Browsing category powers

Ask Uncle Colin: A Huge Power Of Two

Dear Uncle Colin, I've been asked to find $2^{64}$ without a calculator, to four significant figures. How would you go about this? -- Large Exponent, Horrific Multiplication, Extremely Repetitive Hi, LEHMER! To get a rough answer, I'd usually start with the rule of thumb that $2^{10} \approx 10^3$. I'd conclude

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Estimating $e$

Here at the Flying Colours Maths Blog, we're never afraid to answer the questions on everyone's lips - such as, why is $\left(1 + 9^{-4^{7\times 6}}\right)^{3^{2^{85}}}$ practically the same as $e$? When I say ‘practically the same’, I mean… well. 20-odd decimal places of $\pi$ are enough to get the

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$\left(1+ \frac {1}{n}\right)^n$

This doesn't appear to work on all models of calculator. Let me know whether yours handles it properly... "I saw this thing about Euler's identity," said the student, and the words "ut" and "oh" forced themselves, unbidden, into my head. You've maybe seen it: it's $e^{\pi i} + 1 \equiv

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