# Infinitely Zooming Circles: Sunday Maths Animations Week 3

Week 3 of my Sunday Maths Animations grew from a puzzle at February’s MathsJam that involved calculating the shaded area in a shape involving infinitely recursing circles. Can you tell which circles are changing in size and which are staying the same?

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# Spiky Feathers and Geometric Fish

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.

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# 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.

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# 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.

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# 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?

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