Saturday, March 29, 2014

Circadian clock - Google Play

Posted the new "Circadian clock" at: Google Play:

Circadian clock

The mechanism :
The green outer ring with 5 primary partitions and and 300 smaller partitions gives 59/300 turns per minute counterclockwise: 11.8 turns per hour.
The planetary gear of the seconds, in green color, is driven by the outer ring and gives 59 rph counterclockwise. And in turn, the axis makes a complete turn clockwise, rolling on the inside of the crown of the minutes, by hour.
The hand of the minutes, in blue color, turning on the central axis and linked to the axis of the planetary gear of the seconds, makes a complete turn every hour.
The wheel that rotates clockwise integrally with its base and with the hand of the minutes, make to spin counterclockwise two blue planetary wheels. These two planetary wheels spins counterclockwise a third planetary gear.
The third planetary wheel rotates one turn per hour clockwise and transmits the rotation to the fourth planetary wheel. The fourth planetary wheel spins counterclockwise and progresses clockwise.
The fourth blue planetary wheel gives 2 turns on itself and its axis gives the entire turn around the sphere of the clock every 12 hours.
On the four planetary wheels is mounted the hour hand: a big red triangle, giving rigidity to the structure and indicating the hours and rotating clockwise.
The big red triangle, linked to a freewheel on the central axis, drives the rotation of the three static planetary yellow wheels of the day. Turning counterclockwise about its fixed axis, rotates counterclockwise the yellow big crown that distinguishes the day light hours, of the darkness of the night and makes a complete turn every 24 hours.
The big red triangle, also linked to another freewheel on the central axis, drives the rotation of three static planetary wheels magenta of the week, much bigger than those for the day. Turning counterclockwise about its fixed axis, and spinning counterclockwise the crown magenta indicating the day of the week, and makes a complete turn every week.

Technical drawings for the Circadian Clock:
© 2014 Maurici Carbó, architect.

The circadian clock in action:


Notes from the developer:

About the word 'circadian':
The term 'circadian' comes from the Latin 'circa', meaning "around" (or "approximately"), and 'diem' or 'dies', meaning "day".
This app is only a clock, with many layers, showing many overlapped mechanisms, with zoom. The triangle of the hours is manually adjustable, and has an algorithm to reset the clock to the system time after any adjustment.
Nothing concerning the biological circadian cycle.
But one of the layers of the clock represents daylight.

Clarification after some questions:
The Circadian Clock has no relationship with the 'Circassian Circle'.
The Circassian Circle is a dance whose origin is possible in the Circassian people.
The Circassians are a people that was displaced during the conquest of the Caucasus in 1862 and still suffering the effects of the Circassian diaspora:

Wednesday, March 5, 2014

RAE (Real Academia Española): Answer about Quintillón to Centillón

En relación con su consulta, le remitimos la siguiente información:

      Ni el DRAE ni el DPD, ni tampoco otros escritos gramaticales de la Real Academia recogen ningún numeral superior al cuatrillón. El Diccionario del español actual de M. Seco trae uno más, quintillón. Por otra parte cabe decir que tampoco se documentan en nuestros bancos de datos, lo cual es indicativo del escaso uso que tendrían en español. En páginas de Internet pueden localizarse series más amplias de numerales, formados por analogía: sextillón, septillón, octillón, nonillón, decillón, undecillón, duodecillón, tridecillón/tredecillón, cuatridecillón/cuatordecillón, quindecillón, sexdecillón, septidecillón/septendecillón, octodecillón, nonidecillón/novendecillón, vigillón/vigintillón.       Lamentamos no poder ayudarle, pero nuestro cometido se limita a resolver dudas concretas sobre el uso normativo del español, y su consulta se refiere a hipotéticas voces que no tienen ningún uso en nuestra lengua.

     Reciba un cordial saludo.
Departamento de «Español al día»
Real Academia Española


Despues de esta carta, pudimos desarrollar:
Calculadora natural

Muchas gracias!!!

Versión inglesa:
How looks a centillion?

Versión española:
Calculadora natural:

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:

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

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

Tuesday, March 4, 2014

Letter: ToRAE_Quintillion_Centillion.txt

For the: 'Real Academia Española' (RAE)

In we are developing an application that writes numbers in Castilian.
Specialized in writing extremely large numbers.
We did not find any official confirmation of the name of the numbers from 10 ^30 to 10^ 594 

We need confirmation of our proposal:


Confirmation of these data would be very important to us.
We would provide a right product version in the Castilian language.

