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Brick Patterns

November 27, 2017

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Carnival of Mathematics #157

I checked and it turns out 157 is a prime number . As is its reverse, 751 . It looked prime but there are some tricky ones out there that are designed to catch you out. It turns out 157 is actually a sexy prime , this is when n and n+6 are both prime. In fact it is part of a sexy prime triplet; 151, 157 and 163 are all prime. In researching this I found the neat little proof about the only sexy prime quintuplet : In an arithmetic progression of five terms with common difference 6, one of the terms must be divisible by 5, because the two numbers are relatively prime. Thus, the only sexy prime quintuplet is (5,11,17,23,29); no longer sequence of sexy primes is possible. I also discovered that 157 is the smallest three-digit prime that produces five other primes by changing only its first digit and it is palindromic in 2 different bases. Nice! Anyway, on to the amazing mathsy things that people have been writing about this month... Firstly on his own blog , John D Cook wr...

Similar Triangles Mathematical Art

I have been following along with Annie Perkins ' twitter #MathArtChallenge . She has been posting a starting point each day and whenever I have had time I've joined in. Here is the initial prompt for the similar triangles activity: The #mathartchallenge today is from @shskaercher : similar right triangle patterns. See below for a link to a fabulous video he made explaining. pic.twitter.com/RP1HV4tJJa — Annie Perkins (@anniek_p) April 19, 2020 I had a moment and some coloured paper so I joined in. My explorations can be seen in this twitter thread . I wanted to take a moment to reflect on the process I went through while working on this project. I started out with Annie's examples in my mind. I liked the spiral she had created and I wanted to examine it closely. Why does it spiral? Which sides match? How quickly does it shrink and so on. Once I had the pieces in my hands however I realised there was so many possibilities to explore. I did explore a whole...

L Triominoes

I have been working on creating some interactive content for NRICH over the last few days and it has thrown up some really interesting thoughts. For each interactive I have been considering the following questions: Who is the user? Is it the teacher who might use it for demonstration purposes or is it a student as part of their learning experience? What is the purpose? Is it to demonstrate a principle? Is it to encourage inquiry? Is it a hook? Is it scaffolding for a hard to access problem? Does it add to the experience? Does it self check? Does it need to? If it is a resource to be used in the classroom, does it reduce prep time e.g. printing and laminating and cutting? Should there be printable resources along side the interactivity for flexibility? Here is an interactive I created for the NRICH problem, L Triominoes . Let me know what you think! Which enlargements can you tile with the small L shaped tiles? I also considered accessibility needs,...

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