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Thinking In Math
United States
Registrace 11. 03. 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!
Maximizing Sums with Cauchy-Schwarz: A Competitive Math Challenge
In this video, we dive into an intriguing problem involving an arithmetic sequence and the powerful Cauchy-Schwarz inequality. Learn how to approach this competitive math challenge step by step and discover the maximum value of the sum of the first 10 terms, S_10, in an arithmetic sequence. Perfect for high school students aiming to sharpen their skills in problem-solving and inequality applications. Don't miss out on this essential trick for competitive exams!
#CompetitiveMath #CauchySchwarzInequality #ArithmeticSequence #MathChallenge #HighSchoolMath #MathOlympiad #AMCPrep #AIMEPrep #MathTricks #ProblemSolving #ThinkingInMath
#CompetitiveMath #CauchySchwarzInequality #ArithmeticSequence #MathChallenge #HighSchoolMath #MathOlympiad #AMCPrep #AIMEPrep #MathTricks #ProblemSolving #ThinkingInMath
zhlédnutí: 125
Video
2024 GaoKao Math | Strictly Increasing Functions Explained | Problem 6 Breakdown
zhlédnutí 774Před 2 měsíci
In this video, we delve into Problem 6 from the 2024 GaoKao Math exam, focusing on the intriguing properties of strictly increasing functions. Understanding how to determine the range of a parameter for which a piecewise function remains strictly increasing is crucial for mastering this problem. Key Insights: - The fundamental properties of quadratic functions and their influence on the behavio...
2024 GaoKao Math | Multiple Choice Questions 1-5 Explained | China’s College Entrance Exam
zhlédnutí 2KPřed 3 měsíci
In this video, we dive into the first five multiple-choice questions from the 2024 GaoKao Math exam, China's rigorous college entrance test. Whether you're a student preparing for the exam or just interested in challenging math problems, this video will provide detailed solutions and explanations. Content Overview: Set Theory and Intersections - Learn how to find the intersection of sets with c...
Product of Segment Lengths in an 8-Sided Polygon Inscribed in a Unit Circle
zhlédnutí 183Před 3 měsíci
In this video from 'Thinking in Math,' we explore the geometric properties of an 8-sided regular polygon inscribed in a unit circle. We prove that the product of the lengths of all segments connecting one vertex to all others equals 8. Using symmetry and the half-angle formula, we uncover this fascinating result. We also introduce a challenging question for polygons with 𝑛 = 9,11,… and hint at ...
Solve Using Complex Numbers?!!!! Solving Sin(π/14)Sin(3π/14)Sin(5π/14) with Roots of Unity
zhlédnutí 208Před 3 měsíci
In this episode of the "Mastering Complex Numbers" series, we tackle the problem of finding the value of sin(π/14)sin(3π/14)sin(5π/14) using the product-to-sum trigonometric formula and the intriguing properties of the 7th roots of unity. High school students preparing for AMC10/12 or AIME exams will learn how to apply these advanced concepts to solve challenging problems. Discover how the sum ...
Mastering Complex Numbers: Solving Sin(π/14)Sin(3π/14)Sin(5π/14) Using Euler's Formula
zhlédnutí 2,1KPřed 3 měsíci
In this video, part of our "Mastering Complex Numbers" series, we dive into solving the trigonometric product sin(π/14)sin(3π/14)sin(5π/14) using the power of complex numbers and Euler's formula. Perfect for high school students preparing for AMC10/12 or AIME exams, we'll break down the steps to find the value of this expression. By understanding that sin(θ) can be expressed as (e^(iθ) - e^(-iθ...
Cracking the 2024 AIME II: Master the Art of Logarithmic Equations!
zhlédnutí 270Před 6 měsíci
Dive deep into the world of logarithms with us on "Thinking in Math" as we tackle an intriguing problem from the 2024 AIME II exam. In this video, join our brilliant young mathematician as she guides you through a fascinating journey to solve a system of logarithmic equations involving positive real numbers x, y, z. Whether you're a math enthusiast keen on enhancing your problem-solving skills ...
