sequences of one through nine (or nine through one) that evaluate to a number. All previous work on this type of puzzle has focused only on base ten numbers and whether a solution existed. We generalize this concept and examine how this extends to arbitrary bases, the ranges of possible numbers, the combinatorial challenge of finding the numbers, efficient algorithms, and some interesting patterns across any base. For the analysis, we focus on bases three through ten. Further, we outline several interesting mathematical and algorithmic complexity problems related to this area that have yet to be considered.

Palabras clave

  • representations
  • algorithms
Acceso abierto

Infinite Tiles of Regular rep-tiles

Publicado en línea: 07 Feb 2020
Páginas: 49 - 105

Resumen

Abstract

Here I describe an infinite number of fractal tiles of regular rep-tiles in all dimensions above 1. Each rep-tile’s set of tiles can be divided into subsets based on certain visual characteristics. As fractals, they can be programmed and rendered in any size. They can be arranged in groups according to their aesthetic properties; used as an unending visual and pattern-recognition training ground for AI; and even animated as increments from one to the next.

Palabras clave

  • rep-tiles
  • fractal
  • tiles
  • square
  • triangle

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