The Flying Colours Maths blog has been running posts twice weekly since 2012, covering maths from the basics to… well, the most advanced stuff I have a clue about.
Here they all are, sorted by date. Some day, other ways to filter them will be possible.
Dear Uncle Colin, There is a famous puzzle where you’re asked to form 100 by inserting basic mathematical operations at strategic points in the string of digits 123456789. This can be achieved, for example, by writing $1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100$. Brazilian Mathematician Inder J …
On this month’s episode of Wrong, But Useful, @icecolbeveridge and @reflectivemaths are joined by special guest co-host @christianp. This time, we talk about: Christian, who is involved in @mathsjam and the @aperiodical, and has a number of the podcast: 13. He dislikes it because of its times …
Every so often, a puzzle comes along and is just right for its time. Not so hard that you waste hours on it, but not so easy that it pops out straight away. I heard this from Simon at Big MathsJam last year and thought it’d be a good one to share and analyse. I’ve adopted (and slightly …
Dear Uncle Colin, Apparently, you can use L’Hôpital’s rule to find the limit of $\left(\tan(x)\right)^x$ as $x$ goes to 0 - but I can’t see how! - Fractions Required, Example Given Excepted Hi, FREGE, and thanks for your question! As it stands, you can’t use L’Hôpital - …
This is a guest post from @ImMisterAl, who prefers to remain anonymous in real life. It refers to the problem in this post: a semi-circle is inscribed in a 3-4-5 triangle as shown; find $X$. As with any mathematical problem, my first thought was to sort out exactly what I know or can easily find, …
Dear Uncle Colin, I don’t understand why the normal gradient is the negative reciprocal of the tangent gradient. What’s the logic there? -- Pythagoras Is Blinding You To What’s Obvious Hi, PIBYTWO, and thanks for your message! My favourite way to think about perpendicular gradients …
One of my favourite quotes is from Stefan Banach: “A good mathematician sees analogies between theorems. A great mathematician sees analogies between analogies.” This post is clearly in the former camp. I’m fairly sure it’s a trivial thing, but it’s not something …
Dear Uncle Colin, When I have an angle in the second quadrant, I can find it just fine using $\cos^{-1}$ - but using $\sin^{-1}$ or $\tan^{-1}$ gives me an angle in the fourth quadrant. I don’t understand why this is! -- I Need Verbose Explanations; Radians Seem Excellent Hi, INVERSE, and …
Every so often, my muggle side and mathematical side conflict, and this clip from @marksettle shows one of them. My toddler’s train track is freaking me out right now. What is going on here?! pic.twitter.com/9o8bVWF5KO — marc blank-settle (@MarcSettle) April 6, 2016 My muggle side says …
Dear Uncle Colin, I’m struggling a bit with my C4 vectors. Most of it is fine, except when I have to find a point $P$ on a given line such that $\vec{AP}$ is perpendicular to the line, for some known $A$. How do I figure that out? -- Any Vector Insight Lavishly Appreciated Hi, AVILA, and …
This month on Wrong, But Useful, @reflectivemaths and @icecolbeveridge are joined by @evelynjlamb, who is Evelyn Lamb in real life. She writes the Roots Of Unity column for Scientific American. We discuss: How Evelyn got into maths, into writing and into France Evelyn picks the numbers of the …
A nice puzzle this week, via NRICH’s magnificent @ajk44: a semicircle is inscribed in a 3-4-5 triangle as shown. Find $X$. I think it’s a nice puzzle because Alison’s way of doing it was entirely different to mine, but thankfully got the same answer. You might like to try it …
Dear Uncle Colin, I’m struggling to understand why, if you know a triangle has two sides the same, the base angles must be the same. Can you explain? -- I’m Struggling Over Some Coherent Explanation Leveraging Equal Sides Hi, ISOSCELES, and thanks for your message! There are several good …
“Did you know,” asked a student at third-hand1, “that the in-circle of a 3-4-5 triangle has a radius of 1?” That’s the kind of thing I’d normally just fire up GeoGebra to check, but I was in the middle of a podcast! The best I could do was check to see if it …
Dear Uncle Colin, I need to find an angle! ABC is a triangle with median AD, while angles BAD and CAD are 110º and 20º, respectively. What’s angle ACB? -- Angle Being Evasive, LOL Hi, ABEL, and thanks for your question! Even if you’ve used degrees. For heaven’s sake, get a grip. …
