Balloon, art and mathematics

After (or before?) @StartsWithABang's balloon animals' post?

A couple of week ago Ethan Siegel published a post about ballon animals, so I decide to repost an old piece that I wrote in 2011 for my italian blog: the english version is lost, but it is magically reposted here!

Two one-balloon constructions and their associated graphs

I recently discovered this interesting site, vihart. In the site there are some interesting paper and today I want to write something about Computational Balloon Twisting: The Theory of Balloon Polyhedra by Erik and Martin Demaine and Vi Hart (the paper was reported in 2010 by the Improbable Research blog).
The interest about ballon twisting was motivated by...

Balloon twisting is fun: the activity can both entertain and engage children of all ages. Thus balloon twisting can be a vehicle for teaching mathematical concepts inherent in balloons. As we will see, these topics include graph theory, graph algorithms, Euler tours, Chinese postman tours, polyhedra (both 3D and 4D), coloring, symmetry, and even NP-completeness. Even the models alone are useful for education, e.g., in illustrating molecules in chemistry.

There's also a second motivation: building architectural structures with air beams (Army blows up building, Center manages technology of inflatable composite structures).

Our approach suggests that one long, low-pressure tube enables the temporary construction of inflatable shelters, domes, and many other polyhedral structures, which can be later reconfigured into different shapes and re-used at different sites. In contrast to previous work, which designs a different inflatable shape specifically for each desired structure, we show the versatility of a single tube.

Twisting baloons

The problem of the researchers is to determine the twistable graphs. Referring to a phisical balloon like a bloon, we have the following definitions:

(...) a bloon is a (line) segment which can be twisted at arbitrary points to form vertices at which the bloon can be bent like a hinge. The endpoints of a bloon are also vertices. Two vertices can be tied to form permanent point connections. A twisted bloon is stable if every vertex is either tied to another vertex or held at a nonzero bending angle.

The three researchers also defined two models

The chirality at the beginning of the universe

A new clue about the #quarkgluonplasma from @RHIC_STAR at @BrookhavenLab

Within the particles that constitute atomic nuclei, protons and neutrons, there are the quarks, the elementary particles with fractional charges, linked to each other thanks to the gluons, bosons that carry the nuclear interaction. Thanks to the gluons it is impossible to observe, at present, free quarks, but it is expected that in the very first stage of the universe, matter was in a state called quark-gluon plasma. Thanks to the observation of so-called quark jets we know, indirectly, that the interior of the accelerators RHIC and LHC, in particular in heavy ion collisions, this kind of plasmas were created and, according to the theory, in the presence of axial anomalies, dued by the presence of strong electromagnetic fields, we can create two special effects: the Chiral Magnetic Effect (CME) and the Chiral Separation Effect (CSE).

The CME is the phenomenon of electric charge separation along the axis of the applied magnetic field in the presence of fluctuating topological charge.
The Chiral Separation Effect (CSE) refers to the separation of chiral charge along the axis of external magnetic field at finite density of vector charge (e.g. at finite baryon number density)⁽⁵⁾

These two effects are generated by the topology of the system: indeed, within the theory^{(1, 2, 3)} is contemplated the existence of some numbers (called topological invariants, or winding number⁽⁴⁾) that, while not associated with an observable, still generate effects physically relevant because of their link with the fundamental symmetries of the system.

The fifth shot of a tau neutrino

http://t.co/urnbKwoiSY by @ulaulaman about #neutrino #tau #Opera #particlephysics

From the press release:

The OPERA (Oscillation Project with Emulsion-tRacking Apparatus) international experiment at the National Institute for Nuclear Physics (INFN) Gran Sasso Laboratory (Italy) has detected the fifth occurrence of a tau neutrino. The neutrino started its flight at CERN as muon neutrino and, after traveling 730 km through the Earth, it arrived at Gran Sasso Laboratories showing up as a tau neutrino. This important result was announced yesterday during a seminar held at the Gran Sasso Laboratories. According to the Spokesperson of the international research team, Giovanni De Lellis, from Federico II University and INFN in Naples, "The detection of a fifth tau neutrino is extremely important: the direct observation of the transition from muon to tau neutrinos has now achieved for the first time the 5 sigma statistical precision, the usual particle physics threshold for a discovery. We can thus definitely report the discovery of the appearance of tau neutrinos in a muon neutrino beam." The detection of tau neutrinos from the oscillation of muon neutrinos was the motivation of the OPERA project, designed in the late nineties. "This task is extremely difficult due to two conflicting requirements: a huge, massive detector and a micrometric accuracy. The challenge is to bring to the thousands ton scale a detector based on the nuclear emulsion technology, a photographic technique unique in ensuring the required accuracy", De Lellis says.

The tau neutrino was discovered in july 2000 by DONUT collaboration (arXiv). It is produced in the tau decay, where tau is a lepton, an elementary particle with a negative electric charge and spin 1/2 and with a mass of 1776.82 ± 0.16 MeV: with a great simplification we can say that tau is an electron with a very big mass!
Now, first of all I share the paper about the fourth observation:

Math education: calculus in South Korea and the Rubik's cube

#abstract from #arXiv via @ulaulaman

A couple of mathematical abstracts from arXiv:

N. Karjanto (2015). Calculus teaching and learning in South Korea Jurnal Matematika Integratif 9(2): 179-193, 2013 arXiv: 1504.07803v1

This article discusses an experience of teaching Calculus classes for the freshmen students enrolled at Sungkyunkwan University, one of the private universities in South Korea. The teaching and learning approach is a balance combination between the teacher-oriented traditional style of lecturing and other activities that encourage students for active learning and classroom participation. Based on the initial observation during several semesters, some anecdotal evidences show that students' learning is improved after implementing this student-oriented active learning approach, albeit a longer period of time is definitely needed to transform general students' attitude from passive learners to active ones.

From the conclusion I would emphasize the following paragraph:

From this study we have seen some anecdotal evidences that students' learning is improved when they are actively engaged with the study material, instead of only sitting passively in the classroom and listening to the lecture. More success can be achieved when the classroom activities are also fun. With a proper balance between lecturing and engaging students new concepts and activities in which students, alone or in groups, need to struggle themselves with these concepts, makes the learning time in the classroom more effective and the time spent in class becomes more enjoyable for the students. Students also show appreciation for this style of teaching. Despite classroom participation and group activities are generally more successful in classes with a small number of students, some promising and good results have been accomplished even though the class sizes were relatively large.

Sandor Kiss (2015). Educational Challenges of Rubik's Cube X Workshop on Particle Correlations and Femtoscopy arXiv: 1505.00750v1

The first 2x2x2 twisty cube was created as a demonstration tool by Erno Rubik in 1974 to help his students understand the complexity of space and the movements in 3D. He fabricated a novel 3x3x3 mechanism where the 26 cubies were turning, and twisting independently, without falling apart. The cube was dressed in sophisticated colors which made it a unique puzzle. Even without instruction is the aim of the game was self-explanatory. Its educational value in VSI (Visual-Spatial Intelligence), developing strategy, memorization and logistics, improve concentration and persistence in problem solving is high in every age group. A logical puzzle has outreach far beyond. Those aspects are briefly covered in this article.

LHC restars at 13 TeV

http://t.co/jLPjvDAT6V greeting to @CERN from @ulaulaman and all network

Today at CERN, LHC restarts after a stopping period, at the energy of 13 TeV. It's a great day because we expect signals of new physics beyond particle standard model.

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