Touch Natural Numbers

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." http://www.investigacionyciencia.es/files/3486.pdf 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, here: http://plus.maths.org/content/catching-primes

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:
http://play.google.com/store/apps/details?id=com.nummolt.number.natural.touch
 

 

Touch Natural Numbers at Youtube:

 

Maurici Carbó

www.nummolt.com

From here I recommend the book "You Can Count on Monsters" from Richard Evan Schwartz, with a similar approach to the natural numbers:

Javier Chavarriga Soriano

These last days, I was thinking I needed the help of a professional mathematician.
I remember a friend of my adolescence sure had career in the field of mathematics.
I found that he did indeed run than expected.

At the same time, I see that I am late:
He died in 2005

I found his obituary on:
http://blogs.iec.cat/scm/wp-content/uploads/sites/20/2011/02/N23.pdf

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Javier Chavarriga Soriano:

We offer these notes to give testimony and gratitude to a life dedicated to mathematics.

Javier Chavarriga attended degree in mathematical sciences at the Faculty of Mathematics at the University of Barcelona in the period 1974-1979, specialized in mathematical analysis.
He graduated in June 1979 and obtained the degree of BA, dissertation form in December 1981.
Later, he received his doctorate in mathematical sciences in the same Faculty in November 1985 and obtained the qualification cum laude fit under the direction of Dr. Charles Simon Torres.
During the years 1979-1983 he served as Assistant Professor in the Department of Applied Mathematics and Analysis, University of Barcelona.
Many former students who are now teachers still remember that brand new graduate who taught differential equations and, although he was new to the job, with great intensity transmitted his permanent enthusiasm for mathematics.

He began the 1983-1984 academic year as a lecturer teaching and research at the Faculty of Informatics of the Technical University of Catalonia.
In November 1984 he obtained a position as assistant professor of mathematics interim general at the Faculty of Pharmacy, University of Barcelona, where he developed his teaching activity in the period between November 1984 and June 1992.
In January 1985 he was appointed Associate Professor of Acting and applied mathematics.
In May 1987 contest won by opposition Plaza university professor of applied mathematics at the Department of Applied Mathematics and Analysis, University of Barcelona.

The nineties, there is the restructuring of the Catalan university system. At that time, had only three universities in Catalonia, with several offices in the four provinces of Catalonia.
With such restructuring will restore or create new universities such as the University of Girona, Lleida University and the University Rovira i Virgili.

Emotional and family ties to the land west of the Strip, specifically the town of Sena, a little more than fifty kilometers from the city of Lleida, meant that during this period of change, relying on its joining the University of Lleida, which later feel very proud.
So in October 1992 he joined the mathematics section of Segriá Polytechnic University of Catalonia, the School of Agricultural Engineering of Lleida.

This center was assigned to the University of Lleida in November of the same year.

Finally, in June 1995 he obtained the post of Associate Professor of Applied Mathematics at the Department of Mathematics of the University of Lleida.

From then until his death, we have shared with him a good part of their research interests and scientific study.
It is in this latter university where he developed the main and most fruitful of his teaching and research work.

Javier was one of the initiators of the new Department of Mathematical our University and served as director for a long period.

His big dream was to form a research group in dynamical systems: I wanted to create a school.

To achieve his aim he began to search students and started a PhD course entitled Mathematical Modelling, some members of our Department we take as his disciples.
Of these, Jaume Gine remained as doctors and thus created the initial core of our research group. In 1995 it incorporated Isaac A. García.

The beginning was quite hard and narrowness: we still remember the office of four square meters shared by all three of the old rectory building.
It is a period marked by great sacrifices and many hours of dedication to work.
In this period, Javier showed some of the great virtues that characterize such drive and willpower, he can overcome any obstacles magnitude, and high estimate for a job well done.

The fruits of these efforts are evident with the recognition of many members of the international scientific community and are held the first collaborations and visits.
Establishing scientific collaborations major national and international scale.
Without pretending to be exhaustive, teachers like Hector Giacomini, University of Tours, and Jaume Armengol Gasull Book, UAB Mijhail Popescu, Institute of Mathematics, Bucharest, Laurent Cairo, University of Orleans, Mircea Sofonea, University of Perpignan, Marco Sabatini, University of Trento, etc.., were some of the visiting professors during this initial period.

The consolidation of the research group and Dynamical Systems Seminar these collaborations contributed to the organization of congresses, among which we highlight the Catalan Days of Applied Mathematics and two editions of the Symposium on Planar Vector Fields.

Later, the group was expanded with PhD Joseph Mallol George Sorolla y Maite Grau, so that the continuity of the School of Dynamic Systems, created by Javier, was guaranteed and, therefore, the initial goal of Javier, accomplished.

About the research done, we can frame the continuous dynamic systems and, in particular, in dimension two. These systems can be thought as ordinary differential equations that have been parameterized by a temporary variable.
Are remarkable his contributions to the problem of the center and the integrability problem. He also devoted to the study of topics such as isochronous centers, reversibility, nilpotent and degenerate systems, bifurcations, limit cycles (Hilbert's 16th problem) Lie symmetries, differential equations in the complex projective plane etc..

In recent times was one of the main proponents of the theory of Darboux integrability . This theory is based on the fact that the determination of a sufficiently high number of algebraic solutions to a dynamical system in the plane , if they exist, can give a first integral of the system. The French mathematician Gaston Darboux started this theory and , after reading the report , Javier , with his proverbial mathematical intuition , saw the beginning ideas of Darboux theory of algebraic differential equations , which aims to study the characteristics of invariant algebraic curves of a differential system and its relationship with other system solutions .
Was led largely to the study of these invariant algebraic curves , which allowed him to find families of systems with properties integrability interesting new examples of algebraic limit cycles for quadratic systems and identify properties for systems with quadratic rational first integral.

