Perfect Planet

…8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679… You might be wondering: are these two out of their minds?! What are these numbers? We’re not sure if your opinion of us will improve when we reveal that this is just a tiny snippet of an infinite sequence. So rejoice! We've simply listed the first 100 digits of the mathematical constant π (pi). The discovery that the ratio of a circle’s circumference to its diameter is constant – represented by π – dates back to antiquity and has fascinated humanity ever since. The ancient Egyptians and Babylonians measured it; Greek geniuses like Archimedes proved it and established limits (between 3.1408 and 3.1428); Chinese and Indian scholars refined its accuracy; and medieval and modern mathematicians revealed its true nature. What began as a simple observation in circular objects became a profound mathematical constant. Thus, the story of π is a testament to intercultural discoveries, conti...

  We are pleased to share with you the publication of a scientific article (authored by us), whose empirical analysis is motivated by physical inactivity and overweight and obesity as significant risk factors for global mortality. The article can be accessed here:  link . In this study, we explore the role of mobile applications in promoting physical activity, highlighting their relevance as a public health tool. The results indicate that the use of these applications is associated with the adoption of healthy habits, mainly due to the possibility of self-assessment, continuous monitoring, and personalized goal setting. Users' motivation seems to be more related to tracking their own performance rather than traditional loyalty strategies, although gamification can play a relevant role when properly balanced. The article also presents policy implications to maximize the benefits of these tools. Governments can encourage the development and adoption of applications aligned with ...

  Urban Myths.  When we started writing this column, we felt like a woman on the verge of a nervous breakdown —something that, according to stereotypes, seems to be an exclusively female privilege . Naturally, Priscila  had the meltdown , while Pedro remained stiff and firm like an iron bar . It was just like that classic moment when we had to attend an event and suddenly realise, to our horror, that we have absolutely nothing to wear! Everyone knows how women are: indecisive, emotional, ignorant, uneducated, resentful, and vengeful . They make decisions based on other people’s opinions , try to fit into imposed standards , and, of course, are so obsessed with appearances, gossip, and what others think that they hardly have time to form their own ideas. But let’s leave that behind and move on to what really matters: men. Women are complicated , and writing about them would be exhausting ; men, conversely, are simple, brilliant, and natural problem solvers . Hence the que...

1, 2, 3, 4, 5, 6, 7… 8. No, dear reader, we are not learning to count, nor are we reciting the 8 times table in digital root . We are talking about the alignment of eight planets taking place this February . Yes, you read that correctly: EIGHT! A Planetary Parade Worth Counting News reports mentioned that six planets paraded across the sky in January and that in February, seven would align—since Mercury , not wanting to miss this grand event, has joined the group. However, when looking at the Solar System’s layout , we can identify eight planets , arranged in order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Now, to avoid any discrimination , we must include in our count the "third rock from the Sun" (who remembers the TV show with that name?). After all, we observe a parade of seven planets from Earth, but Earth itself is also a planet , so it must be part of the event —don’t you agree? Thus, as reported, the parade will not...

Facing the World with Beauty When confronting the world, it is easy to feel overwhelmed by its adversities. Like you, we are fully aware of the imperfections and challenges of reality. Yet, we choose to direct our reflections toward beauty . When we speak of the “beautiful,” we do not do so in opposition to “ugliness.” Instead, we speak of beauty as a timeless source of inspiration , a driver of scientific progress , and an agent of transformation . The idea that “in numbers lies the nature of all things” ( ἐν τῷ ἀριθμῷ δέ τε τὰ παντ' ἐπέοικε ) is often associated with the Pythagorean school , reflecting the belief that the essence of the universe resides in numbers and mathematical proportions . Likewise, the concept of the “music of the spheres” —attributed to Pythagoras and later revisited by philosophers such as Plato —suggests that planets in motion generate an inaudible harmony resulting from  the mathematical relationships between celestial bodies and their orbits. To a...

  On our journey through the Pythagorean Table ( see Correio do Minho, 12/12/2024 ), we observed that the table displayed regular patterns when analyzed using the elimination of the nine methods ( modulo 9 ). Surely, you must have heard of the mathematical trick “ Casting out Nines .” This method works because, in the decimal system (base 10) , there is a fundamental property: 10 ≡ 1 (mod 9). This rule allows us to  replace a number with the sum of its digits to determine the remainder when divided by 9. Modular arithmetic exposes intrinsic patterns within numbers, which are essential both in the elimination of nine methods and in the structure of the Pythagorean Table . For example, as analyzed in “A Journey through the Pythagorean Table,”  we identify predictable cycles in the values obtained by recursively reducing the results of multiplications. This reflects the periodic nature of modular arithmetic , which fascinated ancient mathematicians, including the ...

  The sun was setting on the horizon. It was a late afternoon on one of those days still under the old time, meaning an hour ahead of where we are now. Despite the time being ahead, I will not talk about the future. On the contrary, I will speak of two recent and distant pasts. In the recent past, while traveling on a highway, I was suddenly struck by a beam of light (fortunately, not a lightning bolt) that made me reflect on the multiplication table and transported me to a distant past. Suddenly, as if in a leap through time, I found myself in the 6th century BC, on an island in ancient Greece, face to face with Pythagoras. Who does not know the well-known rhyme that describes his famous theorem? "On the way to Syracuse, Pythagoras told his grandchildren: The square of the hypotenuse is equal to the sum of the squares of the other two sides." Although the theorem is fascinating, it is irrelevant to today’s topic. Beyond the theorem and many other significant contributions...