March, 2017

Ask Uncle Colin: Why does the constant term vanish?

Dear Uncle Colin, When I differentiate $y=2x^2 + 7x + 2$ and apply the $nx^{n-1}$ rule, why do I only apply it to the $2x^2$ and the $7x$ but not the 2? — Nervous Over Rules, Mathematically A Liability Hi, NORMAL, and thanks for your message! There are several ways

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