Posted in ask uncle colin.

Dear Uncle Colin, In Basic Maths For Dummies, you mention a method for multiplying numbers from 6 × 6 to 10 × 10 on your fingers. It's almost magical! Why does it work? -- Does It Guarantee Interesting Times Sums? Hello, DIGITS, I'm glad you're finding the book helpful! The

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Posted in ask uncle colin.

Dear Uncle Colin1, Supposing $\pi$ were to start repeating -- how long would it take to confirm that it actually was? - Recurring Over Uncanny Numbers of Decimals Dear ROUND2 , Great question! $\pi$, as I'm sure you know, is a number close to 3.1416 that represents the ratio between

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Posted in ask uncle colin, matrices.

Dear Uncle Colin, I'm working on a (3D) computer graphics course, and my notes have some equations in that I don't understand. I have a point light at (4D) position $\vec L$, an object translated by a 4D matrix $\bb M$ and a (4D) point on the surface at $\vec

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Posted in ask uncle colin, modulus.

Dear Uncle Colin, I have an inequality that involves two pairs of modulus signs, and I can't make head nor tail of it. It's $\left| \left| 3 - x \right| - 2x\right| \le 9$. Please help! -- Absolutely Bewildered, Driven Absolutely Barmy Well, ABDAB, I'd normally recommend sketching something like

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Posted in ask uncle colin, geometry.

Dear Uncle Colin, I've carelessly interlocked a couple of regular pentagons together like this and need to find the area of the overlap because of reasons. For still other reasons, I don't want to use trigonometry. How do I negotiate my way through this minefield? Trigonometry's Always Overrated Hi, TAO,

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Posted in ask uncle colin, logarithms.

Dear Uncle Colin, I have a problem with a limit! I need to figure out what $\left( \tan \left(x\right) \right)^x$ is as $x \rightarrow 0$. -- Brilliant Explanation Required Now! Our Understanding's Limited; L'Hôpital's Inept Right, BERNOULLI, stop badmouthing L'Hôpital and let's figure out this limit. It's clearly an indeterminate

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Posted in ask uncle colin, number theory.

Dear Uncle Colin, I've been asked to find the last two digits of $19^{100}$. For what reason, I cannot tell. However, my calculator bums out before I get to $19^{10}$! -- Many Other Digits, Unfindable Last Ones Hi, there, MODULO! What do you know, the clue to your problem is

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Posted in ask uncle colin.

Dear Uncle Colin, I've been struggling to get my head around what happens if you chop infinity in two? Is half of infinity still infinity? Help! How Infinity Lies Beyond Every Reasonable Theory Hi, HILBERT1 The short answer is yes: halving infinity gives you infinity. (Once you get to infinity,

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Posted in ask uncle colin, revision.

Dear Uncle Colin I'm in year 9 and really annoyed: my little sister keeps beating me in maths tests! I've only ever beaten her once, and even then only by one point. It's shameful! I always do the exercises in the book and work really hard at revising, but I

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Posted in ask uncle colin, number theory.

Dear Uncle Colin, I wanted to work out $3^{41}\mod 13$: Wolfram|Alpha says it's 9, but MATLAB says it's 8. They can't both be right! What gives? MATLAB Obviously Doesn't Understand Logical Operations Hi, MODULO! First up, when computers disagree, the best thing to do is check by hand. Luckily, you

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