Browsing category ninja maths

How the Mathematical Ninja multiplies by 67

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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The Mathematical Ninja and Ailles’ Rectangle

"$\sin(15º)$," 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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Using continued fractions to generate rational approximations

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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How the Mathematical Ninja explains the Mathematical Pirate’s circle trick

"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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Dividing by 63

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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Taking Trigonometry Further

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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The Mathematical Ninja shuttles some numbers

"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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How would you work out $3^{0.7}$?

So, there you are, stuck on a desert island, you've played your eight pieces of music, burnt the Bible and Shakespeare, and now you're kicking yourself for not bringing a calculator as your luxury item. An emergency has broken out and it's vital for your to work out $3^{0.7}$ as

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Why $\log_{10} (2) \simeq 0.3$

“Coincidence?” said the Mathematical Ninja. “I think not!” He looked at his whiteboard pen as if wondering how best to fashion a weapon out of it. He wrote: $10^3 = 1,000$ $2^{10} = 1,024 = 1.024 \times 10^3$ So $10 \ln (2) = 3 \ln(10) + \ln(1.024)$ But $\ln(1.024) \simeq

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Equation of a circle: the Mathematical Ninja

"Four points," said the student. "On a circle." The Mathematical Ninja nodded, impatiently. "$A(-5,5)$, $B(1,5)$, $C(-3,3)$ and $D(3,3)$," he read from the book, for the third time. A slight crack of a smile. It may have been a snarl. You can never tell with the Mathematical Ninja. "I'm terribly sorry,

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