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Volume 3 (2016): Issue 5 (March 2016)

Journal Details
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English

Search

Volume 3 (2016): Issue 5 (March 2016)

Journal Details
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English

Search

5 Articles
access type Open Access

The Triangular Binary Clock

Published Online: 14 Apr 2016
Page range: 5 - 7

Abstract

Abstract

A new idea for a binary clock is presented. It displays the time using a triangular array of 15 lamps each representing a certain amount of time. It is shown that such a geometric, triangular arrangement is only possible because our system of time divisions is based on a sexagesimal system in which the num- ber of minutes in 12 hours equals the factorial of a natural number (720 = 6!). An interactive applet allows one to “play” with the clock.

Keywords

  • binary
  • clock
  • time
  • sexagesimal system
access type Open Access

Digital Root Patterns of Three-Dimensional Space

Published Online: 14 Apr 2016
Page range: 9 - 31

Abstract

Abstract

In this study, we define vedic cube as the layout of each digital root in a three-dimensional multiplication table. In order to discover the geometric patterns in vedic cube, we adopt two methods to analyze the digital root in a three-dimensional space. The first method is floor method, which divides vedic cube into several X-Y planes according to different Z values (floors) to analyze the geometric characteristics on each floor. The second method is symmetric plane method, which decomposes vedic cube by its main and secondary symmetric planes.

Keywords

  • Digital root
  • pattern
  • vedic square
  • vedic cube
  • symmetry
access type Open Access

Allégorie de la Géométrie. A Mathematical Interpretation

Published Online: 14 Apr 2016
Page range: 33 - 45

Abstract

Abstract

In this work, we present a mathematical interpretation for the masterpiece Allégorie de la Géométrie (1649), painted by the French baroque artist Laurent de La Hyre (1606-1656)

Keywords

  • Laurent de La Hyre
  • “Allégorie de la Géométrie"
  • baroque art
  • mathematical interpretation
  • perspective
access type Open Access

Star Tangrams

Published Online: 14 Apr 2016
Page range: 47 - 60

Abstract

Abstract

The Tangram is a puzzle in which seven tiles are arranged to make various shapes. Four families of tangram shapes have been mathematically defined and their members enumerated. This paper defines a fifth family, enumerates its members, explains its taxonomic relationship with the previously-defined families, and provides some interesting examples

Keywords

  • Tangrams
  • combinatorics
  • spatial puzzles
access type Open Access

Endless Love: On the Termination of a Playground Number Game

Published Online: 14 Apr 2016
Page range: 61 - 78

Abstract

Abstract

A simple and popular childhood game, loves or the love calculator, involves an iterated rule applied to a string of digits and gives rise to surprisingly rich behaviour. Traditionally, players’ names are used to set the initial conditions for an instance of the game: its behaviour for an exhaustive set of pairings of popular UK childrens’ names, and for more general initial conditions, is examined. Convergence to a fixed outcome (the desired result) is not guaranteed, even for some plausible first name pairings. No pairs of top-50 common first names exhibit non-convergence, suggesting that it is rare in the playground; however, including surnames makes non-convergence more likely due to higher letter counts (for example, “Reese Witherspoon loves Calvin Harris”). Difierent game keywords (including from difierent languages) are also considered. An estimate for non-convergence propensity is derived: if the sum m of digits in a string of length w obeys m > 18=(3=2/)w-4, convergence is less likely. Pairs of top UK names with pairs of ‘O’s and several ‘L’s (for example, Chloe and Joseph, or Brooke and Scarlett) often attain high scores. When considering individual names playing with a range of partners, those with no loves letters score lowest, and names with intermediate (not simply the highest) letter counts often perform best, with Connor and Evie averaging the highest scores when played with other UK top names.

Keywords

  • Number games
  • name statistics
  • dynamic integer sequences
  • mathematics in schools
5 Articles
access type Open Access

The Triangular Binary Clock

Published Online: 14 Apr 2016
Page range: 5 - 7

Abstract

Abstract

A new idea for a binary clock is presented. It displays the time using a triangular array of 15 lamps each representing a certain amount of time. It is shown that such a geometric, triangular arrangement is only possible because our system of time divisions is based on a sexagesimal system in which the num- ber of minutes in 12 hours equals the factorial of a natural number (720 = 6!). An interactive applet allows one to “play” with the clock.

Keywords

  • binary
  • clock
  • time
  • sexagesimal system
access type Open Access

Digital Root Patterns of Three-Dimensional Space

Published Online: 14 Apr 2016
Page range: 9 - 31

Abstract

Abstract

In this study, we define vedic cube as the layout of each digital root in a three-dimensional multiplication table. In order to discover the geometric patterns in vedic cube, we adopt two methods to analyze the digital root in a three-dimensional space. The first method is floor method, which divides vedic cube into several X-Y planes according to different Z values (floors) to analyze the geometric characteristics on each floor. The second method is symmetric plane method, which decomposes vedic cube by its main and secondary symmetric planes.

Keywords

  • Digital root
  • pattern
  • vedic square
  • vedic cube
  • symmetry
access type Open Access

Allégorie de la Géométrie. A Mathematical Interpretation

Published Online: 14 Apr 2016
Page range: 33 - 45

Abstract

Abstract

In this work, we present a mathematical interpretation for the masterpiece Allégorie de la Géométrie (1649), painted by the French baroque artist Laurent de La Hyre (1606-1656)

Keywords

  • Laurent de La Hyre
  • “Allégorie de la Géométrie"
  • baroque art
  • mathematical interpretation
  • perspective
access type Open Access

Star Tangrams

Published Online: 14 Apr 2016
Page range: 47 - 60

Abstract

Abstract

The Tangram is a puzzle in which seven tiles are arranged to make various shapes. Four families of tangram shapes have been mathematically defined and their members enumerated. This paper defines a fifth family, enumerates its members, explains its taxonomic relationship with the previously-defined families, and provides some interesting examples

Keywords

  • Tangrams
  • combinatorics
  • spatial puzzles
access type Open Access

Endless Love: On the Termination of a Playground Number Game

Published Online: 14 Apr 2016
Page range: 61 - 78

Abstract

Abstract

A simple and popular childhood game, loves or the love calculator, involves an iterated rule applied to a string of digits and gives rise to surprisingly rich behaviour. Traditionally, players’ names are used to set the initial conditions for an instance of the game: its behaviour for an exhaustive set of pairings of popular UK childrens’ names, and for more general initial conditions, is examined. Convergence to a fixed outcome (the desired result) is not guaranteed, even for some plausible first name pairings. No pairs of top-50 common first names exhibit non-convergence, suggesting that it is rare in the playground; however, including surnames makes non-convergence more likely due to higher letter counts (for example, “Reese Witherspoon loves Calvin Harris”). Difierent game keywords (including from difierent languages) are also considered. An estimate for non-convergence propensity is derived: if the sum m of digits in a string of length w obeys m > 18=(3=2/)w-4, convergence is less likely. Pairs of top UK names with pairs of ‘O’s and several ‘L’s (for example, Chloe and Joseph, or Brooke and Scarlett) often attain high scores. When considering individual names playing with a range of partners, those with no loves letters score lowest, and names with intermediate (not simply the highest) letter counts often perform best, with Connor and Evie averaging the highest scores when played with other UK top names.

Keywords

  • Number games
  • name statistics
  • dynamic integer sequences
  • mathematics in schools

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