- Видео 543
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Thinking In Math
США
Добавлен 11 мар 2017
Angela Shao and Weidong Shao
We tackle specific problems / topics in math, usually that of high school level or beyond. Our videos can be watched to prepare for competitions such as AIME, AMC, USAMO, or simply for fun!
We tackle specific problems / topics in math, usually that of high school level or beyond. Our videos can be watched to prepare for competitions such as AIME, AMC, USAMO, or simply for fun!
Complex Numbers and Geometry: Solving a 2019 AIME I Problem
Explore the fascinating intersection of complex numbers and geometry with this 2019 AIME I problem! We analyze the function f(z) = z^2 - 19z and uncover how z , f(z) , and f(f(z)) form a right triangle in the complex plane. Using geometric insights into complex number multiplication and addition, we solve for m and n in the complex number z = m + \sqrt{n} + 11i . A must-watch for competitive math enthusiasts and anyone looking to enhance their problem-solving skills!
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#AIME2019 #ComplexNumbers #Geometry #CompetitiveMath
👉 Subscribe to Thinking in Math for more competitive math insights and problem walkthroughs!
🔔 Don’t forget to like, comment, and share to help others discover this content!
#AIME2019 #ComplexNumbers #Geometry #CompetitiveMath
Просмотров: 25
Видео
Power of a Point is Everywhere! #5 AIME 2024
Просмотров 377 часов назад
Join us as we tackle a fascinating geometry problem from the 2024 AIME I! Two rectangles, a circle, and collinear points create a unique puzzle. Given specific dimensions of rectangles ABCD and EFGH, can we determine the length of CE? Watch this step-by-step walkthrough to explore advanced geometry techniques and deepen your problem-solving skills. Perfect for competitive math enthusiasts and a...
2024 AMC12A Full Solve Through - All 25 Problems Explained!
Просмотров 1192 месяца назад
Welcome to an in-depth, full solve-through of the 2024 AMC12A! This video covers all 25 problems from the exam, providing detailed explanations, key insights, and problem-solving techniques tailored for competitive math enthusiasts. Over the course of 80 minutes, we’ll explore a variety of challenging topics ranging from algebra, geometry, number theory, and combinatorics. This video is perfect...
The Secret Formula Linking In-radius and Altitudes! (AMC12B 2024 Insight)日
Просмотров 962 месяца назад
Discover a powerful geometric relationship that connects the in-circle radius (r) and the altitudes (h_a, h_b, h_c) of any triangle with this beautiful identity: \frac{1}{r} = \frac{1}{h_a} \frac{1}{h_b} \frac{1}{h_c}. In this video, we break down the proof step-by-step, showing its derivation through triangle areas and perimeter relations. We then demonstrate its practical application by solvi...
An Uncommon Trig Identity: Useful in Solving 2024 AMC12A Problem 23
Просмотров 2442 месяца назад
Discover the beauty of a unique trigonometric identity: \tan \theta \cot \theta = \frac{2}{\sin 2\theta}. In this video, we’ll derive this intriguing formula step-by-step and show how it becomes a powerful tool in tackling Problem 23 from the 2024 AMC12A competition. Ideal for math enthusiasts and students aiming to sharpen their competitive math skills!
Calculus Challenge: Solving Tough Integrals of sin^2(x)/x^2 and sin^3(x)/x^3
Просмотров 1112 месяца назад
In this video, we tackle two challenging integrals involving powers of sine: 1. Integral of sin^2(x) / x^2 from 0 to infinity 2. Integral of sin^3(x) / x^3 from 0 to infinity Starting from the known result that the integral of sin(x) / x from 0 to infinity equals pi/2, we use integration by parts and trigonometric identities to evaluate these integrals step-by-step. This tutorial provides insig...
Geometry Theorems for Competitive Math: Exploring Ceva’s Theorem and Triangle Centers
Просмотров 1382 месяца назад
In this video, we introduce Ceva’s Theorem, a powerful tool in geometry for understanding the concurrency of lines in a triangle. We provide two proofs of Ceva’s Theorem-one using triangle areas and another with Menelaus’ Theorem-giving a comprehensive view of how it works. We then apply Ceva’s Theorem to prove three essential geometric facts: the medians, altitudes, and angle bisectors of a tr...
Geometry for Competitive Math: Solving Shaded Area with Menelaus’ Theorem
Просмотров 1323 месяца назад
In this video, we dive into a complex geometry problem involving triangle areas and line segment ratios. We’ll use Menelaus’ Theorem and the area formula for triangles to find the shaded area in this diagram. The challenge lies in identifying the correct triangle and line segment to apply Menelaus’ Theorem effectively. Watch as we explore the solution step-by-step, revealing the thought process...
A Surprisingly Easy Problem: Powers of (1 + \\sqrt{5})
Просмотров 1283 месяца назад
Sometimes, what seems like a complex problem can turn out to be surprisingly simple! In this video, we explore a problem involving powers of (1 \sqrt{5}) raised to the 2023, 2024, and 2025th powers. With just one key insight, you’ll see how this daunting expression can be simplified with ease. Perfect for anyone interested in math competitions or elegant algebraic solutions. Don’t forget to sub...
