@carlosmattessich3883
For those intrigued, the number is equal to approximately 6606.4
@diaz1511_.
Whenever you think you are useless, remember this guy.
@FamousMovieScenes09
Bro said "WON'T SOMEBODY THINK OF THE PAPER!?"
@jasondearham8243
Should have just covered the top half with... Anything.
@Vladimir_Lenins_Soviet
Comprehensive Mathematical Overview Mathematics consists of numerous expressions, techniques, operations, levels, and points, each serving different purposes in calculations and problem-solving. ⸻ 1. Mathematical Expressions Mathematical expressions are combinations of numbers, variables, and operations that represent values. They differ from equations as they do not contain an equal sign. Types of Expressions: • Algebraic expressions: 3x + 5, a^2 - b^2 • Polynomial expressions: x^3 + 2x^2 - 5x + 7 • Rational expressions: (x^2 + 3x) / (x - 2) • Trigonometric expressions: sin(x) + cos(x) • Exponential & logarithmic expressions: e^x, log_2(x) ⸻ 2. Mathematical Techniques Techniques are systematic methods used to solve mathematical problems across various fields. Common Techniques: • Factoring (e.g., factoring quadratics) • Completing the square • Synthetic division • Substitution method (for solving equations) • Elimination method (for solving systems of equations) • Derivative and integral rules (in calculus) • Matrix operations (row reduction, determinants, inverses) • Fourier transforms (used in signal processing) • Laplace transforms (used in solving differential equations) ⸻ 3. Mathematical Operations Mathematical operations are fundamental actions performed on numbers, variables, and functions. Basic Operations: • Addition (+) • Subtraction (-) • Multiplication (, ×, · )* • Division (÷, / ) Advanced Operations: • Exponentiation & roots: x^n, √x • Logarithmic operations: log_b(a), ln(x) • Modular arithmetic: a mod b • Vector operations: Dot product (a · b), cross product (a × b) • Set operations: Union (∪), intersection (∩), complement (A^c) • Differentiation & integration: d/dx, ∫ f(x) dx ⸻ 4. Mathematical Levels Mathematics is structured into different levels, increasing in complexity. Levels of Mathematics: • Elementary Mathematics: Basic arithmetic, fractions, percentages • Pre-algebra: Negative numbers, simple equations • Algebra: Equations, polynomials, functions • Geometry: Shapes, theorems, trigonometry • Pre-calculus: Exponential/logarithmic functions, sequences, limits • Calculus: Differentiation, integration, limits • Linear Algebra: Matrices, vectors, transformations • Differential Equations: Solving equations involving derivatives • Probability & Statistics: Distributions, regression, hypothesis testing • Abstract Mathematics: Number theory, topology, combinatorics ⸻ 5. Mathematical Points “Points” in mathematics refer to different concepts, depending on the field. Types of Mathematical Points: • Geometric points: Specific locations in coordinate space (e.g., (3,4) in 2D) • Inflection points: Where a function’s concavity changes • Critical points: Where the derivative is zero or undefined • Singular points: Discontinuities or undefined behavior in functions • Fixed points: Solutions where f(x) = x, relevant in iterative methods ⸻ History of Mathematics Ancient Mathematics (Pre-3000 BCE – 500 CE) 1. Prehistoric mathematics (~20,000 BCE): Early counting marks found on bones (e.g., Ishango bone). 2. Egyptian & Babylonian mathematics (~3000 BCE – 500 BCE): • Base-60 system (Babylonians), early geometry, multiplication tables. • Rhind Mathematical Papyrus (~1650 BCE): Egyptian arithmetic and algebra. 3. Pythagorean theorem (~600 BCE): Pythagoras formalizes relationships between triangle sides. 4. Euclid’s Elements (~300 BCE): First systematic treatise on geometry. 5. Archimedes (~250 BCE): Contributions to calculus, geometry, and physics. 6. Chinese mathematics (~200 BCE): Nine Chapters on the Mathematical Art introduces matrix methods. 