Ever get a hint of confusion about what an exponent was doing? I sure have.| betterexplained.com
The Rule of 72 is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here’s the formula:| betterexplained.com
Ratios summarize a scenario with a number, such as “income per day”. Unfortunately, this hides the explanation for how the result came about.| betterexplained.com
A sense of scale helps us better understand the world, and convey ideas more effectively. What’s more impressive?| betterexplained.com
Our initial exposure to an idea shapes our intuition. And our intuition impacts how much we enjoy a subject. What do I mean?| betterexplained.com
How do you wish the derivative was explained to you? Here's my take.| betterexplained.com
Math uses made-up rules to create models and relationships. When learning, I ask:| betterexplained.com
Logarithms are everywhere. Ever use the following phrases?| betterexplained.com
We’re taught that exponents are repeated multiplication. This is a good introduction, but it breaks down on 3^1.5 and the brain-twisting 0^0. How do you repeat zero zero times and get 1?| betterexplained.com
There are two types of exponential growth, and it's easy to mix them up:| betterexplained.com
Here’s a trick for thinking through problems involving exponents and logs. Just ask two questions:| betterexplained.com
A common question is why e (2.71828...) is so special. Why not 2, 3.7 or some other number as the base of growth?| betterexplained.com
Here’s a collection of time-saving math shortcuts, great for back-of-the-envelope estimates.| betterexplained.com
Seeing the same math concept from a few perspectives helps build intuition. Seeing that e is my favorite constant (sorry, pi), a while back I put the definitions of e together to visualize their connection:| betterexplained.com
e has always bothered me — not the letter, but the mathematical constant. What does it really mean?| betterexplained.com
Interest rates are confusing, despite their ubiquity. This post takes an in-depth look at why interest rates behave as they do.| betterexplained.com
What does matrix multiplication mean? Here's a few common intuitions:| betterexplained.com
Sine waves confused me. Yes, I can mumble "SOH CAH TOA" and draw lines within triangles. But what does it mean?| betterexplained.com
Euler's identity seems baffling:| betterexplained.com
It’s an obvious fact that circles should have 360 degrees. Right?| betterexplained.com
Like making engineering students squirm? Have them explain convolution and (if you're barbarous) the convolution theorem. They'll mutter something about sliding windows as they try to escape through one.| betterexplained.com
Imaginary numbers have an intuitive explanation: they “rotate” numbers, just like negatives make a “mirror image” of a number. This insight makes arithmetic with complex numbers easier to understand, and is a great way to double-check your results. Here’s our cheatsheet:| betterexplained.com
Imaginary numbers perform rotations. So what's the difference between $2 i$ and $2^i$?| betterexplained.com
If the exponential function $e^x$ is water, the hyperbolic functions ($\cosh$ and $\sinh$) are hydrogen and oxygen. They're the technical, rarely-discussed parts that combine into a famous whole.| betterexplained.com
The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations:| betterexplained.com
Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories:| betterexplained.com
After understanding the exponential function, our next target is the natural logarithm.| betterexplained.com
Despite two linear algebra classes, my knowledge consisted of “Matrices, determinants, eigen something something”.| betterexplained.com