Thursday, December 31, 2015

Touch Fraction ℚ (1.4.x)

New version of Android App "Touch Fraction ℚ"  (version 1.4.x and up)

Evolution of the app over the years: (1993-2015)
In 1993 I developed the first executable (for Windows 3.1) of Touch Fraction ℚ (Racional.exe):

It was my first attempt of to show an interactive representation of Rational numbers as fibres in (Z * Z {0}) and arrangement in Q.
As the Rational representation in Wikipedia:  Rational Numbers:

In 2013 I made the new version of the app: The translation of the original executable to the Android OS.
The interaction became extended to the fraction:
The pie fraction to navigate across the fractions, and the rational representation to navigate across the equivalent fractions. (and select the range of available denominators)

In 2015 after the development of Touch Integers ℤ (+ - × ÷) (
This time, I was able to afford the next step:
Explain fractions and rational numbers as the prime factorization of its members: numerator and denominator.
This is the new version of Touch Fraction ℚ:

Interact with the fraction, build fractions adding or removing prime factors in the numerator or in the denominator.
Simplify fractions dragging common prime fractions to the "common" zone, and invert fractions with the "^-1" button.  

Touch Fraction ℚ is a complete tool to understand positive fractions, negative fractions, positive and negative numerators, positive and negative denominators, equivalent fractions, and inverted fraction.

Saturday, December 19, 2015

Ancient garden machinery

Some days ago, I stumbled upon this page:

 Gardens as crypto computers

There, there's also a reference to the work of Chandra Mukerji:  
"Territorial ambitions and the gardens of Versailles".
Chandra Mukerji - Cambridge University Press, Sep 25, 1997 - History - 393 pages

There: "Chandra Mukerji highlights the connections between the seemingly disparate activities of engineering and garden design, showing how the gardens at Versailles showcased French skills in using nature and art to design a distinctively French landscape and create a naturalized political territoriality."

From my point of view is a suggestive research field. I created a group google plus to continue the search :

"Ancient garden machinery"

If someone wants to help, he will be well received in the group.