maths.1089

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In geometry, a Pythagorean tree is a plane fractal constructed from a series of squares arranged in a configuration that repeatedly illustrates the classic Pythagorean theorem. First drawn by the Dutch mathematics teacher Albert E. Bosman in 1942, this intricate geometric structure is created by starting with a single base square, erecting a right-angled triangle upon its top edge, and then building two smaller squares on the remaining sides of the triangle. A defining characteristic of this fractal is its self-similar branching pattern, which resembles the organic structure of a natural tree or broccoli head. If the triangle used in the construction is a symmetric right-angled isosceles triangle, the resulting flat canopy perfectly stabilizes within a bounded rectangular space, whereas varying the internal angles creates an asymmetric, wind-swept aesthetic. The mathematics governing the Pythagorean tree is heavily studied in chaos theory and computer graphics to demonstrate how simple, repetitive geometric rules can generate highly complex, infinite boundaries and lifelike natural simulations. Follow @maths.1089 & @Math Visualizations for more 🔥!

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🏴󠁧󠁢󠁥󠁮󠁧󠁿 The Lévy C curve is a self-similar fractal formed by replacing each line segment with two shorter segments that join at a right angle. Through a simple iteration rule, it evolves into an infinitely detailed, complex structure resembling the letter "C". It is used in mathematics, computer graphics, and digital art. First studied by Cesàro and Faber, it was named after Paul Lévy, who described its geometric structure. Η καμπύλη Lévy C είναι ένα αυτο-όμοιο φράκταλ που σχηματίζεται αντικαθιστώντας κάθε ευθύγραμμο τμήμα με δύο μικρότερα τμήματα που ενώνονται σε ορθή γωνία. Μέσω ενός απλού κανόνα επανάληψης, εξελίσσεται σε μια απείρως λεπτομερή, σύνθετη δομή που μοιάζει με το γράμμα "C". Χρησιμοποιείται στα μαθηματικά, τα γραφικά υπολογιστών και την ψηφιακή τέχνη. Αρχικά μελετήθηκε από τους Cesàro και Faber και ονομάστηκε έτσι από τον Paul Lévy, ο οποίος περιέγραψε τη γεωμετρική της δομή. Lévy C eğrisi, her çizginin dik açıyla birleşen iki kısa parçayla değiştirilmesiyle oluşan özbenzer bir fraktaldır. Basit bir yineleme kuralıyla sonsuz detaylı, karmaşık ve "C" harfine benzeyen bir yapıya dönüşür. Matematik, bilgisayar grafikleri ve dijital sanatta kullanılır. ​İlk olarak Cesàro ve Faber tarafından incelenmiş, geometrik yapısını açıklayan Paul Lévy’nin adını almıştır.

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Have you ever listened to a function discretely? 🎶📈 We mapped discrete points on the graph to musical notes—and let the functions sing! 🎵 Which one is your favourite? 👀 Want to hear any other function discretely? Let us know in the comments, and we’ll make Part 2! 🚀 This is our first collaboration with @beyond the math, and we’re looking forward to many more collabs in the future 🚀 #MathAnimation #Mathematics #DiscreteFunctions #FunctionSound