期刊： AMERICAN MATHEMATICAL MONTHLY, 2021; 128 (6)
It is a 300-year-old counterintuitive observation of Prince Rupert of the Rhine that in the cube a straight tunnel can be cut through which a second c......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2021; 128 (2)
In this note, we show that each positive rational number can be written uniquely as phi(m(2))/phi(n(2)), where m, n is an element of N, with some natu......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (6)
We show how the determinant of a matrix can be calculated using complex analysis of one variable. We also describe the connection between unitary matr......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 128 (1)
In this note, we prove a graph inequality based on the sizes of the common neighborhoods. We also characterize the extremal graphs that achieve equali......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (9)
In this note, we show that each positive rational number can be written as phi(m(2))/phi(n(2)), where phi is Euler's totient function andmandnare posi......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (9)
Do examples as in the title exist? It depends on how the termRiemann sumis understood. For the standard, left, or right Riemann sums such examples do ......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (1)
Let G be an electrical network graph with vertex set V and edge set E, and let be the effective resistance between vertices i and j of G. Foster's fir......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (2)
A probabilistic proof of a recursion formula for sums of powers is given by using some properties of expectations.
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (10)
The Smarandache function of a positive integer n, denoted by S(n), is defined to be the smallest positive integer j such that n divides the factorial ......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (10)
A decomposition of an integer n as a sum of several fractions is called faithful if no positive integer less than n can be obtained by replacing some ......
期刊： AMERICAN MATHEMATICAL MONTHLY, 2020; 127 (3)
Benford's law is an empirical "law" governing the frequency of leading digits in numerical data sets. Surprisingly, for mathematical sequences the pre......
