## Pi aside: Degrees are even worse

Make no mistake: When I run the world, π will be set aside in favor of τ. For those who haven’t heard, there’s a movement to use 6.28318530718… (that is, 2π) as the basic variable relating to circles rather than 3.14159265359…. I personally feel that…

Mathematics

## Factoring quadratics and linear equations

Factoring a quadratic equation involves finding two linear equations whose product is the quadratic equation. This is an example where mathematics teachers often act as if (a) there is one method of solving and (b) there is one solution. The…

## Listening to students (reflection)

One of the greatest benefits to my current teaching position is its small class sizes, which affords me a significant amount of one-on-one tutorial time. I know fairly well how I think about numbers; I don’t know how other people,…

## =

When I was a lad studying mathematics, the equality sign seemed particularly simple: The stuff on the left is equal to the stuff on the right. However, I have since been developing a much more sophisticated perception of the simple…

## Let’s Make a Deal

The Problem In the misnomered “Monty Hall” problem, the rules are set out as follows: You as the contestant are faced with the choice of three doors, behind exactly one of which is money or something else of significant value….

## The Reversible Phone Number

Consider this problem: An absent-minded American mathematician has difficulty remembering his seven-digit phone number until he notices that, when he reverses the digits, he gets another seven-digit phone number that is a factor of his own phone number. After this…

## The Baby Shower game: A Square Deal

The Puzzle Here’s an interesting puzzle: The hostess of a baby shower devises a game in which sixteen tokens are placed in an opaque bag. The tokens are all either pink or blue, and they’re otherwise identical in shape, weight,…

Mathematics

## Three three-digit numbers

Here’s a fun little problem: Find three three-digit numbers that use each non-zero numeral once and add up to 999. Follow-up: How many such sets of numbers exist? If you want, take a moment to work on the problem on…

Mathematics

## Number terms

An interesting question on the G+ Mathematics community I co-moderate asked about the difference between “numbers” and “numerals”. We wound up discussing this at a party I was hosting (which shows the sort of nerds we are), and this post…

## Some thoughts on circumference

This is the formula for the circumference of a circle: $C = 2\pi r$ It’s very simple. My recollection of how it was taught is as a mystical relationship between $$\pi$$ and the circumference, as if it were some magical…

Mathematics

## Expressions as Names

One basic concept in mathematics that I see students struggle with, and with which I struggled myself, is the notion of expressions. However, when we remove the mathematical component, we can see that expressions behave much like a concept that…

## Sums of Positive Consecutive Integers: Proof

In my previous post, I tackled this problem: Try to express positive integers in terms of the sum of two or more consecutive positive integers. For instance, 3 = 1+2, 9 = 2+3+4, and so on. For which numbers 1…

Mathematics