# Mathematics

## 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

## Infinity and String Theory

There’s a Numberphile video that’s hurting people’s brains. It claims to prove (several ways, including in a companion video) that $\sum_{n=1}^{\infty} n = -\frac{1}{12}$ This is, of course, highly counterintuitive. The video itself is misleading in that the speakers refer…

Mathematics

## Probabilities: Consecutive numbers

On a mathematics community on Google+, Michal Nalevanko asked the question (paraphrased here, including my assumptions): Let us say there is a lottery game in which twenty numbered balls are pulled from a pool of eighty. What is the probability…

Mathematics

## Factorials and the meaning of “is”

In a YouTube video, James Grime of NumberPhile makes the claim that the meaning of the factorial is $n! = \prod_{i=1}^n i$ for n > 0, and proceeds to explain why 0! = 1 using a recursive proof. This echoes…

## Numerators and denominators

I remember as a child studying fractions, being told that the top was called the numerator and that the bottom was called the denominator, for reasons that were not made clear to me at the time. In retrospect, it’s possible…