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Flying Colours Maths helps make sense of maths at A-level and beyond.
Site URL: www.flyingcoloursmaths.co.uk/
Feed URL: blog.flyingcoloursmaths.co.uk/feed.xml
Posts: 10
Followers: 1
Ask Uncle Colin: A Factor of 77
https://www.flyingcoloursmaths.co.uk/ask-uncle-colin-a-factor-of-77/
Published: October 30, 2023 00:00
Dear Uncle Colin, I want to show that $(a^{60} - b^{30})ab$ is a multiple of 77 for all integers $a$ and $b$. Where do I even begin? Factoring Expression, Reasonable Methods Arenāt Trivial
A problem from the future
https://www.flyingcoloursmaths.co.uk/a-problem-from-the-future/
Published: October 23, 2023 00:00
A nice puzzle from reddit:
Simultaneous powers
https://www.flyingcoloursmaths.co.uk/simultaneous-powers/
Published: October 16, 2023 00:00
Todayās problem:
Random Number Challenge
https://www.flyingcoloursmaths.co.uk/random-number-challenge/
Published: October 8, 2023 23:00
You have 20 spaces, which you want to fill with numbers, in order. You will be given 20 random numbers between 0 and 999 (inclusive), each of which you must place into a space as soon as you see it. If you can place all 20 while keeping them in order, youā¦
Ask Uncle Colin: Integrating sin(x)
https://www.flyingcoloursmaths.co.uk/ask-uncle-colin-integrating-sin-x/
Published: October 1, 2023 23:00
Dear Uncle Colin How would you prove that the area under the curve $y=\sin(x)$ from $x = 0$ to $x=\pi$ was exactly 2? āCause I Realised Calculus Lacked Explanation
An infinite ODE
https://www.flyingcoloursmaths.co.uk/an-infinite-ode/
Published: September 25, 2023 00:00
Via reddit, a challenge to solve:
How do you prove that $\pi < \sqrt{10}$?
https://www.flyingcoloursmaths.co.uk/prove-pi-smaller-than-root-10/
Published: September 18, 2023 00:00
In the course of solving a puzzle, I had cause to assert that $\pi <\sqrt{10}$. I mean, thatās just true: I know that $\sqrt{10} \approx 3.16$ and $\pi \approx 3.14$; I also know that $\pi < \frac{22}{7}$ and that $\left(\frac{22}{7}\right)^2 < 10$. Butā¦
Randomer and randomer
https://www.flyingcoloursmaths.co.uk/randomer-and-randomer/
Published: September 11, 2023 00:00
A post on Hacker News descended into an argument in the comments ((finish the sentence before you go āoh, quelle surpriseā, please.)) about whether random(random()) and random() * random() gave different distributions.
Ask Uncle Colin: An Ugly Sum
https://www.flyingcoloursmaths.co.uk/ask-uncle-colin-an-ugly-sum/
Published: September 3, 2023 23:00
Dear Uncle Colin, As a challenge, I need to work out $1024 - 512 + 256 - \dots + 1$, but Iām getting mixed up on the fractions and signs. Can you help? Colin, Help! Answer Largely Lacking for Evaluating Negative Geometric Expression
Powers of 2 and logs base 10
https://www.flyingcoloursmaths.co.uk/powers-of-two-and-logs-base-10/
Published: August 28, 2023 00:00
A trick I learned from Colin Wright: