Formulas for Squircles

The Desmos online graphing calculator is useful for visualizing mathematical equations such as the squircle.

The formula for the red circular arc is for comparison. The blue line is the squircle and the orange and green lines are higher order shapes. Odd values produce tangents. Closer inspection of the higher order shapes reveals a gap above of the x-axis. Why is this?

Additionally, the calculator supports sliding variables so the numbers 2,4,6,8 above can be replaced by the variable "a" in a single equation and assigned a stepping value of 2. (Also try 0.2)

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