China Math Olympiad 2024 Problem 1: Solving Logarithms with Change of Base - Thinking in Math
Просмотров 5543 месяца назад
e are tasked with finding \log_3(\log_2 m) . Using the change of base formula and its variants, we break down the solution step by step to arrive at the final answer, \log_3(\log_2 m) = 4049 . If you’re interested in mastering logarithmic identities and exploring advanced math problems, this is the perfect challenge for you! Subscribe to ‘Thinking in Math’ for more competitive math problems and...
Advanced Trigonometry Problem Solved: CMO 2024 - Finding cos C Using Trig Identities!
Просмотров 1943 месяца назад
Join me as we solve a fascinating trigonometry problem from the China Math Olympiad 2024. In this problem, we are given the equation \cos C = \frac{\sin A \cos A}{2} = \frac{\sin B \cos B}{2} and tasked with finding \cos C . The key trick involves recognizing that \sin A \cos A = \sqrt{2} \sin(A \frac{\pi}{4}) . I’ll guide you through the algebraic manipulations and trigonometric identities nee...
Solving a Tricky Geometry Problem: Find sin(∠BOX), from BMT 2023
Просмотров 843 месяца назад
Solving a Tricky Geometry Problem: Find sin(∠BOX), from BMT 2023
Pure Geometry Proof: Proving Triangle PAB is Equilateral in a Square
Просмотров 1913 месяца назад
Pure Geometry Proof: Proving Triangle PAB is Equilateral in a Square
Prove Triangle PAB is Equilateral in a Square | Analytical Geometry Solution
Просмотров 753 месяца назад
Prove Triangle PAB is Equilateral in a Square | Analytical Geometry Solution
Maximizing Sums with Cauchy-Schwarz: A Competitive Math Challenge
Просмотров 2245 месяцев назад
Maximizing Sums with Cauchy-Schwarz: A Competitive Math Challenge
2024 GaoKao Math | Strictly Increasing Functions Explained | Problem 6 Breakdown
Просмотров 1,5 тыс.7 месяцев назад
2024 GaoKao Math | Strictly Increasing Functions Explained | Problem 6 Breakdown
2024 GaoKao Math | Multiple Choice Questions 1-5 Explained | China’s College Entrance Exam
Просмотров 5 тыс.7 месяцев назад
2024 GaoKao Math | Multiple Choice Questions 1-5 Explained | China’s College Entrance Exam
Product of Segment Lengths in an 8-Sided Polygon Inscribed in a Unit Circle
Просмотров 2227 месяцев назад
Product of Segment Lengths in an 8-Sided Polygon Inscribed in a Unit Circle
Solve Using Complex Numbers?!!!! Solving Sin(π/14)Sin(3π/14)Sin(5π/14) with Roots of Unity
Просмотров 2838 месяцев назад
Solve Using Complex Numbers?!!!! Solving Sin(π/14)Sin(3π/14)Sin(5π/14) with Roots of Unity
Mastering Complex Numbers: Solving Sin(π/14)Sin(3π/14)Sin(5π/14) Using Euler's Formula
Просмотров 2,1 тыс.8 месяцев назад
Mastering Complex Numbers: Solving Sin(π/14)Sin(3π/14)Sin(5π/14) Using Euler's Formula
Cracking the 2024 AIME II: Master the Art of Logarithmic Equations!
Просмотров 30211 месяцев назад
Cracking the 2024 AIME II: Master the Art of Logarithmic Equations!
2007 AIME Problem 7: A Unique Logarithmic Puzzle Solved
Просмотров 279Год назад
2007 AIME Problem 7: A Unique Logarithmic Puzzle Solved
Maximizing Sums: 2023 Number Challenge Inspired by 1987 China CMO
Просмотров 354Год назад
Maximizing Sums: 2023 Number Challenge Inspired by 1987 China CMO
1987 China CMO Challenge: Complex Numbers & Geometric Insights
Просмотров 333Год назад
1987 China CMO Challenge: Complex Numbers & Geometric Insights
Master AMC12B Problem 25 with Pentagon Secrets: A Must-Know for AMC & AIME Aspirants
Просмотров 311Год назад
Master AMC12B Problem 25 with Pentagon Secrets: A Must-Know for AMC & AIME Aspirants
Problem 22 of AMC12A 2023 Without the Möbius Function - A Step-by-Step Guide
Просмотров 758Год назад
Problem 22 of AMC12A 2023 Without the Möbius Function - A Step-by-Step Guide
Master the AMC12A with a Smart Trick: Quick Summation of Cubes
Просмотров 249Год назад
Master the AMC12A with a Smart Trick: Quick Summation of Cubes
Unlocking Complex Numbers with Geometry: 2023 AMC12A Problem Solved!
Просмотров 487Год назад
Unlocking Complex Numbers with Geometry: 2023 AMC12A Problem Solved!
2023 AMC12A The Hidden AM/GM Inequality (Problem 23)
Просмотров 665Год назад
2023 AMC12A The Hidden AM/GM Inequality (Problem 23)