# Browsing category ask uncle colin

## Ask Uncle Colin: Dividing Decimals

Dear Uncle Colin, I’m trying to work out $0.03 \div 0.1$. The answer is apparently 0.3, but I don’t understand why a division would make something bigger! Division Isn’t Very Intuitive, Decimals Especially Hi, DIVIDE, and thanks for your message! There are several ways to tackle this. I’ll start with

## Ask Uncle Colin: The Area Between Two Curves

Dear Uncle Colin, I need to find the area between the graphs of $y=\sin(2x)$ and $y=\cos^2(x)$ in the interval $0 \le x \lt 2\pi$. I’ve found four solutions, but I think that means I need to do five separate integrals! Is there an easier way? Trigonometric Expressions: Double Integration Of

## Ask Uncle Colin: A Fraction of a Square

Dear Uncle Colin, I have been presented with this diagram: the marked points are a third of the way along the sides. I need to know what fraction of the grey square is shaded blue. Any ideas? Somehow Hued Area Defies Evaluation Hi, SHADE, and thanks for your message! There

## Ask Uncle Colin: An Octahedral Angle

Dear Uncle Colin, I have an octahedron, and I’m not afraid to use it! But I am afraid to find the angle between two adjacent faces. How would you do that? Protractors Lack Accuracy Tackling Octahedron Hi, PLATO, and thanks for your message! An octahedron is a shape made from

## There is no Ask Uncle Colin today #strike4blacklives

In support of #strike4blacklives, there is no Ask Uncle Colin today. Please see Shut Down STEM to learn more. I will be spending the time I would have spend working reading Superior by Angela Saini in an attempt to fill some of the gaps in my knowledge. Black lives matter.

## Ask Uncle Colin: Two Numbers Close To 1

Dear Uncle Colin, How do I tell which is larger, $2^{-10^{-20}}$ or $1 - 2^{-10^{20}}$? - Unexpectedly Narrow Interval… Thank You! Hi, UNITY, and thanks for your message! As you’ve doubtless realised, both of those are “pretty much 1”. The question is, which is closer? As usual, there are several

## Ask Uncle Colin: A difference of polynomials

Dear Uncle Colin, Can two polynomials be equal everywhere in some non-trivial interval $[a,b]$ but not equal elsewhere? - Lacking A Good Reasonable Answer, No Good Explanation Hi, LAGRANGE, and thanks for your message! The answer is “no”, but to explain why, I need to give you a few pieces

## Ask Uncle Colin: Flipping Signs

Dear Uncle Colin, Is there a rigorous explanation of why the direction of the inequality changes when you flip the sign? - Fuzzy Logic, Inequality Puzzle Hi, FLIP, and thanks for your message! Here are my best efforts at a rigorous explanation; I’d be interested to read anyone else’s go

## Ask Uncle Colin: A Fractional Equation

Dear Uncle Colin, I’m trying to solve $\frac{x}{x-1} = \frac{1}{x-1}$. I think the answer should be 1, but my teacher disagrees. What do you think? - First Results Are Contradicting Teachers’ - Is One Nonsense? Hi, FRACTION, and thanks for your message! It’s tempting, here, to multiply both sides by

## Ask Uncle Colin: The Empty Product

Dear Uncle Colin, Why does $0! = 1$ and not 0? - Nothing Is Logical Hi, NIL, and thanks for your message! My best explanation for this - by which I mean, the one I can get some people to accept, goes like this: \$4! = 4 \times 3 \times