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Wallet

In mathematics , the wallet is a curve that has been studied and named by Gabriel Cramer in 1750.

Equations

Cartesian equation: $c ^ 2 y = ax + bx ^ 2 \ sqrt {c ^ 2 - x ^ 2} \ quad \ quad c = bx ^ 2y ^ 2 - ax \ sqrt {c ^ 2-x ^ 2} \, with \ quad c = \ sqrt {a ^ 2 + b ^ 2}$ .

Cartesian parametrization: $\ Left \ {\ begin {matrix} x = a \ cos tb \ sin t \ \ y =- (\ sin t) x \ \ 0 \ le t \ le 2 \ pi \ end {matrix} \ right. (\ Sin t = - \ tan \ theta)$