Been using AI to learn @autodeskfusion.bsky.social so I could design these French cleats to 3D print for invisibly attaching a mantlepiece to the wall. Feels nice and solid, but I can remove it in half a second (you know, for when you take your mantlepiece on holiday...)
Somewhat biased questioning methods here?! And someone at this company (which as far as I can gather is a broker of brokers of insurance companies) will be proudly reporting how many people complimented them (100% of those surveyed!)
It's that time of year again - anyone with students who can do volumes of revolution might like to calculate the volume of a creme egg from my implicit equation:
Thanks for the nudge - yeah, this one includes the 2025 papers as well. Disclaimer: every question is categorized by its main two topics, so some topics may be over- or under- represented depending on whether they comprise the bulk of the question. thechalkface.net/papers/topic...
If we create a distribution from a subset of the normal distribution, we usually lose symmetry. In this one, we can calculate the mean using improper integrals (the centre-of-mass formula turns the Gaussian integral into a simple inspection one), and we get a mean of sqrt(2/pi).
FWIW, chatgpt can't do this... ;)
Tip for anyone who uses Eratosthenes sieve with students to filter for primes: with lines of 21, all the early primes make nice lines (3 and 7, the sneakiest ones, are both vertical lines, and the rest are 45 degree diagonals).
My students wanted to know if they could bring my 'sine ruler' into their A level Maths exam. Not hugely surprised that the answer was 'no', but the reason surprised me! Apparently students aren't even allowed a normal ruler! Is this common knowledge??
www.tinkercad.com/things/dJFfk... just made in tinkercad - this should let you download the stl, or adapt it if you like. I'm thinking of doing a few for my classes (maybe let them keep them if they demo questions at the front...)
I made a thing!
Used @geogebra.org to create 3D versions of polar curves so I could print them. SOO helpful for teaching integration when you can physically see the overlapping regions and trace the shape with your finger. Increasing theta is in the z direction.
Sounds like the start of a simultaneous equations question!
A fractal that splits the unit square into 1/4 + 1/16 + 1/64 + ... = 1/3
The rose curve r = cos(2theta) takes up 1/2 of the space of the unit circle
The cardioid is enclosed within a circle such that the space in the circle but not the cardioid takes up 1/4 of the circle.
A few more obscure ones.
A one-radian sector of a unit circle filling exactly half the unit square.
The curves y = x² and y = √x between x = 0 and x = 1 splitting the unit square into thirds.
Two circles that perfectly fit side by side within a larger circle, each covering a quarter of the total area, leaving behind two 'batman' shapes which must, by symmetry, also cover 1/4 of the total area.
I love breaking the unspoken rule about fraction diagrams (all pieces congruent, not just equal in area). Here are a few of my favourite non-standard representations. A one radian sector fills half the unit square, the curves y = x² and y = √x enclose 1/3 of the square. Can you come up with more?
Quite pleased with this little @geogebra.org animation of mine - shows how the area of a fixed perimeter rectangle changes as we vary the side length.
Rock-Paper-Scissors-Minus-One: what if both players had to reveal what they were about to play in advance? More mathematically interesting than it might sound... youtu.be/Xv7PnN5vVaU
Using p5js to create an animated version of the 'paceometer' seen in a @rorysutherland.bsky.social talk: youtu.be/Bc9jFbxrkMk. editor.p5js.org/thechalkface...
3D CAD image from TinkerCad
Photo of the broken part
Using TinkerCad to design a replacement part for my retractable Stanley knife. At this rate, I only need to break another 40 or 50 household objects and the printer will have paid for itself ;)
I tried a few things before factoring the LHS and bisecting the asymptotes - I knew I was on the right lines because the numbers all worked so nicely! Well constructed :) how would you go about rotating if you don't already know the angle? I thought of trying it but couldn't see how.
I've used the 'any 4 points... parallelogram ' before - nice vectors proof. Never thought to do this though! Thanks
@sparksmaths.bsky.social Been trying to model your Binomial-not-binomial data with some Terrible Python Code (tm). Any chance I can access your weird data? Simulating different drop-out rates and want to chi-squared against your actual data. I attach a @geogebra.org visual to get your attention ;)
