Author: Thought Thrill

The Fahrenheit scale, with units of degrees Fahrenheit (°F), is likely familiar to those living in the United States of America. Its story begins in 1724 with Polish-Lithuanian physicist and inventor Daniel Gabriel Fahrenheit. The Original Definition The Final Revision The Original Definition Daniel Gabriel Fahrenheit. Public domain, via Wikimedia Commons read more

The Kelvin Scale: The Foundation of Temperature Measurement A Note on Notation The History of the Kelvin Scale The Kelvin scale is the temperature scale used in the International System of Units (SI). The SI is exactly what it says on the tin: a standardized measurement system to be used by read more

The Sierpiński Triangle: A Fractal Built from Itself A Fractal with Infinite Detail The Sierpiński Triangle: A Fractal Built from Itself Take three identical equilateral triangles and join them at the vertices so that they form another equilateral triangle in the middle. Then shrink this shape down by a factor of read more

The Tesseract: A Cube in Four Dimensions Visualizing the Fourth Dimension The Tesseract: A Cube in Four Dimensions Tesseract. Public domain, via Wikimedia Commons The tesseract is the four-dimensional analog of the cube. Just as a line segment is formed by connecting two points, a square by connecting four line segments, read more

The Möbius Strip: The Surface with Only One Side What Is a Nonorientable Surface? The Möbius Strip: The Surface with Only One Side Let’s start with a Möbius strip, named after German mathematician August Ferdinand Möbius. This is an object you could make at home. Just take a paper strip, give read more

The Coastline Paradox: Why Coastlines Have No True Length Do you think you know how long a coastline is? Measuring one seems simple, but the smaller your ruler, the longer the coast becomes. This happens because coastlines are jagged and detailed. Every smaller measurement catches more twists and turns. A coastline’s length is not fixed read more

The Klein Bottle: A Surface with No Inside or Outside Constructing a Klein Bottle The Klein Bottle: A Surface with No Inside or Outside The Klein bottle, named after German mathematician Felix Christian Klein, is another example of a non-orientable surface. However, unlike the Möbius strip, it has no boundary, meaning read more

The Mandelbrot set, named after French-American mathematician Benoît B. Mandelbrot, arises in the study of complex numbers. How It Works A Fractal of Extraordinary Detail How It Works We begin by picking some number c in the complex plane. Using c, we define a function: take a number, multiply it by read more

A unit square is a square with a side length of one unit. Suppose you have a collection of some number of unit squares, and we will call this number n. You want to pack all these squares into a large square enclosure with no overlap. For a given number of unit squares n, what read more