Category: Visual Math
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Every Fractal Dimension Explained
Fractals are geometric objects that have a fascinating property: they are self-similar. This means that their structure repeats itself at different scales, no matter how close or far away you are looking. Imagine an object whose shape repeats itself over and over again, just at different sizes. These structures are not just abstract objects but… read more
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Every Weird Number System Explained Part 2
Base 10 may seem like a natural choice for humans based on our number of fingers, but it has its inconveniences. One major detail is that 1/3, which is one of the simplest fractions, can’t be represented without a repeating decimal. This extends to any fraction which is 1 divided by a positive multiple of… read more
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Every Weird Measurement System Explained
One of the oldest surviving documents is an ancient Mesopotamian tablet that details a complaint by a customer who was sold 1,080 pounds of substandard copper ingots. A Mesopotamian pound was roughly equivalent to a mina, which was made up of 60 shekels and weighed approximately 1.25 pounds. It was not until after the French… read more
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Every Trigonometric Curve Explained
When describing trigonometric functions, it’s necessary to talk about concepts such as radians, sexagesimal degrees, and gradians. Radians Sexagesimal Degrees Gradians Converting Angles Transcendental Functions Trigonometric Functions Sine Function Cosine Function Tangent Function Reciprocal Trigonometric Functions Trigonometric Identities Basic Identities Inverse Trigonometric Functions Hyperbolic Functions Hyperbolic Sine Function Hyperbolic Cosine Function Hyperbolic Tangent Function Hyperbolic… read more
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Every Coordinate System Explained
Cartesian Coordinate System The Cartesian Plane in Two Dimensions Slope of a Line Equations of Lines Vectors Conic Sections Three-Dimensional Cartesian Plane Quadric Surfaces Polar Coordinate System Main Differences with Cartesian Coordinates Conversion Between Polar and Cartesian Coordinates Degrees vs Radians Cylindrical Coordinate System Main Differences Conversion Spherical Coordinate System Main Differences Conversion Comparing Coordinate… read more
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Every Binary Operation and Logic Gate Explained
The binary system is the foundation of all computing. Without it, there would be no computers, cell phones, internet, or modern technology as we know it. What Is the Binary System? Converting Between Decimal and Binary Binary Arithmetic Operations Boolean Algebra and Logic Gates Basic Logic Gates Derived Logic Gates Properties of Boolean Algebra Further… read more
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Every Method to Complete the Square Explained
Completing the Square: Why It’s Actually About Squares If you’ve ever taken an algebra class, you’ve probably been asked to solve for x. Before you get to quadratic equations, you usually start with linear equations, which are equations that can be put in the form ax + b = 0 for a ≠ 0. Once… read more
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Every Non-Newtonian Fluid Explained
What Is a Non-Newtonian Fluid? Time-Independent Non-Newtonian Fluids Time-Dependent Non-Newtonian Fluids The Mathematical Challenge Rheological Models Real-World Applications and Open Problems What Is a Non-Newtonian Fluid? A non-Newtonian fluid is one whose viscosity does not remain constant under different rates of deformation. Unlike Newtonian fluids such as water or air, where the relationship between shear… read more
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Every Weird Number Set Explained
The Extended Real Number Line The Hyperreal Numbers Increasing Dimensions: Why Not Three Components? Quaternions The Extended Real Number Line We all know and love the real numbers. But infinity is not a real number, at least not in the mathematical sense of the term. Since this is math, though, we can make up new… read more
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Every Real Function Explained
Every Type of Mathematical Function Explained Linear Functions Quadratic Functions Polynomials of Degree n Rational Functions Radical Functions Exponential Functions Logarithmic Functions Trigonometric Functions Inverse Trigonometric Functions Hyperbolic Functions The Absolute Value Function Constant Functions Floor and Ceiling Functions The Sign Function Piecewise Functions Linear Functions Linear functions have the form f(x) = mx +… read more
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