Categories
Geometry Math Trigonometry

Area of Regular Polygon-General Strategy

Finding the area of a polygon seems impossible given just the side length or just the length of a radius or apothegm. But here’s how to do it, step by step.

Categories
Complex Numbers Math Math Analysis Pre-Calculus Trigonometry

Sin x from Euler’s Formula

Here’s one of the things about complex numbers which is easier if you know it so well you don’t have to think about it: the formula for sin x. Nice and easy. Assumes you already know Euler’s formula, eix = cos x + i sin x.

Categories
Calculus Limits Math

Precise Definition of a Limit

A clear explanation of the epsilon-delta definition of a limit

Categories
Math Analysis Pre-Calculus Proofs Proving Identities Trigonometry

Proving Trig Identities: Some Strategies

Assuming you know the basics (tan=sin/cos, etc), here are strategies and examples for proving simple trig identities.

Categories
Algebra 1 Math

Fraction Exponents

What are fraction exponents? Why is x=∛x? Here’s an explanation.

Categories
Algebra 1 Math

The Zero Power

You probably already know that 20=1. In fact any number to the power of 0 is one. But why?

Categories
Math Math Analysis Pre-Calculus Proofs

Ten-year-old Finds Math Secret! (Summing an Arithmetic Series)

Gauss was just ten years old when he discovered how to quickly add up a long series of numbers. Here I tell the story of how he outwitted his teacher and I also walk you through a mathematical proof.

Categories
Algebra 1 Math Word Problems

Algebra 1 Word Problems Involving Motion

A lively presentation of how to solve a two different word problems involving motion, using distance = rate * time. The text is a little small so click the “full screen” option to really see it. (I’ll redo this eventually — still learning ins and outs of Zoom!)

Categories
Chemistry Science

Chemistry: An Equilibrium Problem

This video walks you through the multifarious steps and guides you past all the gotchas in solving an equilibrium problem. I’ll assume you know what equilibrium problems *are* and just need some practice *doing* them.

Categories
Calculus Differential Equations Math ODE

What is a Differential Equation?

Lots of calculus students learn to solve differential equations without understanding what they really mean. Here’s a simple example of a differential equation so you can see how it works.