2007 AIME Problem 7: A Unique Logarithmic Puzzle Solved
zhlédnutí 257Před 7 měsíci
🌟 Join us on an exciting mathematical journey as we delve into the 2007 AIME (American Invitational Mathematics Examination) Problem 7. This video offers a detailed walkthrough of a challenging logarithmic puzzle that will intrigue and educate math enthusiasts of all levels. 🔍 The problem in focus is: \[ N = \sum_{k = 1}^{1000} k ( \lceil \log_{\sqrt{2}} k \rceil - \lfloor \log_{\sqrt{2}} k \rf...
Maximizing Sums: 2023 Number Challenge Inspired by 1987 China CMO
zhlédnutí 283Před 8 měsíci
Welcome back to our 2023 Number Challenges series! In this episode, we dive into a fascinating problem inspired by the 1987 China Mathematical Olympiad, perfectly suited for the year 2023. Our challenge: how to maximize the sum 3m 4n, where 'm' and 'n' represent distinct even and odd numbers respectively, adding up to the special number 2023. This video takes you through an intriguing mathemati...
1987 China CMO Challenge: Complex Numbers & Geometric Insights
zhlédnutí 283Před 8 měsíci
Dive into the fascinating world of complex numbers and geometry with our latest video! We tackle a challenging problem from the 1987 China Mathematical Olympiad, where we explore the intriguing equation z^{n 1} - z^n - 1=0 and its deep connections to geometric interpretations of complex numbers. Discover how the condition |z| = 1 opens the door to an elegant solution, leading us to the beautifu...
Master AMC12B Problem 25 with Pentagon Secrets: A Must-Know for AMC & AIME Aspirants
zhlédnutí 275Před 9 měsíci
Unlock the mystery of AMC12B 2023 Problem 25 with the fascinating world of regular pentagons! In this in-depth video, we explore the essential properties of regular pentagons and their surprising link to solving one of the most challenging problems in the AMC12B 2023. This is a crucial watch for anyone preparing for the AMC or AIME. Building on our previous CZcams Shorts about the intriguing si...
Problem 22 of AMC12A 2023 Without the Möbius Function - A Step-by-Step Guide
zhlédnutí 556Před 9 měsíci
Struggling with AMC12A 2023's Problem 22? Think you need advanced knowledge like the Möbius function to solve it? Think again! Join us as we dive into an explorative and intuitive approach to tackle this challenging math problem. Perfect for students and enthusiasts who want to enhance their problem-solving skills without delving into complex mathematical theories. This video offers a step-by-s...
Master the AMC12A with a Smart Trick: Quick Summation of Cubes
zhlédnutí 222Před 10 měsíci
🌟 Get ready to unlock the secrets of efficient summation with our new video, showcasing a smart 'compensation trick' to solve an intriguing problem from the 2023 AMC12A! 🧠💡 In this educational journey, we dive into a fascinating problem: quickly evaluating the sum \( 2^3 - 1^3 4^3 - 3^3 \ldots 18^3 - 17^3 \). This may seem daunting at first, but with our unique 'compensation trick', you'll see ...
Unlocking Complex Numbers with Geometry: 2023 AMC12A Problem Solved!
zhlédnutí 434Před 10 měsíci
🌟 Dive into the fascinating world of complex numbers with our latest video, where we tackle a challenging problem from the 2023 AMC12A exam using a unique geometric interpretation. 📐✨ In this video, we explore the intriguing problem of finding the maximum imaginary part of a complex number z under the condition |1 z z^2| = 4. Rather than relying on traditional algebraic methods, we delve into a...
