# Touch Math Apps (Android)

In February 2010, the magazine "Scientific American" ISSN 0210136X number 401 in the Mathematics Games section, published the article of Agustin Rayo (philosophy professor at MIT) on: "bricks, locks and progressions." There are specific items on the RSA encryption method.
And on the Theorem of Ben Green and Terry Tao
The article touched me.
And what attracted me was the beautiful graphics representing natural numbers in the form of combinations of spheres and worms were colored graphic representation of primes. (See  Scientific American article in *.pdf cited above).
At nummolt.com, I spent many years trying to graph the numbers. You can see my work from 1997 that I mean: http://www.nummolt.com/nummolt/numdown.htm

It is an old tool, based on the reflections made from quotations by Barbara Scott Nelson and others, read online about children's learning when to add and subtract with borrowing.
But while it is easy to graphically represent the addition and subtraction of natural numbers is however much more difficult to make a simple representation of the multiplication, the amount of calculations involving multiplication algorithm that are used and taught in schools, after memorizing the "multiplication tables".
There have been many attempts to make graphic representations of multiplication multiplication Mayan eg: Mayan Multiplication video

And myself, I also made my attempts in my programs.But the mere fact that prime numbers as the basic bricks which are built from all natural numbers, had not ever considered.
When I read the article, I sent a letter to Agustin Rayo to tell him that I had really liked the article, and I naively I asked if the graphs corresponded to any investigation being carried out.

He politely replied that the drawings he had done in the best way that he had come to illustrate the article, and do not corresponded to any investigation.

At this point, I already had developed for years with Wendy Petti program for Mathcats "Place Value Party": http://www.mathcats.com/explore/age/placevalueparty.html In this program we tried to show the value of the position of the numbers from birthday cakes with candles.
A few years after,  Ulrich Kortenkamp published the Place Value Chart: Seeing Ulrich Kortenkamp program I wrote to MathForum saying that this program was a lesson for me, and I congratulate the author:http://mathforum.org/mathtools/tool/181488/

Few years later, talking with Joan Jareño about a game with primes, from Creamat they warned me about the existence of a poster with primes:
http://esquemat.es/algebra/factores-primos-por-colores
In reference to the original from John Graham-Cumming:http://blog.jgc.org/2012/04/make-your-own-prime-factorization.html

At this time (2013), I understood that I had all the pieces to build a tool that I dreamed.
When I was looking at the internet to address program development, in addition to the well-known Ulam spiral, I had knowledge of the parabolic sieve: shown by Yuri Matiyasevich  and Boris Stechkin form the Steklov Mathematical Institute of the Russian  Academy of Sciences.

There's an explanation for this, h

The first had to do was to assign a color to each prime number.Because the app is dedicated to the children, I decided to give the three basic colors first three prime numbers, and intersperse the following numbers.Therefore, red is 2, green 3 and 5 is blue, 7 yellow, magenta 11 cyan and 13. And from there, putting the colors go.The purpose of this distribution is that the resulting color of the product color is the sum of the colors of the prime factors or filtration of colors of the prime numbers.Thus, the color corresponding to 30 (2 * 3 * 5) will be white, and the color corresponding to 1001 (7 * 11 * 13) will be black.

Having decided this, the work was left to do was clear:
Show prime numbers as small circles within a larger circle, usually corresponding to a composite number.Removing prime circles from the circumference, equals to divide.Add a prime circle, equivalent to multiply.In parallel, the the app displays numbers in a place value format, but in vertical, as in the  Mathcats "Place Value Party"
program.

And adding the display parabolic sieve, and all the numbers well placed within the Ulam spiral and the representation of the module number.
In the end, the program Touch Natural Numbers is a small laboratory that can be studied composition and numbers, and make elementary operations within the set of natural numbers.
And never there is a division that is not resulting integer.
Nor has there ever the possibility of subtraction with a negative result.

Hope you like it, and especially useful for teaching math in elementary school.

Touch Natural Numbers App at Google Play:

## Touch Natural Numbers Small laboratory of Natural Numbers:

The Prime numbers are like the building blocks of the numbers.

With this app you can:

Analyze the factors of a Composite number.

Build a Composite number from its factors. (multiplication and division of Natural Numbers)

Localize or select a number in the Ulam Spiral.

Verify all the possible products between Primes in a composite number with the Parabolic Sieve.

Analyze or build a number with the Place Value activity (Addition or Subtraction)

Understand the Modulo of a number.

Introducing the polygonal numbers.

Know the numbers as the sum of two prime numbers or as the sum of three prime numbers. ## Touch Fraction Interactive fraction.

About fractions, and the construction of the rational numbers.

To play with proper and improper fractions, positive and negative also.

All fractions in order from least to greatest. You can increase or decrease the fractions included in the app, increasing or decreasing the density of lines in the lower graph framework. The accuracy of the application depends on the capabilities of the device.

The application lets you play with fractions: Provides two representations: a circle and a straight line whose has the slope of chosen fraction

Spin the fraction: You can choose different fractions in order from low to high within the possibilities included in the grid at the bottom formed by pairs of integers. Select equivalent fractions with the rational representation diagram (the lower grid). Change range of fractions affordable with a "pinch zoom" on the lower grid.

In the vertical strip of the grid graph goes from 0 to 1 you can see the number of units containing the selected improper fraction: Each unit is a black square.

The program is useful to understand: fractions, coordinate geometry, rational numbers, cartesian plane, slope, and the equivalent classes of pairs of integers. ## Touch Pythagoras The Pythagorean Theorem Interactive: a^2 + b^2 = c^2

App:

You can change the lengths of the legs (dragging). You can change the length of the hypotenuse with two fingers. You can zoom (pinch zoom) and rotate the figure (dragging).

There are 6 ways to view the Pythagorean theorem:
• - Unit surfaces.
• - Two equivalent square containing the same surface.
• - The square for each leg in the square of the hypotenuse (Euclid)
• - Pingi - Dudeney proof.
• - Da Vinci.

You can change the precision of the lengths. (In the contextual menu)

This application is also a small laboratory to investigate about the Pythagorean Theorem: For example, you can experiment easily, looking for the exact solutions of the Pythagorean Theorem:

3² + 4² = 5² is not the only exact solution:

Below 21, there are 6 solutions:
• 3² + 4² = 5²
• 5² + 12² = 13²
• 6² + 8² = 10²
• 8² + 15² = 17²
• 9² + 12² = 15²
• 12² + 16² = 20²

Likewise it is also possible to find the solutions below 31 (11 solutions in all). Or solutions below 101 (52 solutions in all). (Or maybe the 127 exact results under 201 in the best tablets). 