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Understanding the Concept Let’s imagine an organism🐛 that lives attached to a two-dimensional sphere \( S^2 \) (what we normally think of as a sphere🌐). In other words, to that organism, the sphere is the universe itself. Let’s call that organism \( A \). Loops on the Sphere Now, consider any loop⭕️ (a closed curve…

When casually playing an RPG (Role-Playing Game🎮️), you might not notice it, but when it is pointed out to you, you may think “That make sense💡”. Visualizing the World Map as a Torus Imagine the square world map of an RPG🗺️. First, the top and bottom edges of the map can be identified as the…

A topic related to infinity♾️. What does \( 0.9999… \) (with an infinite number of \(9\)s after the decimal point) equal? The answer is \( 0.9999… = 1 \). The proof can be easily shown by using an infinite geometric series. Let the first term be \( a = 9/10 \), the common ratio be…

Understanding Linear Algebra and the Kanji for “Linear” One of the mathematics studied in university is “llinear algebra.” It is a mathematics that uses matrices and vector spaces, and there have been many books on linear algebra published to date. In these books, two different kanji characters are used for “linear.” The Japanese translations for…

The Surprising Similarity Between a Coffee Cup and a Donut I can’t tell the difference between a coffee cup☕ and a donut🍩. Of course, they look different, but from a certain perspective, they are considered to be the same shape. In the field of mathematics called topology, the two shapes are not distinguished. In fact,…