Maurici Carbó 
R&D Manager at:

This letter was written after developing:
Whole Calculator

Monday, March 3, 2014

"Whole Calculator"
(Android app) 

    This week (after a month of work) we started a new project : "Double Struck Capital ".
    And for the first time we can post about it on this blog.
    The first visible result of this project is the calculator of natural numbers: "Whole Calculator" 
    It works in the set of the Natural Numbers (ℕ0 in the mathematical text books)
    'ℕ' is the character named 'Double-struck Capital N'  
    Our new calculator has the particularity to work with arbitrarily large numbers (up to centillion). And it can show the numbers written in words.

    One purpose of this program is to support the teaching of reading whole numbers, and to be able to read and operate with numbers and huge numbers too.

    And has another intention:
    In the attempt to understand the numbers and its elementary operators in a first stage of education, it is relatively easy to explain the sum , and multiplication.
    But subtraction and division operations are another level :
    Subtraction and division are operations whose result that is not restricted into the set of natural numbers:
    Therefore, you can only partially explain those operations :
    Subtraction, only when the result is always positive.
    The division only when a provided that the dividend is a multiple of the divisor.
    The Whole Calculator , tries to show this same state of bewilderment :
    While it is capable of displaying numbers to barely imaginable figures (is able to show correct results in numbers and letters up to 10 ^ 303) however it is not able to operate with negative numbers, and if the divisions are not exact , the result has a remainder .
    "Whole calculator " is a coherent and 'trustable' product . But, when results are not within the set of natural numbers , warns the user that the " this calculator of natural numbers is not able to give the correct result" , because it is outside the scope of the natural numbers, and recommends the use (and "download" from anywhere) a better calculator: integer calculator (ℤ) or rational (ℚ) as appropriate: As if the app were a damaged or a incomplete product.
    We want to show that the "whole calculator" is a damaged product, by fault of the Natural Numbers.

    In turn, all this can be seen as a joke by program users .
    But in "Double Struck Capital - nummòlt " we think it is a way to teach the numbers from the beginning:
    Understand that in a first step , we learn to live with the numbers used to count and to list . But when we operate with them, and as we operate, we have not enough with these numbers (natural numbers) and we need to expand the range of numbers to use, to meet the needs that appear when we afford the subtraction and the division.
    At the time of making this app, we had to deal with the construction of the natural numbers from zero :Internally, the program works with the natural numbers as a String variable , so that the numbers do not remain limited to the small dimensions of the variables of type ' int ' or ' long' .This has forced the developer to implement the algorithm of addition, subtraction, multiplication and division from text strings.
    And we have faced the same problem as has a child when learns to add, subtract, multiply and divide.
    Recovering these skills almost lost in time for us, we has discovered that we never fully understood the algorithms of subtraction, or multiplication or division. 

  •     We have not clear enough the mechanism of "I carry" in the addition or "borrowing" in subtraction .
  •     We don't know subtract if the result will not be positive .
  •     We do not understand what we do when we multiply numbers: ( The needed zeros are obviated in the mechanism we were taught in school)
  •     We do not understand almost nothing of the procedure that we follow when we divide .
    In the development of the app, we had to overcome these difficulties. And we had to return to deduct procedures , modifying them to make the program work properly.
In the development of this program, we felt like little kids , having to learn the most basic things.    

    And at the same time , we felt like kids happy when it was finished.
    We expect that when the program will be downloaded, the users will can get to enjoy it as we have enjoyed making it .
    The program can be downloaded at:
(There's only the Android App, no version in other operative systems)

Whole Calculator Youtube:

How looks a Centillion?:
The app spells the natural numbers from 1 to the Centillion (10^303) in english, working with the Short Scale
There's also a paid version in Castilian ( Spanish ) spelling the natural numbers from 1 to the "Centillón" (1^600) working with the Long Scale:

Calculadora Natural

Video of the Update (Version 1.0.4):
Cyclic numbers:

Video of the Update (version 1.0.7) added Catalan:

Video about Factorials: From 2! to 50!:

Thanks for the help:
Wendy Petti (
Joan Jareño (CREAMAT)

Maurici Carbó (nummolt webmaster)