2023 AMC12A The Hidden AM/GM Inequality (Problem 23)
zhlédnutí 524Před 10 měsíci
🌟 Embark on a mathematical adventure with our latest video, where we tackle the challenging Problem 23 from the 2023 AMC12A using the powerful AM/GM Inequality! 🧩📈 In this video, we delve into a complex equation: \((1 2a)(2 2b)(2a b) = 32ab\), which on the surface asks for the number of non-negative number pairs \((a, b)\). However, we unveil a more profound approach by employing the AM/GM Ineq...
Mastering Linear Congruence: Step-by-Step Solutions to Commonly Seen Equations
zhlédnutí 13KPřed 10 měsíci
Mastering Linear Congruence: Step-by-Step Solutions to Commonly Seen Equations
Finding the Minimum of tan A + tan B + tan C: A Trigonometric Exploration
zhlédnutí 203Před 10 měsíci
Finding the Minimum of tan A tan B tan C: A Trigonometric Exploration
Tangent Identity in Triangles: Quick Derivation
zhlédnutí 231Před 10 měsíci
Tangent Identity in Triangles: Quick Derivation
Unveiling Sine Identities in Triangles: Sum and Difference Explored
zhlédnutí 164Před 10 měsíci
Unveiling Sine Identities in Triangles: Sum and Difference Explored
Solving cos(π/7) + cos(3π/7) + cos(5π/7) Using Trigonometry
zhlédnutí 1,1KPřed 10 měsíci
Solving cos(π/7) cos(3π/7) cos(5π/7) Using Trigonometry
Unlocking the Coefficient Mystery: x square term in Polynomial Expansions
zhlédnutí 139Před 10 měsíci
Unlocking the Coefficient Mystery: x square term in Polynomial Expansions
CMO 2020 Challenge: Unraveling the Intricacies of Concyclic Points
zhlédnutí 159Před 10 měsíci
CMO 2020 Challenge: Unraveling the Intricacies of Concyclic Points
IMO-Inspired Number Theory Challenge: The Powers of 2023! #2023Challenge
zhlédnutí 222Před 10 měsíci
IMO-Inspired Number Theory Challenge: The Powers of 2023! #2023Challenge
Beyond Basics: An Advanced Twist on the Handshake Problem! 🔄🤝 with Graph Theory
zhlédnutí 403Před 10 měsíci
Beyond Basics: An Advanced Twist on the Handshake Problem! 🔄🤝 with Graph Theory
Unraveling Nested Radicals: A Deep Dive into Simplifying Complex Expressions | Math Explorers 🧭
zhlédnutí 229Před 10 měsíci
Unraveling Nested Radicals: A Deep Dive into Simplifying Complex Expressions | Math Explorers 🧭
Why Does Lasso Suppress the Coefficients? Linear Regression Essentials with Notebook Walkthrough
zhlédnutí 86Před 10 měsíci
Why Does Lasso Suppress the Coefficients? Linear Regression Essentials with Notebook Walkthrough
the Minimum Value of a Fraction Sum: the Method of Undetermined Coefficients & AM/GM Inequality
zhlédnutí 215Před 11 měsíci
the Minimum Value of a Fraction Sum: the Method of Undetermined Coefficients & AM/GM Inequality
Unlocking the Secrets of Concatenated Perfect Squares | A Mathematical Exploration
zhlédnutí 99Před 11 měsíci
Unlocking the Secrets of Concatenated Perfect Squares | A Mathematical Exploration
Unlocking the Minima: Dive into an Intriguing Optimization Problem Using Advanced Mathematics
zhlédnutí 410Před 11 měsíci
Unlocking the Minima: Dive into an Intriguing Optimization Problem Using Advanced Mathematics
Chaining Logarithms: An Elegant Solution to a Tricky Problem
zhlédnutí 319Před 11 měsíci
Chaining Logarithms: An Elegant Solution to a Tricky Problem
p and q could be both positive or both negative, so we may assume WLOG they are both positive.
very elegant!
No need to open convert all of them into perfect squares
WHAT WORD DID YOU SAY? “The answer is yes…if we know how to use (#*%}*#) here.”
