The astroid curve is an example of a hypocycloid – a curve generated by rotating a fixed point on a small circle around a larger circle. Specifically, it is a hypocycloid with four cusps.
Continue reading Spiky Feathers and Geometric Fish
Hyperbolic Paraboloid in Matchmakers
For this year’s MathsJam Bakeoff I made a hyperbolic paraboloid out of matchmakers. For anybody who doesn’t know, matchmakers are thin chocolate sticks with crunchy bits, traditionally mint but now available in orange, salted caramel and possibly other flavours. They are delicious even when they are not being used for maths.
Continue reading Hyperbolic Paraboloid in Matchmakers
Rupert Polyhedra: Dodecahedron
A polyhedron is Rupert if you can cut a hole in it that’s large enough for an identical polyhedron to fit through. I’ve talked about the Rupert tetrahedron, the Rupert cube and the Rupert octahedron. Today it’s the dodecahedron.
Continue reading Rupert Polyhedra: Dodecahedron
Carnival of Mathematics 188
Parametric T-shirts
I’m excited to share my new TeeMill site, selling T-shirts based on graphs of parametric equations.
There are three designs currently available, and all can be bought in loose fit or fitted, and with or without the equations that created the design displayed underneath.
You can also find GeoGebra files, where you can play with the graphs of the equations yourself, here.
Spin, Laugh and Dance
I’d like to introduce you to the graph of $x=\sin(f_1t)e^{d_1t}$, $y=\sin(f_2t)e^{d_2t}$, a curve that spins, laughs and dances.
Continue reading Spin, Laugh and Dance
The Carpeted Hexaflake
I’m trying to imagine a solid. From the front, it looks like a Koch snowflake. From the top, it looks like a Sierpinski carpet. How might it look from the side? How would it feel? Is it even possible?
Continue reading The Carpeted HexaflakeCube Shadows
Drag the sliders to rotate the cube and see how its shadow changes.
Continue reading Cube ShadowsWhat’s Going On with my Knees?
A poem that’s mostly about nerves, and a little bit about lowest common multiples.
Continue reading What’s Going On with my Knees?
Rupert Polyhedra: Octahedron
A polyhedron is Rupert if you can cut a hole in it that’s large enough for an identical polyhedron to fit through. I’ve already talked about the Rupert tetrahedron and the Rupert cube. Now it’s the turn of the octahedron.
Continue reading Rupert Polyhedra: Octahedron