✓ Про золотое сечение и числа Фибоначчи | Ботай со мной #137 | Борис Трушин

Today we'll talk about the golden ratio, Fibonacci numbers, and how they're related. How to support the channel: Bitcoin: bc1qwzx9t9mz5h5q8sgtz74mdgedxd5wu0g9kq6q5m Ethereum: 0xAE872DcA8B135cf62Df4B36bE576a2EE64c6066a Regular donations (Boosty): https://boosty.to/trushinbv Regular donations (YouTube): https://www.youtube.com/trushinbv/join Regular donations (Patreon):   / trushinbv   Regular donations (Sponsr): https://sponsr.ru/trushinbv One-time donations (Yu-money, formerly Yandex.Money): https://yoomoney.ru/to/410011017613074 One-time donations (PayPal): https://paypal.me/boristrushin One-time donation (Donation Alerts): https://www.donationalerts.com/r/bori... One-time donation (Sberbank): 2202 2001 0398 5451 This school year, I'm teaching three courses: ✔ "Preparation for the Unified State Exam in Advanced Mathematics from 0 to 70 points (Grades 10-11)": http://trushinbv.ru/ege70 This course is suitable for both tenth-graders who want to consistently score 70+ points a year before the Unified State Exam, and for eleventh-graders who know next to nothing but want to achieve decent scores within a year. This course will cover the entire test section, as well as many problems from the difficult part of the Unified State Exam. ✔ "Preparation for the Unified State Exam in Advanced Mathematics from 60 to 100 points (11th grade)": http://trushinbv.ru/ege100 For those who already have a basic understanding of mathematics and want to master it to a score of 90+ in a year. We'll primarily focus on solving problems from the difficult part of the Unified State Exam, but we'll also delve into some of the more meaningful problems from the test section. (If an eleventh-grader is sufficiently motivated, they can take both of these courses simultaneously – http://trushinbv.ru/egepack – their programs are coordinated.) ✔ "Preparation for Listed Mathematics Olympiads (Grades 10-11)": http://trushinbv.ru/olymp This course is primarily for eleventh-graders who have mastered the standard school curriculum with at least a B and want to prepare for Olympiads like Phystech, Lomonosov, OMMO, and PVG in six months, with a chance to earn a diploma in at least one of them. Also, my recorded courses from last year are available: ✔ "Preparation for the Basic State Exam": http://trushinbv.ru/oge9 This is a recording of a larger year-long course I taught a couple of years ago. I will not be offering any new courses for ninth-graders this year. ✔ Mini-courses on individual Unified State Exam tasks: Probability Theory from Beginning to the Unified State Exam (Tasks 3 and 4): http://trushinbv.ru/egeTV Equations and Inequalities (Tasks 12 and 14): http://trushinbv.ru/egeAL Stereometry (Task 13): http://trushinbv.ru/egeST Economic Problems (Task 15): http://trushinbv.ru/egeEC Planimetry (Task 16): http://trushinbv.ru/egePL Problems with Parameters (Task 17): http://trushinbv.ru/egePR Number Theory (Task 18): http://trushinbv.ru/egeTC ✔ Mini-courses on listed Olympiads: Phystech Olympiad: http://trushinbv.ru/fizteh OMMO Olympiad: http://trushinbv.ru/ommo Lomonosov and PVG Olympiad: http://trushinbv.ru/lomonosov Other Foxford courses: http://trushinbv.ru/courses Foxford tutors: http://trushinbv.ru/coach Merchant store: http://trushinbv.ru/shop Book by Trushin: http://trushinbv.ru/book VKontakte: https://vk.com/ege_trushin TikTok:   / trushinbv   Twitter:   / trushinbv   Instagram:   / trushinbv   Telegram: https://t.me/trushinbv Facebook:   / trushinbv   YouTube:    / trushinbv   Personal website: http://TrushinBV.ru