Colorized Math Equations

Years ago, while working on an explanation of theFourier Transform, I found this diagram:

啊!为什么不以这种方式引入更多的数学概念?

Most ideas aren't inherently confusing, but theirtechnical descriptioncan be (e.g., reading sheet music vs. hearing the song.)

我的学习策略是找到在学习一个概念时真正有用的东西，并做得更多。Not the stodgy description in the textbook -- what made it click foryou?

The checklist of what I need is世界杯2022赛程时间表最新 : Analogy, Diagram, Example, Plain-English Definition, and Technical Definition.

Here's a few reasons I like the colorized equations so much:

The plain-English description forces an analogy for the equation. Concepts like "energy", "path", "spin" aren't directly stated in the equation.
The colors, text, and equations are themselves a diagram. Our eyes bounce back and forth, reading the equation like a map (not a string of symbols).
技术描述——我们的最终目标——并不隐藏。We're not choosing between intuition or technical, it's intuitionforthe technical.

Of course, we still need examples to check our understanding, but 4/5 ain't bad!

Creating Colorized Equations

I colorized a few of my favorite math topics below. Making the colorizations was surprisingly fun. Like writing a haiku, there's a game to trimming down a concept to its essence.

Colorized: e (universal base of growth)

The number e (2.718...) is the base of growth, generated from universal ideas. Take unit interest, with unit time and compound it perfectly.Read article.

Colorized: Euler's Formula

Euler's Formula is one of the most important in math, linking exponents, imaginary numbers, and circles. The intuition: constant growth in a perpendicular direction traces a circle.Read article.

Colorized: Fourier Transform

The Fourier Transform builds on Euler's Identity. Using your circular path, spin a signal at a certain speed to isolate the "recipe" at that speed (like separating a smoothie into its ingredients).Read article.

Colorized: Pythagorean Theorem

勾股定理通常被认为只适用于三角形。In fact, it applies toanyshape,anytype of 2d area. Triangles are just a convenient starting point.Read article.

Colorized: Bayes Theorem

贝叶斯定理有一个简单的直觉:证据必须被假阳性稀释。(狼来了，你就不可信了。)Read article.

Going Forward

These colorized equations are an experiment in conveying the most intuition in the simplest package possible. We don't need VR/AR, holograms, or brain-computer interfaces to understand math -- have we exhausted the possibilities of crayon on a piece of paper?

My short-term goal is create colorized equations for the top 25 equations on the site. Then (not trying to look directly at the sun), gather colorizations for the top (100?) topics we're meant to learn in high school and college.

The idea is to find explanation styles that work, and do more of them.

Happy math.

Appendix: How to Create Your Own

I have a half-built visual tool to make these. For now, here is the LaTeX template I used:

https://www.overleaf.com/read/cvmtqywqgvvw

Appendix: Initial Feedback

The idea got a strong reception on Twitter (thanks Jan):

colorized math equations makes it easier to understand. Great idea!!#ux #math https://t.co/8Btua0cpTl pic.twitter.com/2569UG2Zv4
— Jan Willem Tulp (@JanWillemTulp)December 14, 2017

最重要的反馈是为色盲读者提供可访问12强赛积分榜最新的版本;I plan to make options available here too.