#223. МИФЫ И ЛЕГЕНДЫ школьной математики

10 Most Interesting Misconceptions in and About Mathematics, or School Facts from the Perspective of Mathematical Analysis, Non-Euclidean Geometry, Algebra, and Projective Geometry! UPDATE: I spotted a typo with quaternions—a good reason to make a separate episode about them. My courses: https://vk.com/market-135395111 VK: https://vk.com/wildmathing Problem Book: https://vk.com/topic-135395111_35874038 Donate: http://www.donationalerts.ru/r/wildma... 0:00 — Lobachevsky Geometry 0:30 — Parallel Lines 0:58 — On the Roots of a Quadratic Equation 1:43 — On the Sum of the Angles of a Triangle 2:27 — Is Abstract Applicability? 3:15 — Asymptote of the graph of a function 3:58 — On the formula for the square of a sum 4:53 — Definition of a circle 6:24 — There are fewer natural numbers than integers 7:30 — Misconceptions about mathematics 1. In Lobachevsky geometry, parallel lines intersect. 2. Parallel lines do not intersect in any geometry. 3. The equation x² + 2x + 2 = 0 has no roots. 4. The sum of the angles of a triangle is always equal to 180°. 5. Lobachevsky geometry, complex numbers, and multidimensional spaces are all inventions of mathematicians that have no relation to reality. 6. An asymptote never intersects the graph of a function. 7. (a + b)² ≠ a² + b². 8. Definition of a circle 9. There are fewer natural numbers than integers. 10. The Biggest Misconceptions About Mathematics Regarding 4:45. The field F₂ has only two elements: 0 and 1. By definition, for any elements a and b, the sum a + b must belong to the field, just like the product a × b. This explains the addition and multiplication tables (included in the video)—look at them carefully and think about them. Can 1 + 1 = 2 in such a field? No, there's no element 2 here at all. Can 1 + 1 = 1? No, otherwise 0 = 1. Therefore, 1 + 1 = 0, and that's it. If the topic is completely new, it's worth first looking up the definition of a field (in the mathematical sense, of course). MORE INTERESTING VIDEOS ABOUT MATHEMATICS 1. Why do we need mathematics:    • #200. ЗАЧЕМ НУЖНА МАТЕМАТИКА?   2. The most beautiful formula:    • #161. САМАЯ КРАСИВАЯ ФОРМУЛА В МАТЕМАТИКЕ ...   3. The Millennium Problem:    • #170. ГИПОТЕЗА РИМАНА — ПРОБЛЕМА ТЫСЯЧЕЛЕТИЯ!   4. How to extract long roots:    • #140. КАК ИЗВЛЕКАТЬ КОРНИ В СТОЛБИК? В ШКО...   5. The slide rule:    • #107. КАК ПОЛЬЗОВАТЬСЯ ЛОГАРИФМИЧЕСКОЙ ЛИН...   6. Understanding numbers (feat. A. Savvateev):    • #182. Постижение числа π (feat. Алексей Са...   #science #mathematics #sciencepop