Posted in ask uncle colin, circles, geometry.

Dear Uncle Colin, I’m told there are two circles that touch the x-axis at the origin and are also tangent to the line $4x-3y+24=0$, but I can’t find their equations. Any ideas? - A Geometrically Nasty Example Seems Impossible Hi, AGNESI, and thanks for your message! I’m going to start

Read More →Via nRICH: A circle touches the lines OA extended, OB extended and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle. $\blacksquare$

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Posted in ask uncle colin.

Dear Uncle Colin, In my non-calculator paper, I’m told $\cos(\theta) = \sqrt{\frac{1}{2}+ \frac{1}{2\sqrt{2}}}$ and that $\sin(\theta) = -\left(\sqrt{\frac{1}{2}-\frac{1}{2\sqrt{2}}}\right)$. Given that $0 \le \theta \lt 2\pi$, find $\theta$. I’ve no idea how to approach it! - Trigonometric Headaches Evaluating This Angle Hi, THETA, and thanks for your message! My third thought

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Posted in ninja maths.

“I would have to assume the teacher means $\sqrt[4]{81}$ instead.” “That’s as may be. But $4\ln(3)$ is 4.4 (less one part in 800). A third of that is $1.4\dot 6$, less one part in 800, call it 1.465.” “So you’d do $e$ to the power of that?” “Indeed! $\ln(4)$ is

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Posted in ask uncle colin.

Dear Uncle Colin, I have to work out $\cot\left( \frac{3}{2}\pi \right)$. Wolfram Alpha says it’s 0, but when I work out $\frac{1}{\tan\left(\frac{3}{2}\pi\right)}$, my calculator shows an error. What’s going on? - Troublesome Angle, No? Hi, TAN, and thanks for your message! The cotangent function is slightly unusual in that it

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Posted in arithmetic.

I’m a Big Fan of both @standupmaths and @sparksmaths, two mathematicians who fight the good fight. I was interested to see Ben tackling the square root of 3 using the ‘long division’ method. It’s a method I’ve tried hard to love. It’s a method I just can’t bring myself to

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Posted in ask uncle colin.

Dear Uncle Colin, I need to evaluate $\int_0^{\piby2} \frac{1}{1+\sin(x)}\dx$ but I end up with $\infty - \infty$ and that’s no good! How should I be doing it? Big Integral, Not Exactly Trivial Hi, BINET, and thanks for your message! This is a fun problem! I can think of several possible

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Posted in dome.

While my thesis has the word ‘topology’ in its title, at heart I’m a vectors-in-3D person. Give me matrices, not manifolds! So today’s entry in the Dictionary of Mathematical Eponymy is one that brings me joy. What is Wahba’s Problem? The mathematical statement of Wahba’s Problem is as follows: Given

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Posted in ask uncle colin.

Dear Uncle Colin, How would you solve $5^{2x+2} + 16\cdot15^x -9^{x+1} = 0$? Doesn’t It Seem Genuinely Unpleasant? Insoluble? Strange, Even? Hi, Disguise, and thanks for your message! It turns out that this does have solutions! The trick is to ask “what would make it less unpleasant?” - and given

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Posted in dialogue.

I could probably have framed this post as an “Ask Uncle Colin”, but it feels somehow different, so I’m going to do it as a Monday post. My blog, my rules. On Twitter, @sharanjit asked: I had a point in my education where maths went from being easy to suddenly

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