Buffon’s needle Problem, which was first posed in 1777 by its namesake Georges-Louis Leclerc, Comte de Buffon, is a fantastically simple problem which allows us to calculate, or at least approximate, the value of π through a simple experiment. It can be stated in many different formulations, but we will consider the following one:*Suppose a needle of length L is dropped onto a piece of paper which has been lined with evenly spaced parallel lines. What is the probability of that the needle will cross one of these lines?*

At first glance it may seem that such a simple…

*By calculating a very simple integral we can see that π ≠ 22/7 regardless to what we were told in school.*

I constantly have students coming into my college classes and trying to interchange between π and 22/7. Let’s be clear, 22/7 is a relatively good approximation for π (it is correct to 2 decimal places) but it certainly is not equal to π. I want to show you an integral I like to get my class to calculate at the end of an ``Introduction To Calculus Course” to exemplify the fact that these numbers are not equal. …

In a previous article, I discussed how a division trick won me $100.

In this article, I want to show you how similar tricks can be used for other numbers.

Originally I planned to prove how some of these tricks worked, but in talking through the tricks for other numbers the article ended up getting rather large and so I have instead decided to just present the tricks in the article, with the promise of proving some of them in the next article.

In particular, I want to give you some rules for telling whether or not a particular number…

Let me first clarify, when I said my math teacher, it wasn’t my regular math teacher, who was a wonderful woman and an excellent teacher. Instead, it was a substitute who embodies everything wrong with teaching. This substitute, let’s call her Miss Y, was arrogant, impatient, and simply did not know anything more than what she was regurgitating from the math book she read in front of us. If anyone in the class was to ask her a question her replies were generally: “I’ll come back to that later”, which she never did, “Why don’t you just think about that”…

In this article, I want to discuss a recent problem a student provided me with. According to the student, this problem comes from a set of Swedish Mathematical Olympiad problems, although I am unsure what year.

The problem is the following:

Find all integers n such that

In a recent article of mine,

I was asked a very interesting question which basically translates to “can you generalize Fermat’s last theorem to non-integer exponents?”. If you are unsure about some of those words, don’t worry, I will explain it all below and do my best to answer this question. My thanks to Astoria Bob for proposing the question.

Consider the equation

where x, y, and z are positive integers. For those unfamiliar with math notation, we generally write this as x, y, z ∈ ℕ. We are curious as to what values of n can we find solutions…

A few nights ago my partner had me sit down and watch the movie “Mean Girls” with her. For those unfamiliar, near the end of the film, the lead character is involved in a math competition in which two teams face off to answer questions for the state championship. We hear three of the questions the contestants are challenged with, after which my partner turned to me and asked if any of them made any sense. Quite often in movies when some sort of math, or any other science, is used, some random equation is thrown in to sound and…

In this article, I want to discuss one of the earliest problems which completely changed my viewpoint of mathematics and pushed me to pursue a career in it.

This problem is from the 2009 British Mathematical Olympiad which I first came across when attending a problem session ran by my University’s mathematics society. The problem is the following:

*Find all nonnegative integers a and b such that*

Before looking at one possible way of solving this problem, which requires nothing more than school-level arithmetic, I want to explain why I like this problem, and problems of this nature, so much…

In this article, I present a formal proof that the recurring decimal 0.999…. is in fact equal to 1. In doing so, however, I will sidestep a little of the more formal notation and strictness that a truly airtight proof would require. Instead, I will opt for presenting the main concepts required for the proof and show the construction of the proof based off these.

With this in mind, before we can begin the construction of our proof, we require the use of some techniques and ideas from a branch of mathematics known as real analysis. …

In this article, I present 14 interesting math facts that I have gathered over the past few years of teaching. I generally present a collection of these to first-year students on their first day to ease them into college and also to just get them thinking. Some of these are more of an “oh, ok” level of interesting, others are a “really, how come?” level. I’ll let you be the judge. Some of these facts are self-explanatory and only take a moment’s thought, others require a little more thought and so I have made some comments along the way. …