7. Indian numeral system (~200 BCE – 500 CE): Foundations of Hindu-Arabic numerals, zero, and place-value system. ⸻ The Hardest Equation in College-Level Mathematics One of the hardest equations that incorporates major mathematical techniques, operators, symbols, and operations is the Navier-Stokes Equation, a Millennium Prize Problem that remains unsolved in the general 3D case. Navier-Stokes Equation (General Form): ρ [∂u/∂t] + (u · ∇) u = -∇p + μ ∇²u + f where: • u = velocity vector field • p = pressure • ρ = density • μ = dynamic viscosity • ∇ = gradient operator • ∇² = Laplacian operator • f = external forces ⸻ Why is the Navier-Stokes Equation So Difficult? 1. Involves all major mathematical techniques: • Calculus: Partial derivatives (∂/∂t), integrals • Linear algebra: Matrices, vector fields • Topology & set theory: Fluid behavior in different spaces • Fourier analysis: Used in solving fluid flow equations • Chaos theory & dynamical systems: Predicting fluid stability 2. Uses multiple mathematical symbols & operations: • Operators: Gradient (∇), Laplacian (∇²), Partial derivative (∂/∂t) • Algebraic structures: Vector fields, nonlinear terms • Points & sets: Defined in coordinate spaces 3. Still unsolved in the 3D general case: • A $1,000,000 prize from the Clay Mathematics Institute is offered for proving smoothness & existence for all solutions. ⸻ Other Famous Unsolved Mathematical Problems 1. Riemann Hypothesis: Concerns the distribution of prime numbers. 2. P vs NP Problem: Asks if problems that can be verified quickly can also be solved quickly. 3. Birch and Swinnerton-Dyer Conjecture: Deals with rational solutions to elliptic curves. 4. Hodge Conjecture: Relates to algebraic geometry and topology. ⸻ Another explanation: 1. Arithmetic (Basic Math) Covers fundamental operations: • Addition (+), Subtraction (−), Multiplication (×), Division (÷). • Exponents (², ³, etc.) and Roots (√). 2. Algebra Uses variables (x, y) to form equations: • Linear Equations (y = mx + b), Quadratic Equations (ax² + bx + c = 0). • Factoring, Functions, and Expressions. 3. Geometry Studies shapes, sizes, and angles: • Triangles, Circles (π, radius, diameter), Polygons, 3D Shapes (Cubes, Spheres). • Pythagorean Theorem (a² + b² = c²). 4. Trigonometry Deals with angles and triangles: • Sine (sin), Cosine (cos), Tangent (tan). • Unit Circle, Trigonometric Identities. 5. Calculus Studies change and motion: • Derivatives (rates of change). • Integrals (area under curves). • Limits and Infinite Series. 6. Probability & Statistics Analyzes data and uncertainty: • Mean, Median, Mode (Data Analysis). • Probability (Likelihood of Events). • Standard Deviation (Data Spread). 7. Discrete Mathematics Focuses on separate values: • Logic (AND, OR, NOT), Sets, Graphs, Counting Methods. 8. Linear Algebra Deals with Vectors, Matrices, and Transformations (used in physics, AI, and 3D graphics). 9. Number Theory Studies integers, prime numbers, divisibility, GCD, and LCM. 10. Complex Numbers Includes Imaginary Numbers (i = √-1) and Operations with Complex Numbers (a + bi). Common Math Symbols • + (Plus), − (Minus), × (Multiply), ÷ (Divide), √ (Square Root), π (Pi), ∑ (Summation), ∫ (Integral). • > (Greater Than), < (Less Than), ≠ (Not Equal), ≥ (Greater or Equal), ≤ (Less or Equal).
@noureddinealjazairi6063
This isnt an equation, not even something to solve its just a number
@cashisking7410
Remember guys if your ever feeling hopeless just remember this guy exists.
@runabegum3192
“What’s your name?” Him:mr yappington💀
@GenX_Yaya
Guess you've never seen watercolor paper before.
@michaelc7014
It's almost like he knew what was gonna happen and was reading his fake reaction script
@DisventureCampGacha
"Thats awsome!" He sounds like Zee from Total Drama Reboot🔥🔥
@Crazy_huhh
This dude is a pro yapper 💀
@manikandans8119
❤Red colour is I Love You 👍
@raixhatv6666
Equation? That's just a number.
@Kingepticon
That's some Star Wars Prequel Trilogy level acting. I'm talking Mannequin Skywalker, "danger..... danger....my shitty acting is ruining Saga."
@georgeyousif3079
Bro got a 99.5 percent in yappanology
@liamfebery6636
This dude is fully regarded
@ItsKatakuriBoi
Bro accidentally drank a yappochino
@ccsasha
Love it😊
@Illytbh