Posted in logarithms, ninja maths.

"$\ln$", said the student, "of 123,456,789." He sighed, contemplated reaching for a calculator, and thought better of it. "18.4," said the Mathematical Ninja, absent-mindedly. "A bit more. 18.63." The student diligently wrote the number down, the Mathematical Ninja half-heartedly pretended to visit some violence on him, and the student squeaked

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Posted in ask uncle colin, ninja maths.

Dear Uncle Colin Somebody told me that the sequences $\left \lfloor \frac {2n}{\ln(2)} \right \rfloor$ and $\left \lceil \frac{2}{2^{\frac 1n}-1} \right \rceil$ were equal up to the 777,451,915,729,368th term, and I shivered in ecstasy. Is there something wrong with me? -- Sequences Considered Harmful When Agreeing Really Zealously Hi, SCHWARZ

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Posted in logarithms, ninja maths.

"So that works out to be $10^{1.6}$," said the student, reaching for the calculator -- and, of course, recoiling as the Mathematical Ninja yelled "yeeha!" and lasso-ed it out of her hand. "Forty," he said. "Too high by half a percent or so. 39.8." The student paused. She would normally

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Posted in ninja maths.

A few months ago, @preshtalwalkar at Mind Your Decisions showed off how he'd advise someone to work out $43 \times 67$ using one of my favourite tricks, the difference of two squares. In fact, that's how I'd have approached the question at first, too: the two numbers are 12 either

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Posted in ninja maths, trigonometry.

"$\sin(15º)$," said the GCSE student, and the Mathematical Ninja -- recognising that the qualification recognised idiotic angle measures -- let it slide. "0.2588", he muttered, under his breath, knowing full well that the exact answer -- $\frac{\sqrt{6} - \sqrt{2}}{4}$ -- would get him a blank stare. He sighed the sigh

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Posted in fractions, ninja maths.

A redditor asks: How would I find a good rational approximation to something like $\log_{10}(7)$? The Mathematical Ninja mutters 0.85 under his breath, as a matter of course, reasoning that $\log_{10}(7) \approx \log_{10}\left(\sqrt{ \frac {10^2 }{2} } \right)$, although my calculator says 0.845098, so he's off by about 0.6%. However,

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Posted in calculus, circles, core 4, ninja maths, pirate maths.

"Let me see that!" commanded the Mathematical Ninja, looking at one of the Mathematical Pirate's blog posts. "That's... but that's..." "It's not wrong!" said the Mathematical Pirate, smugly. "It just works!" "But you're presenting it as magic, not as maths." The Mathematical Pirate nodded eagerly. "Lovely magic! How does it

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Posted in ninja maths.

At a recent MathsJam, @brownmaths -- who really should have known better -- showed up with a calculator. Dear oh dear. His excuse was that it was in his teaching satchel, and he sometimes needed it to work out trigonometric functions (the Mathematical Ninja rolled his eyes, but I said

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Posted in ninja maths, trigonometry.

On a recent episode of everyone's second-favourite maths podcast, Taking Maths Further, @stecks and @peterrowlett asked: You want to calculate the height of a tall building. You set up a device for measuring angles, on a 1m high tripod, which is 200m away from the building. The angle above horizontal,

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Posted in ninja maths.

"So, the least common multiple of $52$ and $64$," said the Mathematical Ninja, "is $13 \times 16 \times 4$, which is $832$." "H-how did you do that?!" asked the student. The student was clearly new around here, so the Mathematical Ninja went easy on him. "Very simple," he said. "I

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