# The Magic Sand Slicer

I have recently published for the first time a project on Instructables: a website specialised in publishing interesting DIY projects by an effervescent community of makers and educators.

The project is called the Magic-Sand Slicer and it is an education project initially conceived as a STEM activity to learn using Arduino, a 3D printer, and some exciting science. It is also a collaboration with my little son Leonardo who helped me in evaluating the device as a STEM student. We have learned a lot together, and we want to share the results of this long journey. This project aims to create a device that automatically makes sections of a cylinder of easy-to-cut colored material. That can be used for practicing 3D image reconstruction of the colored blogs hidden in the column. The so-called Magic-Sand (c), also known with other trademarks names, becomes suitable for this experiment.
What is the point of making pictures of thin layers of sand and then reconstructing it digitally? Is it just for the fun of it? It varies on who is using it. However, students and teachers from different disciplines (e.g. geology, biology, medical) can find it a helpful education device to practice with image reconstruction from the serial sections. It could also be of interest to a geologist interested in sedimentary material plasticity to study rock and the secrets it beholds, or to a process, engineering to emulate the packing of fine granular materials. Finally, an artist can make a fantastic program of unraveling magic forms generated by packing colored sand.

I was surprised that the project got so much interest in very short of time and I thank the Instructable community for their nice welcome! If you like to know more about the project (and try it!) then you can read the instructable here.

# Nanoparticles in Biology and Medicine

I am very pleased to announce that the second edition of the book Nanoparticles in Biology and Medicine edited by Enrico Ferrari, Mikhail Soloviev is now out.

This fully updated volume presents a wide range of methods for synthesis, surface modification, characterization and application of nano-sized materials (nanoparticles) in the life science and medical fields, with a focus on drug delivery and diagnostics. Beginning with a section on the synthesis of nanoparticles and their applications, the book continues with detailed chapters on nanoparticle derivatization, bio-interface, and nanotoxicity, as well as nanoparticle characterization and advanced methods development. Written for the highly successful Methods in Molecular Biology series, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and cutting-edge, Nanoparticles in Biology and Medicine: Methods and Protocols, Second Edition serves as an ideal guide for scientists at all levels of expertise to a wide range of biomedical and pharmaceutical applications including functional protein studies, drug delivery, immunochemistry, imaging, and more.

I have contributed with a chapter (14) titled The Molecular Dynamics Simulation of Peptides on Gold Nanosurfaces.

In this chapter a short tutorial on the preparation of molecular dynamics (MD) simulations for a peptide in solution at the interface of an uncoated gold nanosurface is given. Specifically, the step-by-step procedure will give guidance to set up the simulation of a 16 amino acid long antimicrobial peptide on a gold layer using the program Gromacs for Molecular Dynamics simulations.

# Buon Natale e Felice 2020

Gentilissimi/e Lettori e Lettrici, Dear Reader, Sehr geehrte Leserinnen und Leser,

Grazie mille per aver fatto tappa durante le vostre peregrinazioni cibernautiche nel mio sito web e per dedicare un po’ del vostro tempo nel leggere i miei articoli. Spero che li avete trovati tanto interessanti e utili da continuate a tornare a leggermi.
Voglio anticipare alcune delle prossime pubblicazioni.
Tra breve usciranno nuovi titoli:

• The Logistic Map and the Feigenbaum Constants: a Retro Programming Inspired Excursion.
• L’integrazione numerica di equazioni differenziali, parte II: 50 anni fa l’uomo ha messo piede sulla Luna
• Retro Programming: Acid-base Titration.
• Retro Programming: Plant evolution.

Per il momento auguro a tutti voi di trascorrere con le vostri cari un felice Natale e di avere un nuovo anno pieno di buone notizie.

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# The First 150 Years of the Periodic Table of the Elements

This year marks the 150th anniversary of the periodic table of the elements (TPE) which currently has 118 entries, the latest arrival (the Tennessine) was discovered 10 years ago (2009), and I feel obliged as a chemist to give some a small informative contribution to celebrate this important event.

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# The Lissajous-Bowditch Curves

Try to glue a small mirror to an end of a bent piece of wire fixed to a stable platform and let the laser beam of a laser pointer reflect on it. Entangled spires of an ephemeral dragon of light will perform a hypnotic dance on the wall of your room. This voluptuous dance is the results of two mutually perpendicular harmonic oscillations produced by the oscillations of the elastic wire.

