The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

What is it that makes Euler's identity, e]iPi + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most ...

Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so ...

In this paper, an attempt is made to apply the Euler's Totient function and Euler's theorem to organizing calculations of the period of the modular exponentiation function inspired by Shor's quantum ...

A recent entry in the visitor’s book of the James Joyce Tower & Museum in Sandycove, Dublin, perplexed the Friends of Joyce’s Tower, the volunteers who run the museum. The entry, reproduced as the ...

Abstract: This paper is about Jacobi’s triple product identity and Euler’s pentagonal number theorem. To be specific, it gives the proofs of Jacobi’s triple product identity via Gaussian polynomials ...

1 Department of Biomedical Engineering, Toyo University, Saitama, Japan. 2 Department of Mechanical Engineering, Toyo University, Saitama, Japan. In this paper, we calculate the absolute tensor square ...