27 citations · 81 across the 27 of their papers we have counts for
31 papers
Legendre-Teege Reciprocity
Mark B. Villarino
Legendre published the first attempted proof of the law of Quadratic Reciprocity. But, in its final form (1797), it had a gap. Some 125 years later Herman Teege published the first…
A Quadratic Harmonic Approximation
Mark B. Villarino
We obtain the quadratic term in Euler's asymptotic expansion of the nth harmonic number by a simple modification of Young's elementary determination of the linear term.
Archimedes' Revenge
Mark B. Villarino, Joseph C. Várilly, Runze Li
We offer an instructive solution to the problem of computing the volume of the orthogonal intersection of three hyperboloids.
Legendre's Singular Modulus
Mark B. Villarino
We elaborate Legendre's original proof of his discovery of the first singular modulus in the history of mathematics, as well as its appearance in Ramanujan's formula for the arc le…
Hilbert's Proof of His Irreducibility Theorem
Mark B. Villarino, Bill Gasarch, Kenneth Regan
Hilbert's Irreducibility Theorem is a cornerstone that joins areas of analysis and number theory. Both the genesis and genius of its proof involved combining real analysis and comb…
The error in an alternating series
Mark B. Villarino
We give a new proof of Johnsonbaugh's refined error estimates of an alternating series based on an idea of R. M. Young. We also give a new proof of the error estimate and convergen…