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**Summary:**

- **Pi's Evil Twin**: There is a mathematical constant, often referred to as the lemniscate constant, which acts similarly to pi in certain equations but is not equal to it. It is denoted by ϖ (varpi) and has a value of approximately 2.622057554291118.
- **Lemniscate Functions**: Corresponding to the sine and cosine functions, there are lemniscatic sine (sl) and lemniscatic cosine (cl) functions, which are associated with the lemniscate curve rather than the circle.
- **Gauss's Constant**: The arithmetic-geometric mean of 1 and √2 is equal to π/ϖ, known as Gauss's constant.
- **Higher Dimensions**: There are generalizations of these constants and functions (ϖn) related to hyperelliptic curves with n branch points.
- **Book Reference**: "Squigonometry: The Study of Imperfect Circles" by Poodiack and Wood discusses these topics in more detail, connecting them to the modular group and concrete mathematics.
