## Modeling gravity for multiple objects

A former student, JH, recently corresponded with me about some simulations he'd done of a gravitational system. This problem is connected with many problems in physics including molecular dynamics and n-body problems. It is also of particular interest to game … Continue reading

## What good is the secant?

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Students no sooner learn about the sine and cosine functions, which are strange enough at first, when they are exposed to . Years later, they may reflect (as I have) that they never used the function directly. What were mathematicians … Continue reading

## Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47 Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49 Typesetting with  in WordPress

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

When you are blogging about mathematics, you can make your mathematical expressions look professional using . Here are some things you should know. There are plugins available, but if you are hosted on wordpress.com, then you can stick with using … Continue reading

## Calculus Handouts

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

These are all of the handouts for Calculus AB, 2014-2015. Calculus Handout 1: Lab: Graphing Functions Calculus Handout 2: Warming up your algebra Calculus Handout 3: Dropping the ball Calculus Handout 4: Tangents to a parabola Calculus Handout 5: The … Continue reading

## Calculus Website Checklist

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

For help with , see my post on typesetting with in WordPress. Blog Post: 'Differential equations, slope fields, and Euler's Method.' It should contain: Nicely labeled link to your Slope Fields (#74) and Slope Fields lab (#76) handouts Under a … Continue reading

## Folding a dollar bill into a triangle

There is some interesting geometry in this example of paper folding. Start with a dollar bill (actually, most paper currency will do). For the classroom, I print fake dollars for the students. Now, follow this sequence of folds: Repeat the … Continue reading

## LaTeX for math formulae in Schoology

If you are creating content in Schoology and prefer LaTeX to an equation editor, here's how you can do it. I'll assume you already have created a course. Let's say you want to create a test. So, click Add Materials, … Continue reading

## Studying the Weierstrass function with desmos

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

In calculus, we work with functions that are continuous. In fact, we usually require functions that are also differentiable, meaning that at every point, the function can be approximated with a tangent line. If a function is differentiable at a … Continue reading

## Flipping tiles

This is another problem I learned from Mark Saul in i2camp training. In the app below, you can click on a row number or column number, and all of the tiles in the row or column will flip from white … Continue reading

## Three-in-a-row

I learned about the game of three-in-a-row from H. Steinhaus's Mathematical Snapshots. It begins like tic-tac-toe, but with markers instead of Xs and Os. After 6 markers have been placed, players take turns moving their markers one space at a … Continue reading

## Izzi puzzle

I was introduced to Izzi cards today by Mark Saul at i2camp training. There are 64 cards in the deck. All of the cards are constructed according to a simple rule. I wondered if the Izzi deck contains all the … Continue reading

## Inversive Geometry

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Inversive geometry is a nice way to introduce the idea of geometry mappings, which can lead to the study of the PoincarĂ© disk. With a little effort, the ideas are accessible, and there are an abundance of concepts to learn … Continue reading

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

The PoincarĂ© disk is an example of a non-Euclidean geometry. It is a hyperbolic geometry. This means that given a line, and a point not on that line, there are infinitely many parallels through the point. What? Isn't there only … Continue reading

## Overlapping circles

Each of the small circles in the picture below has area one. The large circle is three times the diameter of a small circle. The light grey area is bigger than the dark grey area. How much bigger? … Continue reading

## Perudo and Monte Carlo

Perudo (aka Liar's dice) is a game where players have perfect knowledge of their own dice and imperfect knowledge of other people's dice. Players bid on the collective set of dice that is rolled by all players. A player starts … Continue reading