Browsing category ninja maths

The Mathematical Ninja And The Cubes

The Mathematical Ninja glanced at the Rubik Cube and paused. "And $45^3$ is..." A reach for the calculator. A flurry of colour. "Ow!" "91,125," said the Mathematical Ninja, catching the cube on the rebound and swizzling it solved. "Only needed 12 that time." The student sighed. "Go on, then. I

The Mathematical Ninja and the Tangents Near 1

“Forty-two degrees,” said the Mathematical Ninja, as smugly as possible while still using degrees. The student’s hand had barely twitched towards the calculator. “Go ahead, punk,” said the Mathematical Ninja. “Make my day.” “Righto,” said the student, and tapped in $\tan^{-1} \left( 0.9 \right)$, carefully closing the bracket. “41.987. That’s

The Mathematical Ninja and the Nineteenths

"Look," said the student, "we all know how this goes down. A nasty-looking fraction comes out of the sum, I reach for the calculator, you commit some act of exaggerated violence and tell me how you, o wondrous one, can do it in your head." "You're not as dumb as

Why $\phi^n$ is nearly an integer

This article is one of those 'half-finished thoughts' put together late at night. Details are missing, and -- in a spirit of collaboration -- I'd be glad if you wanted to fill them in for me. The estimable @onthisdayinmath (Pat in real life) recently posted about nearly-integers, and remarked that

Brutal simultaneous equations

I recently became aware of the IYGB papers, available from Madas Maths. Like the Solomon papers, they're intended to stretch you a bit -- they're ranked by difficulty from standard to extremely hard. My student, being my student, demanded we go through one of the extremely hard ones. There were

On the square root of a third

While I'm no Mathematical Ninja, it does amuse me to come up with mental approximations to numbers, largely to convince my students I know what I'm doing. One number I've not looked at much1 is $\sqrt{\frac{1}{3}}$, which comes up fairly frequently, as it's $\tan\left(\frac{\pi}{6}\right)$2 . Ninja-chops taught me all about

The Mathematical Ninja and the twenty-sixths

The Mathematical Ninja played an implausible trick shot, not only removing himself from a cleverly-plotted snooker, but potting a red his student had presumed safe and setting himself up on the black. Again. "One!" he said, brightly, and put some chalk on the end of his cue. The student sighed.

The Mathematical Ninja and The Slinky Coincidence

"No, no, wait!" said the student. "Look!" "8.000 000 072 9," said the Mathematical Ninja. "Isn't that $\frac{987,654,321}{123,456,789}$? What do you think this is, some sort of a game?" "It has all the hallmarks of..." "I'll hallmark you in a minute!" said the Mathematical Ninja. Seconds later, the students arms

Ask Uncle Colin: rearranging $\cos^3(x)$

Dear Uncle Colin, I recently came across a problem in which I had to integrate $\cos^3(x)$. Somewhere in my mind, I recall that the thing to do is to make it into something involving $\cos(3x)$, but I couldn't put the details together. Could you help? -- Not A Very Inspired

The Mathematical Ninja finds the value of $\pi$

This article has also been published as part of the Relatively Prime zine. The student yelped, and found his wrists and ankles strapped to the wheel before the lesson had even started. "Good morning," said the Mathematical Ninja. "I think you and I need to have a little... talk." The