Tag: youtube
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The Basic Math Iceberg Explained
The Math Iceberg Explained, Part 1 Counting Addition Subtraction Multiplication Division Equations Basic Geometry Order of Operations Decimals Factors Fractions Powers and Radicals Data Plots Variables Cartesian Coordinates Functions Additional Context on Number Systems Counting Counting is a method of finding what number of something you have. The number zero indicates read more
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The Discovery of the Atom Explained (From Ancient Greece to Bohr)
The Ancient Idea of Atoms John Dalton and Chemical Ratios J. J. Thomson and the Electron Rutherford and the Gold Foil Experiment The Problem with Classical Physics Niels Bohr and Quantized Energy Levels Toward Quantum Mechanics Further Reading The Ancient Idea of Atoms Our understanding of matter, everything we can touch, read more
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Where the Quadratic Formula Actually Comes From (Derived Step by Step)
What Are Complex Numbers? A Note on the Names Solving Quadratic Equations with Complex Numbers Working with Imaginary Solutions A Quick Aside on the Definition of i Deriving the Quadratic Formula What Are Complex Numbers? Complex numbers often arise when we are solving quadratic equations. We’ll begin with a simple read more
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Every Geometric Shape Used in 3D Printing Explained
The Geometry Behind 3D Printing 2D Profiles and Extrusion Platonic Solids Prisms and Pyramids Solids of Revolution The Torus Boolean Operations Parametric Surfaces The Geometry Behind 3D Printing 3D printing would not exist without geometry. Each generated object begins as a three-dimensional representation constructed from vertices, edges, and faces. This structure read more
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Every Unsolved Circle Problem that Sounds Easy
Five Circle Problems That Are Way Harder Than They Look The Erdős-Oler Conjecture The Gauss Circle Problem The Kissing Number Problem Unequal Circle Packing Sendov’s Conjecture The Erdős-Oler Conjecture A unit circle is a circle whose radius (the distance from the center to the edge) is 1. An equilateral triangle read more
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Unsolved Math Problems That Took Centuries to Solve
Famous Math Problems That Took Centuries to Solve Squaring the Circle Euler’s Sum of Powers Conjecture The Four Color Map Theorem Legendre’s Constant Fermat’s Last Theorem Squaring the Circle We begin with a sheet of paper, a pencil, and only two other tools. The first is a straight edge, a ruler read more
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The Strangest Units of Measurement Still Used Today
Little-Known Scientific Units That Are Still Surprisingly Useful Units of Time Units in Nuclear Physics, Radiation, and Thermal Energy Units of Mass Units of Length Temperature and Astronomical Units Why These Units Stick Around Further reading Little-Known Scientific Units That Are Still Surprisingly Useful There are little-known units of time that read more
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Every Equation That Changed History Explained
Timeline of Equations That Changed the World 6th Century BC: Thales’ Theorem 6th Century BC: Pythagorean Theorem 300 BC: Euclid’s Theorem 250 BC: Archimedes’ Principle of Flotation 200 BC: Conic Sections First Century AD: Heron’s Formula 1202: Fibonacci Sequence 1609: Kepler’s Laws of Planetary Motion 1614: Logarithms 1637: Cartesian Plane 1637: read more
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Every Geometry Paradox That Shouldn’t Be Possible
The Missing Square Puzzle The Laves Paradox The Ebbinghaus Illusion The Klein Bottle The Penrose Stairs The Missing Square Puzzle The triangle puzzle with the missing square is one of the most well-known examples where geometric intuition fails. At first glance, the problem seems simple. Two triangular figures are composed of read more
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Every Core Math Concept Explained
Terminological precision in mathematics is not a mere formality but has profound consequences for the logical structure and understanding of mathematical theories. In the mathematical and scientific field, the concepts of principles and laws play a fundamental role in the formulation of knowledge. Although both terms are often used interchangeably in everyday language, in the read more
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