For sure it's tough ......... but not toughest.....
seems that you just make it up by reverse engineering. as we never know how can you make up all those cosine formula for a, b , c ,d and let e and f work separately. better to study the real geometry and their roots relationship. Though it seems you have find solution by your approach but the initial thinking is not convincing. Is it really the original solution from Gauss, can you provide more information or the related resource for this approach
For the bijection f: (0,1) --> [0,1]... Could I just switch the domain and range? So f(1/2)=0 and f(1/4)=1 to account for the endpoints. Then f(x)=1/2^n (n=1,2,...) if x=1/2^(n+2) and f(x)=x otherwise.
THANK YOU!!!
clear explanation
Bhai Hindi me bhi bata diya karo
How did you find those x, y so quickly? Can you provide some reference? UPD: Got this. It's directly from an unequallity.
The actual solutions are (1,a,-a),(b,1,-b),(c,-c,1) where a,b and c are arbitrary integers and also (1,2,3)(2,4,4)(3,3,3)
Thank you
Plz solve IIT paper
LOW volume pls increase it or change the mic
What about n=0
How did you come up with the sequences for the a^2 + b^2 + c^2 one
Complex numbers solution will be a lot easier
Kaprekar's findings are incorrect There are numbers that do not produce the number 6174 I dare to be tested.
0
Hey what is the the answer for hhtt in a row i am getting 16 is it correct?
1/³a² b²-> ¾->¼->⅓¾->3/3/6/3/3/3->3->13
2 1/in¹-1/in <2
¹¹/16sin²x+cos²x½x² y² sinx³ +cos³x=½+׳->11/16
A¹ a² a³ a⁴ a⁵ a⁶ a=18=a² a³=18->¼
Mnu->-2 -1 0 1
/2×+5>×+1>-2 2 -× 2.5
3x-1ײ->⁶ax⁶ ax⁵ ax⁴ ax½ axⁿ->3-1-1->1-1-3->ax³-axⁿ->ax⁶->f(1)-f(1)
Ax⁶-ax³ ax⁴ ax² ax ¹->3-1-1 1-1-3->f(1)-f(1)
3m-2n
Sin -1 ½ 1pie/¹-
A²+b²/c² sinab²->4t-4i->2i/2/2->2ti
B=a²+b²=c²=Sina sin b/sin²c c²Sina/sinb=sinb->pie/4²-a/2->b->2pie/²
C<a<b>a=0.1e b =⅛+1c=1/9inx²-1=Infinity!/E- k->0!->x¹/ײ! X²/×¹+x³/ײ!->c<a<b
😮
This is wrong. What is your reasoning for ignoring the higher powers? If you put x=0.9 you will find that -ln(1-x) > xe^x so exactly how small does x have to be for your theory to work and why?
Nice Approach
Shldn’t it be 9<= x-y-z<12
US and NATO planes and drones fly from the Black Sea every day for 3 years. What exactly is your problem?
Can other countries student give this exam Pls make video on full detailedinformation about This exam
w
Where available papers pdf in English
i translated these on my own, not sure if full pdfs are out there online
Inequality name?
Jaka muda kolega to je znana Bellova enačba
I understand this was posted over a year ago, but I'm certain that your method 1 solution is incorrect. If t=0 and s=1, you would have x=5, y=160 and z=-208, which gives a large negative number, not 1. I think it came from a typo. What you're looking for is the following: x=-5+11t y=(3+7s)(16-35t) z=(-2-5s)(16-35t)
😂😂😂😂😂 this is 😤😤😤
For instance when a=-1, the vertex of the parabola will have a maximum point of x=1, can you explain how this doesn’t show in the graph at the end?
You better darn well be able to answer that if you're going to college. It's sad the way things are going here in Canada. I think my grandpa, who got pulled out of school in grade 3, was smarter than my nephew. My nephew finished high school.
Great explanation
You didnt show how you got the numbers?? Did you brute force it?