Buckling is a failure mode that occurs in columns and other members that are loaded in compression. It is a sudden change ...

Using a notion called integer partitions, mathematicians have discovered a new way to detect prime numbers while also ...

Euler’s identity is a special case of a foundational equation in complex analysis, Euler’s Formula, which he discovered in 1744. It shows how any complex number can be obtained by rotating a ...

Questions about integer solutions to polynomial equations were asked already in Antiquity, by the Greek mathematician Diophantus of Alexandria. Ever since, Diophantine equations have occupied the ...

What do you get for your leap of faith in complex numbers? For one, trigonometry becomes a lot easier. Instead of memorizing several complicated trig formulas, you need only one equation to rule ...

To this end, we proposed transforming the hyperbolic functions via Euler's formula for complex numbers. These transformations enable us to evaluate the relative stability of the system in terms of ...

Fringe projection profilometry (FPP) is a widely utilized technique in 3-D measurement for its high accuracy, speed, and non-contact capabilities. However, it faces significant challenges when ...

It is hard to pick a single most beautiful equation in mathematics, but I think that the Euler product formula would be near the top of any such list. Let me extol the virtues of this formula.

Maxwell’s equations in electromagnetism can be categorized into three dis-tinct groups based on the electromagnetic source when employing quaterni-ons. Each group represents a self-contained system in ...