## Math Needs Better PR

I was recently reading a book on Greenfoot, a Java-based GUI intended for teaching programming to high schoolers and college underclassman. In the “Newton’s Lab” project, the writer assuaged the reader who might be leery of the mathematics in that…

Mathematics

## 10 vs Ten

What does “ten” mean? Here are some dictionary definitions: The number 10. (MacMillan) The cardinal number equal to 9 + 1. (American Heritage) Equivalent to the product of five and two; one more than nine; 10. (Oxford) Superficially, these seem…

Mathematics

## Intersecting Secants

In this entry, I’m going to be discussing how mathematicians tend to approach the world, and why we need better PR. I’m currently teaching High School Geometry. Here is what the book has to say about the “Segment of Chords…

The topic in my geometry class today involved finding solutions to quadratic equations. The actual topic was on the ratio of lengths of secants in a circle, but that’s for another post. For a specific example, consider this problem. Two…

Mathematics

## Pascal’s Triangle and Dice Rolls

Pascal’s Triangle Pascal’s Triangle represents the coefficients of a binomial such as $$x + 1$$ raised to a power. Row n of the triangle lists the coefficients of $$(x + 1)^{n-1}$$. Here are the first few rows of Pascal’s Triangle:…

Mathematics

## Solving Simultaneous Equations: Multiple Methods

Introduction and Terms Recently, a post on the G+ Mathematics community involved how to determine $$x$$ and $$y$$ when: $3x + 5y = 12 \\ x + y = 2$ This is generally referred to as simultaneous equations or a…

## Finding an Incenter via Formulas

Terms For every polygon, there is a largest circle that fits entirely within that polygon. If that circle touches all sides of the polygon, then it is said to be inscribed; it is called the incircle, and its center is…

Mathematics

## Equatorial temperatures

This one strikes me, and apparently others, as highly counter-intuitive, but it’s true because of mathematics! Take any two places in the world; call these points A and B. Take any two paths between A and B that are the…

Mathematics

## Pseudocode for the Russian peasant method of binary

Just for fun… Here’s the pseudocode for the method of building a binary number from a decimal number, based on the Russian peasant method of multiplication: function mybin(mydec) { mybin = “”; do while mydec > 0 { if mydec…

## Russian peasants, number sense, and bases

Russian peasants do too much work There is a method of multiplication called the Russian peasant method. I’ve seen it mentioned here and there, but I was not explicitly educated in the process; it struck me as being more trouble…

## The Wayward Airline Passenger

This problem was brought to my attention on G+, but I wasn’t satisfied with the solution presented. There are actually two versions, the one that was originally presented on G+ and the corrected one that matches the standard version. I’ll…

Mathematics

## The History of Factorials: Kramp

In an earlier post, I argued that the definition of factorial ($$n!$$) is the number of ways that a number of n distinct objects can be arranged. I have recently been told that, no, the formal definition of factorial is as…

Mathematics