# The Flying Colours Maths Blog: Latest posts

## How the Mathematical Ninja approximates $\ln(5)$

"Isn't it somewhere around $\phi$?" asked the student, brightly. "That number sure crops up in a lot of places!" The Mathematical Ninja's eyes narrowed. "Like shells! And body proportions! And arrawk!" Hands dusted. The Mathematical Ninja stood back. "The Vitruvian student!" The student arrawked again as the circular machine he

## Ask Uncle Colin: A Separable Difficulty

Dear Uncle Colin, I have an equation $3y, \dydx =x$. When I separate and integrate both sides, I end up with $\frac{3}{2}y^2 = \frac{1}{2}x^2$, which reduces to $y = x\sqrt{\frac{1}{3}}+c$. With the initial condition $y(3) = 11$, I get $y = x\sqrt{\frac{1}{3}}+11-3\sqrt{\frac{1}{3}}$, but apparently this is incorrect. What am I

## A common problem: decimal division

I'm a big advocate of error logs: notebooks in which students analyse their mistakes. I recommend a three-column approach: in the first, write the question, in the second, what went wrong, and in the last, how to do it correctly. Oddly, that's the format for this post, too. The question

## Ask Uncle Colin: Are normals… normal?

Dear Uncle Colin, I don't understand why the normal gradient is the negative reciprocal of the tangent gradient. What's the logic there? — Pythagoras Is Blinding You To What's Obvious Hi, PIBYTWO, and thanks for your message! My favourite way to think about perpendicular gradients is to imagine a line

## From Euclid to Cantor

One of my favourite quotes is from Stefan Banach: "A good mathematician sees analogies between theorems. A great mathematician sees analogies between analogies." This post is clearly in the former camp. I'm fairly sure it's a trivial thing, but it's not something I'd noticed before. One of the first serious