The optimal known packing of 17 equal squares into a larger square - i.e. the arrangement which minimises the size of the large square. (I saw a copy my old post

https://twitter.com/KangarooPhysics/status/1469090624536293376

was getting picked up again, and thought people might like a higher resolution image of this beauty.) Generated from the data in link.springer.com/article/10.100…

Here's a fun little kinematic toy that's easy to make - an equilateral orthogonal hexagon linkage with 1 degree of freedom: Just take 6 squares of stiff cardboard and tape them together along half the length of their edges. You can start with them flat and work your way round in a spiral. To make it a bit stronger, you can put tape on both sides of each hinge.

The best known packings of N equal circles into a square and a circle. Best in the sense that they are the arrangements which maximise the circle radius without overlaps.
Patterns don't always hold, and the most symmetrical solution isn't always best.
Coordinate data and references for all these can be found at packomania.com

To give a bit of explanation of this and some of the knot surface animations I've posted previously-
The solid angle of a curve is the signed area inside its projection onto a unit sphere (note the flip as it moves around the outside).