Once you see a triangle this way, you can never unsee it.
Begin with a triangle. Label the vertices A, B and C. Label each side with the lower case letter corresponding to the opposite vertex.
Amaze your friends at parties with this trigonometric proof
Here’s the double angle identity which you may have memorized:
How to fail at maths.
Have you seen my latest blunder? Here it is:
To magnify my shame, here is the video version:
Limit with factorial leads to familiar solution (YouTube).
The goal was to solve this limit:
CHESS
And you can too.
If you have yet to see the new Netflix mini-series, The Queen’s Gambit, worry not. This article contains (almost) no spoilers.
Try it out. Just for fun.
YouTube math aficionado, Dr. Peyam has published a video featuring this limit:
Are you satisfied with the answer in the back of the book?
I received an email the other day — a response to the antiderivative challenge. Enjoy it. And ask yourself: what does maths do for you?
What is it that drives folks … to delight in taking five lines to solve a maths question that we could solve in one line?
Then read further.
Antiderivative — The wrong way
Is it possible to solve ∫(1/t)dt using the reverse power law?
We can write the problem as follows:
CALCULUS
A little geometry; a few infinitesimals
The Power Rule for derivatives is one of the first tricks we learn in Calculus I. It’s such a refreshing alternative to using the limit definition.
Let’s start with a question. For the graph of xⁿ, what is the slope at a given point?
For example, f(x) =x². We can represent f(x) as the area of a square with sides, x. We increase each side by an infinitesimal, dx.
CALCULUS
Solve this simple integral without using the reverse power rule.
Yesterday (October 30, 2020), YouTuber Steven Chow (blackpenredpen) posted a video with this goal: Integrate x² without the power rule. Before seeing Steve’s solution, I posted my own video. (I didn’t want to be unduly influenced.)
Have a crack at it yourself. Then see how I solved it (below).
PRECALCULUS
Wherein we discover the roots of the quadratic formula
You want to find the roots of a quadratic polynomial. Good news! The method of completing the square always works. What makes that so, and what other information can we glean from this method?
Let’s find out with an example. We’ll find the roots of:
A Geometric Illustration
The best way to define the Squeeze Theorem is with an example. We’ll use it to prove the following identity:
Adam Hrankowski
Adam Hrankowski is a maths/physics tutor in BC. His book, "When Am I Ever Gonna Use This Stuff” is available for preorder at: https://amzn.to/3egZUib.