In July 2002, Javier won the position of university professor of applied mathematics, which was the culmination of the academic and research conducted until then in his college career.

Added to the above, Javier Chavarriga worried about the spread and dissemination of mathematics and science in general, and organized several cycles with conferèmcies Lleida Studies Institute (IEI), of which he was director, at the Institute of Education Sciences (ICE), or from the University of Lleida, where he taught elective courses open to all students of the University and for secondary school teachers.
These popular courses we emphasize math lessons, which led to a great turnout.

In teaching and in the Polytechnic School (EPS), we noted that Javier was involved in the establishment of industrial engineering studies from the initial course from 1997 to 1998, as professor the course of calculation, and collaborated actively in the consolidation degree.
We note that Javier knew how to make attractive the subjects taught and was much appreciated and respected by his students. This is evident, for example, the number of times he was required to sponsor various promotions.

The last stage of Javier has been a member of the management team of the Polytechnic School. Over the past year and a half, Javier led all his hopes and efforts towards the school, and promote the creation of technical studies of architecture, which has been a big fan, as well as the opening of the Center Applied Energy Research (CREA).
In recent months participated in the development of a postgraduate course in engineering and information technology, and got the approval necessary to carry out the project.
As we see, one of the features that was defined seek consensus among people.

From his more human side, all we've been close to him can testify to the great devotion toward his father, to his wife, Cristina, and of course and above all, to his children Marta Xavier, of which he was very proud.

In addition to science, Javier has taught us many things in life and not infrequently has served as a model thanks to his drive and his desire to work, to understand the problems, etc..
His legacy remains in us and in any case it would be if we had not known and we have set considerably.

Now we are sure that we encourage everyone with its unique way of life and his laugh, move forward.
Continue its work, the fruit of his work and dedication is the best way to keep remembering it.

A hug, Javier.

Isaac A. García, Jaume Giné, Maite Grau, Josep Mallol i Jordi Sorolla

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A hug from me, too!
(If it really outside possible) 
Maurici

Ferran Sunyer Balaguer:

Exhibition at the Palau Robert (Barcelona, Spain) 

(Visited the 22/02/2014)

From Wikipedia (translated from Catalan wikipedia):

 Ferran Sunyer i Balaguer (Figueres , 1912 - Barcelona, ​​27 December 1967 ) was a self-taught mathematician who worked in Catalonia since the late thirties until his death . His contribution to the sciences was important and his work received the recognition of Catalan and Spanish institutions - that were awarded in several occasions and the international mathematical community .
Ferran Sunyer was born with a severe atrophy of the nervous system which prevented him from attending school and forced him to all kinds of activities help to develop basic and always had to move around in a wheelchair . This severe physical disability forced him to rely on his mother , Angela Balaguer , since his father died when he was two. Then his cousins ​​Mary and Mary of the Angels Carbona they care until her death . He lived between Barcelona and Vilajoana ( the town of Garrigàs Alt Emporda ) .

Self-taught , Ferran Sunyer began in mathematics and physics from the books of his cousin Ferdinand Carbona chemical engineering student . He made the first studies in mathematics at the end of 1930 , with notes on the accounts Rendus Académie des Sciences in Paris , backed by Jacques Hadamard , then one of the world 's most renowned mathematicians . After World War II , came into contact with such important mathematical research as Szolem Mandelbrojt Jean- Pierre Kahane , Waclaw Sierpinski , Yves Meyer , Paul Malliavin , Mascart Henry and John Angus MacIntyre , among others.

Ferran Sunyer published over 30 research articles journals Spanish, French and U.S. mainly. He was awarded several prizes from the Royal Academy of Exact Sciences , Physical and Natural Sciences of Madrid , the Catalan Studies Institute and the Consejo Superior de Investigaciones Científicas , including the Premio Franco de las Ciencias 1955. As of 1957 , despite physical limitations , he attended as a guest at various international conferences .

Her disability severely limited the possibilities professionals . But , however , he was collaborating investigator and later the Consejo Superior de Investigaciones Científicas (CSIC) and worked for years with a contract for the Office of Naval Research ( ONR ) of the Ministry of the United States Navy . In a time of great restrictions and isolation in Spain, Ferran Sunyer was undoubtedly one of the most renowned mathematicians abroad.

Ferran Sunyer is an example of overcoming and fighting against the greatest odds and intelligence in the service of science and the scientific community . And his family , who spared no efforts so that he could perform the investigation it is the values ​​of family solidarity : as could never write all the articles in mathematics, a language very specific and complicated formulas , dictates his mother or his cousins ​​, who were ordered to transfer them to the paper.

(Text translated from catalan wikipedia using Google translate)
Another available biography of Ferran Sunyer i Balaguer: Springer: Birkhäuser Mathematics: http://www.springer.com/birkhauser/mathematics?SGWID=0-40292-6-141489-0
More information (catalan language) from Fundació Ferran Sunyer Balaguer at: http://ffsb.espais.iec.cat/biografia-de-ferran-sunyer/


Video from TV3:

Ferran Sunyer Balaguer: 

https://www.youtube.com/watch?v=yP5ozImCruA

Contract NAVY - Ferran Sunyer (1966) for:
"Properties of a Space of Entire Functions of a Infinite Order"

(Photo taken from the exhibition)