"… I seem […] only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me". – Isaac Newton.
Oh my God. Do you know what this is? This is a dinosaur egg. The dinosaurs are breeding.
Dr. Alan Grant, Jurassic Park movie (1993)
We are again approaching Easter time and, as tradition, I would like to celebrate with an article dedicated to the most perfect thing in nature: the egg. I came across interesting books about the discovery of dinosaur eggs last year. Dinosaurs are the ancestors of birds and modern reptiles, so we will take a little detour from the traditional Easter egg, and with the spirit of equal opportunity justice, we will look at the shape of these.
Sometime ago, I have written about the Lissajous-Bowditch figures. In the same article, it is described how to build a simple device called a kaleidophone to generate Lissajous patterns. Using a small mirror fixed securely to the end of a bent wire on a stable platform and a laser beam from a laser pointer reflects off it, mesmerizing, intertwined spirals of light. The laser beam will appear dancing on the wall of your room. This enchanting display results from two mutually perpendicular harmonic oscillations generated by the vibrations of the elastic wire. These captivating patterns are known as Lissajous-Bowditch figures and are named after the French physicist Jules Antoine Lissajous, who did a detailed study of them (published in his Mémoire sur l’étude optique des mouvements vibratoires, 1857). The American mathematician Nathaniel Bowditch (1773 – 1838) conducted earlier and independent studies on the same curves, and for this reason, the figures are also called Lissajous-Bowditch curves [2].
LB curves result from the combination of two harmonic motions, and therefore, they can be mathematically generated through a parametric representation involving two sinusoidal functions (see Figure and also here). Lissajous invented different mechanical devices reproducing these periodic oscillations consisting of two mirrors attached to two oriented diapasons (or other oscillators) by double reflecting a collimated ray of light on a screen, producing these figures upon oscillations of the diapasons. The diapason can be substituted with elastic wires, speakers, pendulum, or electronic circuits. In the last case, the light is the electron beam of a cathodic tube (or its digital equivalent) of an oscilloscope [3].
The simplest of these devices is the KaleidoPhone, invented (and named) by the British physicist Charles Wheatstone at the beginning of the 19th century [3,4]. The Kaleidophone creates stunning Lissajous patterns and is an excellent example of how science can also be an art form. You can bring the mesmerizing dance of light to life with just a few simple materials and creativity.
In a new Instructable project, I have presented a modern compact version of the kalidophone device fabricated with the help of 3D printing technology and enhanced with a digital camera.
For this last bit of modern technology, the new device is called KaleidoPhoneScope. What makes this little device is the facility to adapt it to record another form of vibrations by adding a speaker and another mirror free to vibrate on its bizarre pattern, recalling SciFi movies promp appear on a free wall (or door) of your studio.
As Christmas approaches, what is the best time to try this device with a traditional song? Here is the result. Activate the captions to see the corresponding frequencies of the tones.
I wish you all to spend a Merry Christmas with your dearest, and I hope to see a peace and
REFERENCES
T. B. Greenslade Jr., “All about Lissajous figures,” The Physics Teacher, 31, 364 (1993).
T. B. Greenslade Jr., “Devices to Illustrate Lissajous Figures,” *The Physics Teacher, 41, 351 (2003).
C. Wheatstone, Description of the kaleidophone, or phonic kaleidoscope: A new philosophical toy, for the illustration of several interesting and amusing acoustical and optical phenomena, Quarterly Journal of Science, Literature and Art 23, 344 (1827).
R. J. Whitaker, “The Wheatstone kaleidophone,” American Journal of Physics, 61, 722 (1993).
Atomic fractional coordinates (AFCs) are used to specify the positions of atoms within a crystal structure. They are expressed as three fractional values that represent the relative positions of atoms within the unit cell of the crystal. If are the cartesian coordinate an the atom in a cubic lattice of lattice parameters , the ACF are calculates as
therefore, the value of ACFs are fractional values between 0 and 1. For example, an atom at (0.25, 0.5, 0.75) is located a quarter of the way along the a-axis, halfway along the b-axis, and three-quarters of the way along the c-axis of the unit cell. Crystal structures often exhibit symmetry, and fractional coordinates are essential for understanding and describing this symmetry. Symmetry operations, such as rotations, translations, and reflections, can be applied to fractional coordinates to elucidate the symmetrical aspects of the crystal, which is crucial for understanding the material’s properties.
To all the Spanish-speaking readers, this is an AI-assisted translation experiment using WordPress. Please bear with me as my knowledge of the Spanish language is limited, so I cannot detect possible incorrect translations of the original test in Italiano. If you appreciate my efforts, please let me know. If you notice any errors in the translation, please send me a message to correct them. You can find my original versions in English, Italian, and German langiage of this text by clicking the links.
Estimados lectores de habla hispana, este es un experimento de traducción asistida por IA utilizando WordPress. Les pido paciencia ya que mi conocimiento del idioma español es limitado, por lo que no puedo detectar posibles traducciones incorrectas del texto original en italiano. Si aprecian mis esfuerzos, por favor háganmelo saber. Si notan algún error en la traducción, por favor envíenme un mensaje para corregirlo. Pueden encontrar las versiones originales en inglés, italiano y alemán de este texto haciendo clic en los enlaces.