The curved patterns are called Lissajous-Bowditch figures and 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. Lissajous invented different mechanical devices consisting of two mirrors attached to two oriented diapasons (or other oscillators) by double reflecting a collimated ray of light on a screen, produce these figures upon oscillations of the diapasons.  The diapason can be substituted with elastic wires, speakers, pendulum or electronic circuits. I the last case, the light is the electron beam of a cathodic tube (or its digital equivalent)  of an oscilloscope. This blog is about these curves and shows demonstrations and applications.

# The Magic Imaginary Numbers

Complex numbers may appear a difficult subject given the name. However, there is nothing of really complicated about complex numbers. However, they definitively add a pinch of \em magic \em in the mathematics manipulations that you can do with them!

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# Frosinone and the Ciociaria

Glie musèu  Tra glie campanìle i l'Annunziàta,'Ntòcce prima della uìa ‘Ngelòne,Stamatìna sò fatte 'na fermàtaPè rattaccà le strengh'a strucenòne. Me uànne gli'òcchie doppe 'na utràtaI uède, tutt'a giòrne, nè salòneAddò 'na raccòta sta urdenàtaDe prete, crete, pièzze de matòne, Cule de uàse, de pile, de pignàte,Màneche de recciòle i de bicchièraAncòra prima de Nuè 'mpastàte. Quante sècule,frà, che sò passàte'Nche gli'Ome a trebbulà 'ncim'a sta TeraI ch'è remàste ? Ddù cocce smenuzzàte.               Irèno Da Vialìra (Poeta ciociaro)

I am European of Italian nationality. I very proud of my background but, unfortunately, my carrier put me in an orbit that does intersect my country only during my holiday vacations. In these close encounters, my landing site is Frosinone. When not-Italian acquaintances want to know about my Heimat, most of them are puzzled about the name and location of my hometown. Usually, I help them to overcome the understandable disorientation by giving as reference Rome and telling them that my birthplace is somewhere 80 km in the South of the Caput Mundi. Last year (2018) my hometown soccer team (Frosinone Calcio, nicknamed Canarini, The Canaries, for their home colours)) moved in the first league (A) of the national soccer championship. So, let see if this success will help to raise its notoriety!

It is a long time that I would like to write about Frosinone. However, in this article, I won’t write about the success of the Canarini football team but about my hometown and the rural place in central Italy where it is located.

In the province of Frosinone, there are many historical famous towns such as Anagni that has the exquisite Anagni Cathedral with its museum, Alatri with its megalitic Acropolis, Ferentino another megalytic city with also a beutyful Romanesque Duomo, Veroli and the closeby Certosa of Trisulti that has been recently on news spot for the sadly attempt to trasform this wolderful medieval santuary of christianity and culture to a private business when instead it should be preserved and nominated instead as an humanity heritage. I will talk about these town in other articles. This just to mention some of the famous towns and cultural places in Ciociaria.

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# Calculus in a Nutshell: functions and derivatives

When I was about thirteen, the library was going to get ‘Calculus for the Practical Man.’ By this time I knew, from reading the encyclopedia, that calculus was an important and interesting subject, and I ought to learn it.

Richard P. Feynman, from What Do You Care What Other People Think?

## Introduction

Calculus is an important branch of mathematics that deals with the methods for calculating derivatives and integrals of functions and using this information to study the properties of functions. It was independently invented by I. Newton and W. Leibniz in the 18${^{th}}$ century and it was further developed by other great mathematicians in the centuries that follows (see Figure below).

It comprises two areas:

• Differential calculus ${\rightarrow}$ It concerns the study of the rate of variation of functions.
• Integral calculus ${\rightarrow}$ It concern the study of the area under functions.

Depending on the nature of the functions involved in the calculations, we can further distinguish between the single- and multi-variable calculus. In this chapter, the main concepts and methods of the single-variable calculus are summarised.

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# The Fourier Series

Pure mathematics is much more than an armory of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations.

George Frederick James Temple In 100 Years of Mathematics: a Personal Viewpoint (1981).

The Fourier Series is a very important mathematics tool discovered by Jean-Baptiste Joseph Fourier in the 18th century. The Fourier series is used in many important areas of science and engineering. They are used to give an analytical approximate description of complex periodic function or series of data.  In this blog, I am going to give a short introduction to it.