Natural Blogarithms

In July, 1999, Paul and Jack Abad presented their list of “The Hundred Greatest Theorems.” I was intrigued and though it might be interesting to re-post.
Their ranking is based on the following criteria: “the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result.”
The list is of [...]

This one is being added to my list just because of how slick the proof is. We finally proved it during Intermediate Analysis on Thursday. By the way, in case you turned glossy eyed at the sight of the following proof, I encourage you to scroll down to the end of this and read the story at the bottom. It is an interesting paradox, somewhat related to this proof.

In doing do preparatory reading for classes next term, I stumbled across this little interestingly named gem of a theorem. It is one that is frequently used in combinatorial analysis. It will also come in handy in our introductory Analysis class.
The reason for its name is that it can be used [...]

Some of you may know of a theorem called the Four Color Theorem. Many of you may not. It has the distinction of being the first major theorem to be proved using a computer. And thus, to many mathematicians the proof is not accepted since faith must be placed in the computer [...]

Scatterplot of first pythagorean triples inside 4500
I had the pleasure of filling in for a colleague in her Discrete Structure class, which is basically our introduction to proof class. Currently they are covering some introductory concepts from Number Theory. One of my favorite results had been covered in the class just before I [...]

The Wobbly Table Theorem
There’s a theorem I have recently come across that is much along the same lines as the Pancake Theorem or the Ham Sandwich Theorem. It’s called the Wobbly Table Theorem (by some). Basically it states that if you’re at a four legged table that does rest evenly on the floor [...]

This one’s a new one for me. It is definitely intuitive but I would have never thought of name for it!
You cannot comb a hairy ball.
The Hairy Ball Theorem states that if you take a ball that is evenly covered with hairs, no matter how you comb the ball, there must be a part [...]

Taylor’s Theorem
I am likely lose too many of my regulars with this one but I have to throw it in since it ranks, by far, at the top of my list of fave’s.
Thm: Let for some interval . For , we have that

where

Taylor’s theorem gives a polynomial approximation to a smooth [...]

The Pancake Theorem
Let me begin by saying that these theorems that will follow in this section of my blog will not be in any particular order, especially not in order of importance or preference. They are just popping up as I recall them or come across them.
Today’s Theorem, the pancake theorem, is one that [...]