Mathematical headaches? Problem solved!
Hi, I'm Colin, and I'm here to help you make sense of maths
Mathematical headaches? Problem solved!
Hi, I'm Colin, and I'm here to help you make sense of maths
A nice puzzle by way of @benjaminleis: This AIME problem is fun: pic.twitter.com/DhbviTqnqr — Benjamin Leis (@benjamin_leis) February 2, 2020 In case you can’t read that, we need to find the sum of the digits in $N = 9 + 99 + 999 + 999\dots999$, where the last number consists
Read More →Dear Uncle Colin, I want to stretch my Year 12 Further Maths class - what extra-curricular topics would you recommend? Something To Really Engage Their Creative Reasoning Hello, STRETCH, and thanks for your message! How excellent to be looking beyond the curriculum for ways to engage and develop your young
Read More →I’m in the process of clearing out old bookmarks, and stumbled on this puzzle from @jase_jwanner: Prime or not prime? No calculators allowed!a. 23567897614^2 - 1b. 34564344^3 -1c. 76543556556625731d. 345643554^{10} - 169 — Jase (@jase_jwanner) August 27, 2016 I shall give you a moment to ponder these, and put my
Read More →Dear Uncle Colin, I’ve figured out that $x^{x^{x^{\dots}}} = 2$ when $x = \sqrt{2}$, but I’m struggling to make sense of the function - it seems to have a vertical gradient when $x = e^{\frac{1}{e}}$, but it doesn’t seem to have what I think of as an asymptote there. What
Read More →“We’ve been through this a hundred times, sensei. I say something like ‘$10^{1.35}$. Hm, let me get my calculator’ and you torture me in some unspeakable way an blurt out the answer…” “22.4” “… thank you, especially for refraining from the torture bit.” “You’re welcome.” “Then, of course, you tell
Read More →Dear Uncle Colin, On a recent revision course, my tutor couldn’t integrate $\int_0^{\piby2} \frac{\sin(2\theta)}{1+\cos(\theta)} \d \theta$. Can you? - Reasonable Expectation For University’s Nameless Don? Hi, REFUND! Far be it from me to disparage a fellow professional’s integration skills, especially in the heat of the moment; I frequently mistake $2\times
Read More →I’m a big fan of the doodle. My lecture notes, even my schoolbooks, are covered with geometric patterns and impossible shapes and simple cartoons. Today’s entry in the Dictionary of Mathematical Eponymy started jumped out of Stanislaw Ulam’s notes while he was listening (according to Martin Gardner) to a ‘long
Read More →Dear Uncle Colin I wonder: at what height is the volume of a cone above that height equal to the volume below? What about the surface area? Are there any cones where it’s the same height? Finally Researching Uniformly Splitting Things Up, Mate Hi, FRUSTUM, and thanks for your message!
Read More →I’m on a bit of a continued fractions jaunt at the moment, as they’re my current “oo! That’s a tool I haven’t played with enough, and that I think might be interesting!” One of their applications (surprisingly to me) is to answer the question “A survey firm says ‘82.43% of
Read More →Dear Uncle Colin, Can you explain why $\frac{a+b}{c + d}$ is between $\frac{a}{c}$ and $\frac{b}{d}$? - Grinding Out Solid Proof Explaining Rationals Hi, GOSPER, and thanks for your message! As per usual, there are several methods to show this. I’m going to assume (since it hasn’t been stated) that $\frac{a}{c}$
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