# Browsing category ask uncle colin

## Ask Uncle Colin: Is my friend crazy?

Dear Uncle Colin, A friend of mine told me that $1 + 2 + 4 + 8 + ... = -1$. Is he crazy, or is there something going on here? -- Somehow Enumerating Ridiculous Infinitely Extended Sum Dear SERIES, There are a couple of 'proofs' of this non-fact that

## Ask Uncle Colin: A logarithmic coincidence?

Dear Uncle Colin, I noticed that $2^{\frac{1}{1,000,000}} = 1.000 000 693 147 2$ or so, pretty much exactly $\left(1 + \frac{1}{1,000,000} \ln(2)\right)$. Is that a coincidence? Nice Interesting Numbers; Jarring Acronym Dear NINJA, The easiest way to see that it's not a coincidence is to check out $3^{\frac{1}{1,000,000}}$, which

Dear Uncle Colin, I've been trying to work out $I = \int_0^{\frac \pi 4} x \frac{\sin(x)}{\cos^3(x)} \d x$ for hours. It's the fifth time this week I've been up until the small hours working on integration and it's affecting my work and home life. I'm worried I'm becoming a calcoholic.

## Ask Uncle Colin: two almost-matching sequences

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

## Ask Uncle Colin: An imaginary curve?

Dear Uncle Colin, I was playing with parametric equations and stumbled on something Wolfram Alpha wouldn't plot: $x=t^i;\, y = t^{-i}$. Does this curve really exist? Or am I imagining it? -- A Real Graph? A Non-existant Drawing? Hi, ARGAND -- what you're trying to plot certainly exists; whether or

## Ask Uncle Colin: how do you find the intersection of three circles?

Dear Uncle Colin, I've been challenged to find the area of the intersection of three circles while drawing a Venn diagram. I don't know where to start!-- Triangle Unpredictably Rounded; I'm No Genius For a moment, TURING, I thought there wasn't a problem in this problem, but then I realised:

## Ask Uncle Colin: Are the log laws… lacking?

Dear Uncle Colin, I have an equation to solve: $\ln(x^2) = 2 \ln(4)\, x \ne 0$. I tried to solve it by applying the log laws: $2 \ln(x) = 2 \ln(4)$, so $x=4$. However, a bit of thought shows that $x=-4$ is also a solution -- but that doesn't seem

## Ask Uncle Colin: Multiple workers

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I have a problem I just can't

## Ask Uncle Colin: simplifying fractions

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I'm having trouble cancelling fractions -- in

## Ask Uncle Colin: A nasty triangle

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I've been given a trigonometry problem I