“$0.819$,” said the Mathematical Ninja, in as weary a voice as the student used to say “I suppose you’re going to tell me how.” The nunchaku looked a little rusty, and the axe was in need of a good sharpening. The throwing knives could have done with a clear, and the …
Dear Uncle Colin, I’ve been challenged to expand $(x-a)(x-b)(x-c)…(x-z)$ so I can experience the ‘joy of mathematics’. I’ve noticed that towards the end, one of the brackets is $(x-x)$ - does that mean the whole thing is zero? Is that the ‘joy of mathematics they …
Usually, when faced with a word problem, I take the most obvious approach and call it done. But then, sometimes, I read of an alternative approach that makes me go “Whoa.” This is one of those times. Here’s the problem: One day, a person went to a horse racing area. Instead of …
Dear Uncle Colin, The equation $67.5 = 10(1.0915)^{10-n} + 30(1.0915)^{10-2n}$ cropped up in a question. Excel can solve that numerically, but I can’t solve it on paper! Any ideas? Problems Occur When Exponentials Recur Hi, POWER, and thanks for your message! That’s an ugly one. First …
In this episode of Wrong, But Useful: @reflectivemaths and I are joined by special guest co-host Elizabeth A. Williams, who is @realityminus3 in real life (and Zeke, who is Zeke everywhere) Dave picks 367 as number of the episode, as it’s the largest number whose square has digits in strictly …
Everybody sit down. Dominika has an important announcement. So…I have a confession to make. Despite the fact that I write maths comic strips, I’m actually a physicist. Pause for gasps of shock. Yes, terrible, I know. But physics in general has a little gem that I wish more people knew about – Fermi …
Dear Uncle Colin, Is there an easy way to write series in sum notation? I have $1 + \frac{1}{2\sqrt{2}}+\frac{1}{3\sqrt{3}} + …$ but no real clue about how to put it into a compressed form. - Summing Is Giving Me Aneurysms Hi, SIGMA, and thanks for your message! I like to make a little table …
On a Crossnumber Clue In the Chalkdust Crossnumber #4, the deadline for which was last week, one of the first clues I looked at and thought “I can work that out easily enough” was this one: 27. The number of straight lines that go through at least two points of a 10 × 10 grid of points. …
Dear Uncle Colin, I have a fraction, $\frac{x^2-x}{x-1}$, and I want to cancel it down to $x$ - but I’m not sure those are the same. Are they? - Got A Lot Of Interesting Sums Hi, GALOIS, and thanks for your message! The short answer is, yes and no. Everywhere except $x=1$, the two things are …
Right, listen up, everyone. I know you’ve already made your new year’s resolutions, and probably broken most of them by now, but I’ve got one for you to add to your list. It concerns images like this one: Anything with a picture of Einstein on it. Anything that says “only for …
Dear Uncle Colin, I have two points and I want to construct a circle of a given radius that passes through them. Is it possible? -- Every Underspecified Circle Lives Its Dream Hi, EUCLID, and thanks for your message! There are three possible answers to this, depending on the size of the radius …
Some charitable suggestions Hello! I’m going to be a bit more personal than usual with this post; it’s Boxing Day and in the spirit of goodwill to all, I wanted to highlight some of my favourite charities. As you know, the Flying Colours Maths blog is absolutely free of charge, and there …
Dear Uncle Colin, I have a binomial expansion of $(1+x)^\frac{1}{2}$ and need to approximate $\sqrt{5}$. Apparently you need to substitute in $x=\frac{1}{4}$, but I’d have thought $x=4$ was a more obvious choice. What gives? -- Roots Are Dangerous If Understood Sloppily Hi RADIUS, and thanks …
Reports are filtering in to Flying Colours Towers about the mock exams recently taken by year 11s. Words like ‘bloodbath’ and ‘disaster’ feature prominently (my students, I should add, have acquitted themselves well and are in line to be mentioned in dispatches for bravery.) …
Dear Uncle Colin, How do you multiply big numbers like $2158 \times 1812$? I try to do it using the column method or the grid, but I always make mistakes. -- A Desperately Desired Error Reduction Hi, ADDER, and thanks for your message! I’ve been playing with something midway between the grid …