Posted in ninja maths.

“We’ve been through this a hundred times, sensei. I say something like ‘$10^{1.35}$. Hm, let me get my calculator’ and you torture me in some unspeakable way an blurt out the answer…” “22.4” “… thank you, especially for refraining from the torture bit.” “You’re welcome.” “Then, of course, you tell

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Posted in logarithms, ninja maths.

The student’s shoulder twitched slightly as he said “So I need to work out $\log_2(10)$…” and the crash of the cane against the table reminded him that the calculator was off-limits. “I think you can estimate that yourself,” said the Mathematical Ninja. “Uh… ok. There’s a change of base formula,

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Posted in ninja maths.

“The square root of two… I don’t even know how to say this. The square root of two to the square root of threeth power?” “$\sqrt{2}^{\sqrt{3}}$?” said the Mathematical Ninja. “I wouldn’t bother saying it, I’d just write it down.” “But what does it mean? I mean, I can just

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Posted in ninja maths.

“How old are you?” asked young Fred. (This is not, technically, an ‘Ask Uncle Colin’. It’s an ‘Ask Daddy’.) “I’m 42, buddy.” “42 days?” “No, 42 years!” “Oh. But how many days is that?” It is not quite 7:15am on New Year’s Day. I have not yet had my coffee.

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Posted in ninja maths.

A physicist. A calculator. The Mathematical Ninja’s face - what could be seen of it - was more snarl than feature. It’s quite tricky to hiss something that doesn’t have any sibilant consonants, but they hissed all the same: “The cube root of 13? You don’t need a calculator for

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Posted in ninja maths.

“Sensei, why have you covered the entire Earth in an area-preserving wrap?” “It’s all @colinthemathmo's doing.” “I’m surprised you’re doing it in hardware rather than working it out in your head.” “Oh, $\frac{1000}{\sqrt{\pi}}$? That’s trivial.” “But of course it is.” “I mean, $\frac{1}{\pi}$ is pretty close to $\frac{1}{\sqrt{10}}$, which is

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Posted in ninja maths.

"The Mathematical Ninja is currently on sabbatical. Leave a message after the tone... or else!" Oh dear! How are we going to figure out $e^e$ now? Let alone $e^{-\frac{1}{e}}$? We'll just have to roll up our sleeves and get our thinking hats on, that's all. OK, $e^e$ First of all,

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Posted in ninja maths.

The Mathematical Ninja peered at the problem sheet: Given that $(1+ax)^n = 1 - 12x + 63x^2 + \dots$, find the values of a and n Barked: “$n=-8$ and $a=\frac{3}{2}$.” The student sighed. “I get no marks if I just write down the answer.” Snarled: “You get no

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Posted in logarithms, ninja maths.

Via @markritchings, an excellent logs problem: If $a = \log_{14}(7)$ and $b = \log_{14}(5)$, find $\log_{35}(28)$ in terms of $a$ and $b$. One of the reasons I like this puzzle is that I did it a somewhat brutal way, and once I had the answer, a much neater way jumped

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Posted in ninja maths.

“I beg your pardon?!” yelled the Mathematical Ninja. The terribly well-dressed gentleman stood his ground. “I said, sensei, I would work $0.8^{10}$ out differently.” A sarcastic laugh. “This, I have to see!” “Well, $8^{10} = 2^{30}$, which is about $10^{9}$.” “About.” “Obviously, we can do better with the binomial: $2^{10}$

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