06:09
The Trapezoid and Parabola Challenge (Analytic Geometry)
The Trapezoid and Parabola Challenge What begins as an innocent geometric shape quickly spirals into an …
Videos
Explore all lectures and proofs categorized under Videos.
Showing 26 lectures
06:09
11:58Learn 30-Second Magic Box Trick (And Be a Genius)
Pick ANY number. In under 30 seconds, this grid will add up to it in every direction—rows, columns, diagonals, …
06:48The $100 Billion Guessing Game Behind Bitcoin
Forget the myth of glowing basement supercomputers cracking impossibly complex Nobel Prize equations to mint …
10:20Can You Inscribe This Quadrilateral? (Analytic Geometry)
At first glance, it looks like a standard analytic geometry problem: trace the locus of a moving point, …
06:51Can You Find the Tangency Point of Circles? (Analytic Geometry)
Most exam questions push you to find an answer. The nastiest ones test whether you dare to prove it’s …
07:34The Hidden Locus in This Moving Triangle (Analytic Geometry)
What happens when an ellipse, a parabola, a tangent line, and a shifting geometric locus collide in a single …
05:31Can You Find the Equation of This Moving Line? (Analytic Geometry)
4 missions. 1 sliding ladder. Pure analytic geometry magic! 📐 Can a sliding segment really create both a …
11:11Can You Find Parameter 'a' from This Trajectory?
Two points. One unknown parameter. A 5-step geometric chain reaction. What starts as a simple ratio problem …
09:47Can This Triangle Area Ever Reach 3?
An incomplete circle, a moving chord, and a triangle whose perimeter never changes—even as its top vertex …
13:32The hidden ellipse in the circle (Analytic Geometry)
At first glance, it looks like a standard high school circle problem: a moving center, a horizontal …
06:29How to Solve Parabola Tangents (Analytic Geometry)
What happens when classic analytic geometry meets calculus shortcuts? In this challenge, we take on a …
06:02How to Find a Tangent Line to a Circle (Analytic Geometry)
What looks like an intimidating multi-part exam problem is actually an elegant geometric puzzle waiting to be …
15:58Degrees vs Radians vs Gradians: Which is better and why?
Think degrees are a fundamental law of physics? Think again. The 360° circle isn’t woven into the fabric …
04:05Stop trying to calculate Pi squared
What happens when you multiply an infinite, non-repeating decimal by itself? With numbers like the square root …
3 Videos
19:11
Pythagorean Triples Trilogy: Mental Math, The Unit Circle & Euler's Totient
The Story: The 2,500-Year Quest for Integer Right Triangles The Pythagorean Theorem, $a^2 + b^2 = c^2$, is …
15:02Can you solve it fast?
Picture this: you’re sitting in a dead-silent examination hall when a proctor scrawls a monstrous quartic …
19:00the math behind the green wave
You’re sitting at an intersection at 2:00 in the morning, foot pressed against the brake pedal, staring up at …
10:00Stop trusting your gut with probability (The Lottery and Birthday Paradoxes)
The Lottery and Birthday Paradoxes Your intuition about how numbers work is lying to you, and two legendary …
02:48Stop freezing at equations like this
At first glance, the equation $9^x + (-3)^x = 702$ looks like an impossible exam trap designed to make you …
4 Videos
33:08The Secret Machinery of Divisibility Rules: From Parity to Prime Patterns
The Story: The Secret Machinery Behind Mental Math Shortcuts In grade school, we were all taught rapid …
2 Videos
14:59How Calculators ACTUALLY Compute Trig Functions: The CORDIC Algorithm
The Story: The Pervasive Myth of the Pocket Calculator When you punch $\sin(37^\circ)$ into a pocket …
05:49Square Root of 3 is irrational (Proven by 2 methods)
Every number in existence belongs to one of two opposing camps: the dependable, well-behaved rational numbers …
08:40I Flipped the Quadratic Formula Upside Down - Here is why
In high school math, the quadratic formula is drilled into our brains like a sacred nursery rhyme: $x = …
2 Videos
00:43Determinant of a 3x3 Matrix: From First Row Expansion to Sarrus' Rule
The Story: Two Perspectives on the $3 \times 3$ Determinant The determinant of a $3 \times 3$ matrix measures …
00:48The limit of sequence
Mathematical Principles & Proof Outline Let $f(x)$ be defined over the field \mathbb{R}. We analyze the …
2 Videos
00:49Gram-Schmidt Process in Plane and Space: Visual Orthonormalization
The Story: Building an Orthonormal World from Arbitrary Directions The Gram-Schmidt Process is an algorithm …