FTP, identify this mathematician who discovered this triangle inequality independent of Schwarz.
His name is given to a random variable with probability density function 1 over the quantity pi plus pi times x squared.  His name also graces a theorem that finds the radius of convergence of a Taylor series in a complex variable with Hadamard.  His name can also be found in a formula for evaluating integrals of analytic functions of complex variables, as well as an inequality that says the dot product of two vectors is less than or equal to the sum of the vectors' lengths.  FTP, identify this mathematician who discovered this triangle inequality independent of Schwarz.
His name is given to a random variable with probability density function 1 over the quantity pi plus pi times x squared.  
Augustin-Louis Cauchy