Category Archives: Math

Starting 2012

Well, early this year has been diabolical. He was the defence of my Ph.D.  project on January 4th, but was rescheduled for January 12, in the middle, I presented the project’s research forum on UIED which has been reviewed by experts (fortunately, since it served me to refine the theoretical framework ).
Later on I will talk about the project in a separate post.
In addition, I still had to prepare the final examinations and the Geometry of Statistics and Probability for my students, who have not yet started to correct, but by their faces in their realization and the look that I gave to tests the situation is not very famous.
But good news, we were accepted for this year SEMIMELISBOA to talk about digital divide and decided to take a different approach, let’s look at digital exclusion through the eyes of digital natives (following the definition of Prensky).

The end of 2011

Well, the final day of 2011, I again remembered the blog.

It has been a troubled year with the PhD and the constant challenges of my classes.

In addition, my colleagues and I initiated our attendance at conferences (well, not initiated, because in 2010 we had already presented some communications), but this year we produced well (and not only in quantity), not only at conferences, but also articles.

We started the year in SEMIME talking about digital inclusion (in portuguese), in ED-MEDIA presented a poster and extended abstract about teacher perceptions of using moodle, afterwards in CHALLENGES we presented a poster (in portuguese) with the continuation of the work about student training and began the study launched in Barcelona last year, which was presented in Berlin in ECER2011 by my colleague (and we in the hangout google + from Portugal).

In between, came the publication of a book of proceedings of Barcelona and published an article on teacher training in moodle environment on eleed.

In the field of the investigation of the PHD, I presented data from a preliminary study and paper in Portsmouth in the ICTMT10 and the results of a mathematical task in SIEM (presentation and paper), and helped to organize a meeting of education on literacy and numeracy where I presented a communication on mathematical illiteracy (in portuguese), based on texts by Lockart and Allen Paulos.

In between, was continuing my first year of the PhD course, where I completed the project, which will now be presented on Jan. 4.

I would like to reference my work colleagues Patrícia Fidalgo and João Paz, and thank you for the work we have done, and my advisor for your patience constant.
Like all my colleagues from my PLE around the world.

It was a busy year, but they envision for the year will come tomorrow will be even more.

Good entries in 2012.

The reason an A4 sheet

Risks and scribbles, letters and numbers, stains and colors … we do every day of A4 paper a kind of Jack-of-all-trades, from literary to a more simple outline of ideas. But the dimensions of the paper format, so ingrained in our culture, have a real reason to be, more specifically 1.4142.


1.4142 is the ratio of the height (297 mm) and width (210 mm) of a sheet of A4 paper.Apparently, this calculation has nothing special, but if we execute the same operation in the dimensions of a sheet of A5, A3, A2 or A1, we obtain, rounded to one decimal place, exactly the same result.

The practical consequence of this phenomenon is simple math: folding the paper in half, we get a sheet with the exact dimensions of the format of paper immediately below. Try it! Take an A4 sheet vertically, fold it in half and turn left or right so to see her in an upright position. Now has in hand a sheet in A5 format. Do the same again, and will be looking at a single A6. And so on, always with the proportion strictly ensured.

In theory, we could carry this size reduction to negligible values, but physics is not on our side.


Mathematicians are not unrelated to phenomena of this nature, since the search for absolute proportion in the relations between quantities is the most fascinating in the realm of numbers.But it was not until 1786 that the scientist Georg Christoph Lichtenberg suggested publicly in the University of Göttingen, Germany, that the application of 1.4142 (the square root of the number 2) as a reason for a paper to ensure harmony of proportions between the different sizes.

This notion was later echoed by German engineer Walter Porstmann, who in 1922 envisioned the proposal on the basis of DIN 476 for paper formats. Starting from a shape with a square meter (A0), all remaining abated in proportion to the tiny dimensions of A10, little smaller than a postage stamp. So standardizing all sizes and reducing the cost of reproduction, distribution and storage, the standard quickly gained success around Europe – including Portugal, where he arrived in 1954 – and is now adopted worldwide, except U.S. and Canada.


The A4 is the most familiar, but the standard covers other variants such as B, C or D, all compatible with each other, an A4 letter fits well into a B4 envelope, which in turn fits like a glove in an envelope C4 bulkier. The balance of the standard is such that the shape of the paper in order to subliminally encourages ideas – there is nothing more conducive to inspiration, in fact, than a blank sheet of A4.