The electronegativity of a chemical element measures the tendency of an atom to attract electrons around it. This definition was formalized for the first time, in a semi-empirical form, by the chemist Linus Pauling in the early 1930s, but it had already been proposed in the late 1800s by the Swedish chemist Berzelius. In molecules, this tendency determines the molecular electronic distribution and therefore influences molecular properties such as the distribution of partial charges and chemical reactivity. Pauling provided an electronegativity scale by comparing bond dissociation energies of pairs of atoms (A, B) using the equation
With $E_{AB}$, $E_{AA}$, and $E_{BB}$ being the dissociation energies of the molecules AB, AA, and BB, respectively.
A few years later, in 1934, Mulliken proposed an expanded definition of electronegativity based on spectroscopically measurable atomic properties such as ionization potential (I) and electron affinity (E):
L’elettronegatività di un elemento chimico misura la tendenza di un atomo ad attrarre intorno a sé elettroni. Questa definizione fu formalizzata per la prima volta, in foma semi-empirica, dal chimico Linus Pauling all’inizio del 1930 ma era già stata proposta nella seconda metà dell’1800 dal chimico svedese Berzelius. Nelle molecole, questa tendenza determina la distribuzione elettronica molecolare e quindi influenza le proprietà molecolari quali per esempio, la distribuzione delle cariche parziali e la reattività chimica. Pauling ha fornito una scala di elettronegatività confrontando le energie di dissociazione di legame di coppie di atomi (A, B) usando la relazione
con , rispettivamente le energie di dissociazione delle molecole AB, AA, and BB.
Qualche anno dopo, nel 1934, Mulliken propose una definizione estesa di elettronegatività basata su proprietà atomiche misurabili spettroscopicamente, quali il potenziale di ionizzazione (I) e l’affinità elettronica (E):
What is the origin of the urge, the fascination that drives physicists, mathematicians, and presumably other scientists as well? Psychoanalysis suggests that it is sexual curiosity. You start by asking where little babies come from, one thing leads to another, and you find yourself preparing nitroglycerine or solving differential equations. This explanation is somewhat irritating, and therefore probably basically correct. David Ruelle, in Chance and Chaos
Here I am again for a new appointment with the Italian version of the column “Retro Programming Nostalgia“, my very own adventure in computer archaeology, rediscovering old programs written some time ago on microcomputers that have made their mark on an era.
This time, in my old floppy disks for the glorious Amiga 500, I found a program in Amiga Basic that I wrote during the early years of my university studies, when I was taking the course on differential equations II. Specifically, I was very fascinated by autonomous systems of differential equations due to their numerous applications in mathematical modeling of physical, chemical, and biological systems, as well as their importance in the theory of chaos. As in the series articles, I want to release an adapted version for the QB64 BASIC meta-compiler, but before presenting the program, I want to briefly explain what an autonomous system of differential equations is.
“Qual è l’origine del desiderio, della fascinazione che spinge i fisici, i matematici e presumibilmente anche altri scienziati? La psicoanalisi suggerisce che si tratti di curiosità sessuale. Si comincia chiedendosi da dove vengano i bambini piccoli, una cosa porta all’altra e ci si ritrova a preparare il nitroglicerina o a risolvere equazioni differenziali. Questa spiegazione è un po’ irritante, e quindi probabilmente fondamentalmente corretta.” – David Ruelle, in “Chance and Chaos”
Eccomi di nuovo per un nuovo appuntamento con la versione in italiano della Rubrica “Retro Programming Nostalgia “, la mia personalissima avventura d’ archeologia informatica alla riscoperta di vecchi programmi scritti qualche tempo fa su microcomputers che hanno segnato un’epoca.
Questa volta, nei miei vecchi dischetti per il glorioso Amiga 500, ho trovato un programma in Amiga Basic che scrissi durante i primi anni dei miei studi universitari, quando studiavo nel corso di matematica II, i sistemi d’equazioni differenziali. In particolare, ero molto affascinato dai sistemi di equazioni differenziali autonomi per via delle molteplici applicazioni nella modellazione matematica di sistemi fisici, chimici e biologici, e per la loro importanza nella teoria del caos. Come negli articoli della serie, voglio rilasciare una versione riadattata per il meta compilatore QB64 BASIC, ma prima di presentare il programma, voglio brevemente spiegare cosa sia un sistema autonomo di equazioni differenziali.
This article describes a new function of the LiStaLiA library. As I mentioned in Part I of this series of articles, I didn’t extensively test the library, so I am releasing it as an alpha version. Please let me know if you find any errors or if you improve the function, and feel free to send me your modified code!
CALCULATING STATISTICS PROPERTIES OF DATA SETS
The new functions perform a statistical analysis of the data set read by the function ReadData(). The source code of this new library functions is reported in the Appendix. The following list report all the descriptor calculated buy the functions.
To all Japanese-speaking readers, this text is part of an experiment using AI translation and WordPress. We kindly ask for your understanding and cooperation. If you find value in this initiative, please let us know. Additionally, if you notice any translation inaccuracies, we would greatly appreciate it if you could contact us. You can find the original text in English, Chinese, Italian, and German by clicking the links.
that represent the relative positions of atoms within the unit cell of the crystal. If 
are the cartesian coordinate an the atom in a cubic lattice of lattice parameters 
, the ACF are calculates as
, rispettivamente le energie di dissociazione delle molecole AB, AA, and BB.
daniloroccatano.blog 