Squigonometry or p-trigonometry is a generalization of traditional trigonometry which replaces the circle and Euclidean distance function with the squircle (shape intermediate between a square and circle) and p-norm. While trigonometry deals with the relationships between angles and lengths in the plane using trigonometric functions defined relative to a unit circle, squigonometry focuses on analogous relationships and functions within the context of a unit squircle.

The term squigonometry is a portmanteau of square or squircle and trigonometry. It was used by Derek Holton to refer to an analog of trigonometry using a square as a basic shape (instead of a circle) in his 1990 pamphlet Creating Problems. In 2011 it was used by William Wood to refer to trigonometry with a squircle as its base shape in a recreational mathematics article in Mathematics Magazine. In 2016 Robert Poodiack extended Wood's work in another Mathematics Magazine article. Wood and Poodiack published a book about the topic in 2022.

However, the idea of generalizing trigonometry to curves other than circles is centuries older.

The cosquine and squine functions, denoted as ${\displaystyle \operatorname {cq} _{p}(t)}$ and ${\displaystyle \operatorname {sq} _{p}(t),}$ can be defined analogously to trigonometric functions on a unit circle, but instead using the coordinates of points on a unit squircle, described by the equation:

where ${\displaystyle p}$ is a real number greater than or equal to 1. Here ${\displaystyle x}$ corresponds to ${\displaystyle \operatorname {cq} _{p}(t)}$ and ${\displaystyle y}$ corresponds to ${\displaystyle \operatorname {sq} _{p}(t)}$

Notably, when ${\displaystyle p=2}$, the squigonometric functions coincide with the trigonometric functions.

Similarly to how trigonometric functions are defined through differential equations, the cosquine and squine functions are also uniquely determined by solving the coupled initial value problem

Where ${\displaystyle x}$ corresponds to ${\displaystyle \operatorname {cq} _{p}(t)}$ and ${\displaystyle y}$ corresponds to ${\displaystyle \operatorname {sq} _{p}(t)}$.