General relativity is one of the most technically difficult physics theories, as it requires uncommon knowledge and mathematical skills. However, it is possible to calculate the relativistic effects induced by the curvature of space-time with good precision, and even to derive its formula, with a few simple arguments.

We know from special relativity that time flows more slowly in a moving system than in a stationary one. Given t as the time elapsed aboard the moving system, the time elapsed for the stationary one is 𝛾t, with 𝛾>1. In other words, time for those moving flows more slowly. A striking…

Transistors are the building blocks of our electronic gadgets: from smartphones to computers, toys, cooking devices, cleaning tools, etc.

Despite their ubiquity, only a few people know about how they work. In fact, understanding their principles of operation is not so hard.

The diode: a transistor building block

In order to understand how a transistor work, we need to understand what a diode is. In fact, a transistor, in practice, is nothing but two diodes.

A diode, essentially, works as a valve for electric current. It lets a flow of electrons flow in one direction only, opposing the movement of electrons in the opposite direction, just…

In a previous post of mine, I illustrated a brief history of temperature scales in which I recalled that the reason for which 0 °F corresponds to －18 °C is that the latter was the lowest temperature that Daniel Gabriel Fahrenheit could achieve in his laboratory.

Such a temperature can be easily reached mixing water, ice and ammonium chloride. This was, in fact, a very common method to produce a frigorific mixture before the invention of the freezer. The melting of the salts in water, in fact, is a chemical reaction that requires heat to proceed. Indeed, as every Italian…

The most widely adopted temperature scale is the Celsius or centigrade scale. Nowadays, we use these terms as synonyms, but, in fact, they were not such, originally. The Celsius temperature scale was invented by Anders Celsius that, in 1742, proposed its use by publishing “Observationer om twänne beständiga grader på en thermometer” (Observations of two constant gradations on a thermometer).

In his paper, Celsius reported the observations, according to which the temperature of melting ice (marked as C) and that of boiling water (marked as D) appeared to be constant, if measured with a mercury thermometer.

He then proposed, on…

Most physics textbooks are similar. They differ (little) for the sequence and for the choice of the mathematical details with which topics are presented. Most authors and teachers do not even ask themselves why they illustrate topics that way. Apparently, there is only one way to introduce something.

I believe this is not true. At least, I find stimulating trying to find alternative ways to introduce something in a different way. It is a difficult task, of course, and that is, maybe, why it is rewarding.

Let me be clear: I am not stating that alternative ways of teaching something…

Calculus

Many programmers believe that the use of higher order integration algorithms, combined with a large number of integration interval divisions, is useful (and sometimes necessary) to achieve good accuracy. In this article we show that this is not always true.

Myth No. 1: Higher Order Methods Are Better

Browsing Cantor’s Paradise articles, one of my favourite publications on Medium, I found an article written by Kazi Abu Rousan, in which the use of the trapezoidal rule for numerical integration is advocated (I am attracted by articles about physics, numerical methods and programming, as well as about the interplay between art and science). It is a well written article…

If you have an elementary knowledge of physics, it is very possible that you are unsatisfied about the metaphoric explanations of the role of the Higgs boson in “giving mass to other particles”. On the other hand we do not explain gravity and electromagnetism in a similar way. We teach them using mathematical equations, whose meaning is very clear and precise, and allow for the computation of measurable quantities.

In a recent post by Ethan Siegel, he correctly pointed it out that most of the mass of the Universe comes, in fact, from strong interactions inside nucleons (protons and neutrons)…

Numerical integration methods are those that allow the calculation of the definite integrals of a function, using computers. Simply stated, numerical integration is the process that leads to the evaluation, in many cases approximate, of the area between a curve y=f(x) and the x-axis, in a region x∈[a,b].

One of the simplest and, at the same time, most widely used method of numerical integration dates back to the time of Isaac Newton (this demonstrates that numerical calculation is not at all, as is believed, closely related to the use of computers). It consists of dividing the interval [a,b] into a…