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Puzzles and Fractals

Today I was asked a simple but innocent question: 'If a number plus 4 is equal to six times the sum of its digits and the number plus eighteen is equal to the number obtained by reversing its digits then find the number.'

Evidently, this is neither simple nor innocent (people who tend to disagree battle it out in the comments). This question is deliberately designed to trick and confuse high school students in the exam. Now, I'm all for tricky problems, but this question isn't a problem: It's a question. And its certainly not a puzzle.

Puzzles are awesome. They confuse you, make your brain twist in new and unexpected ways, and a good puzzle will energize you. In fact, I love puzzles. Not just the jigsaws that we solve at home, but all kinds of puzzles. For instance, this is a classic one that I love. You're at your house. You go one mile south, one mile east, and one mile north. You arrive back at your house. Where is your house? This puzzle's great. It do…
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Axioms, Proofs, and the Delicacy of the Elements

Hey guys!

About 2300 years ago, an old dude with a beard (or possibly several old dudes with beards, there's still controversy over whether Euclid was one person or a whole team) published the biggest mathematical blockbuster ever written: a journal/textbook consisting of 13 books that changed the face of human knowledge forever. It was a collection of axioms, postulates, and proofs that essentially created the subject of geometry and is still the main content of every geometry course taken in school. The old dude, Euclid, christened his book 'Elements'.

Before we delve into the content of the book, let's spend a moment just grovelling over how the book almost literally created the subject of math. Besides from being one of the most published books ever (second only to the Bible), it was also a masterpiece in what we would now call logic. Elements was not entirely Euclid's creation, however. It was largely composed of proofs by earlier mathematicians and was a com…

Geometry

Hey Guys!

The other day I was idly switching channels on TV and happened to come across one of the most overplayed movies ever: The Avengers. Now I'm really not a huge fan of the movie (No offense Marvel Fanboys) but I happened to notice something really cool.


The whole plot of the movie revolves around this random blue thing from Asgard which is the energy source of the future: The Tesseract. It's quite flashy in the movie, being one of the infinity stones, but what most people probably didn't notice is that a tesseract is, in fact, a real mathematical object. A tesseract is the 4 Dimensional equivalent of a Cube. Yep, that's right, the entire movie is based around a 4D cube.

Now, there are probably tons of questions rampaging around in your mind. But what is a 4D cube? What is the fourth dimension anyway?! How can something so outrageous exist? Well, look no further, for all your questions are about to be answered. In this post, I'll be defining what a dimension…