Nicomedes Conchoid is a curve generated by a device involving two sliding joints.
It can be used in this construction for two mean proportionals (which is Greek for finding a cube root).
See if you can use it to extract cube roots of rational numbers.
This app allows you to adjust the zeros of a quadratic function to match the factorization, then verify them with the general function. The examples include more challenging factorizations (a not equal to 1).
Look at the first three iterations of the Newton Raphson method starting from a point you determine on a function you define.
You'll see that when it's good it's very very good and when it's bad its awful.
If a pendulum's motion is small, its period is the square root of its length divided by g. What happens if the pendulum's motion is not small?
Experiment with these two pendulums. Pull one to about a 20 degree angle to vertical and the other to about a 70 degree angle. Do they have the same period?