Красота золотого сечения

Previous (main) episode about the golden ratio:    • Вас обманывают насчет ЗОЛОТОГО СЕЧЕНИЯ!   I RECOMMEND THIS CHANNEL AND VIDEOS: Bayesyatina:    / @bayesyatina   — critical and rational thinking All types of statistical distortions:    • Совпадение? Не думаю! Апофения и родственн...   Opinion formation and rationalization:    • Я ВСЕГДА ПРАВ (рационализация, мотивирован...   Fact checking:    • Какой тип доказательств самый сильный? Исс...   Regression to the mean:    • Регресс к среднему: главная ошибка в стати...   Support the channel and get bonuses: https://boosty.to/wildmathing (or by clicking the "Sponsor" button under the video) How I create mathematical animations:    • Как создавать математические анимации?   About the music in the video: https://boosty.to/wildmathing/posts/1... A channel about culture that I recommend:    / @crosscult   (here the authors will publish a video about the golden ratio in art) Olympiad mathematics: https://vk.com/wall-135395111_24068 Unified State Exam: https://vk.com/wall-135395111_24068 For teachers: https://vk.com/wildmathing?w=product-... VK: https://vk.com/wildmathing Problem book: https://vk.com/topic-135395111_35874038 CONTENTS 0:00 — What have we already discussed? 1:20 — Infinite continued fraction 2:05 — Analogue of a physical chain 2:29 — Nested radicals and spiral 2:58 — Cosine of 36 degrees 3:48 — Regular pentagon 4:20 — Chemical compounds 4:35 — How the Manim library is tested 4:58 — Kata Academy 6:24 — Credit card format 2.0 7:05 — Chicken eggs 7:49 — Venus de Milo 8:39 — Statistical errors 9:29 — Intuition and the number of combinations 10:52 — How to construct the golden ratio? 11:55 — Flag of the Republic of Togo 12:06 — Fractional part of numbers Ф, Ф^2 and Ф^(-1) 12:23 — Kepler's triangle 12:39 — Binet's formula and Lucas numbers 13:08 — Powers of Phi 13:40 — Comparison of spirals 14:07 — Summing up 14:57 — Is the divine proportion? 15:27 — What about mathematics? 16:10 — Comic theory 16:58 — Acknowledgments LITERATURE George Markowsky. Misonceptions about the Golden Ratio: https://www.goldennumber.net/wp-conte... V. P. Zubov. Alberti's Architectural Theory A. V. Radzyukevich. On the Scientific Study of Proportions in Architecture and Art: https://cyberleninka.ru/article/n/k-v... Samuel Arbesman. Math as Myth: https://nautil.us/math-as-myth-234301/ Livio, M. The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number A. Savin. Phidias' Number - the Golden Section: https://kvant.ras.ru/pdf/1997/06/kv06... A. D. Bendukidze. Golden Section: https://kvant.ras.ru/1973/08/zolotoe_... A. I. Prokhorov. Golden Spiral: https://kvant.ras.ru/1984/09/zolotaya... Golden Section. Wiki article in German: https://de.wikipedia.org/wiki/Goldene... MORE COOL VIDEOS ABOUT MATHEMATICS 1. Why do we need mathematics:    • #200. ЗАЧЕМ НУЖНА МАТЕМАТИКА?   2. Revolutionary in mathematics:    • ГАЛУА. Революционер в математике!   3. Hilbert's problems:    • ГИЛЬБЕРТ. Величайшие проблемы XX века   4. Theorems of the 20th century:    • Теоремы XX века!   5. The most beautiful fractals:    • 10 фракталов, которые стоит увидеть!   USED IMAGES https://commons.wikimedia.org/wiki/Fi... https://commons.wikimedia.org/wiki/Fi...