Philosophy, Art, Mathematics, and High-Frequency Applications of Triangular Shapes: from Plato to Sierpinski and beyond

Triangles have inspired several fields of interest depending on the discipline and potential applications. This peculiar shape has fascinated ancient philosophy, art, mathematics, and applied sciences. This paper will review triangles from different points of view, focusing on the equilateral shape and its internal complexity generated by the Sierpinski geometry, the symbolic meaning, and the perspective applications in microwave communications. Specifically, microwave planar components and antennas inspired by the Sierpinski geometry will be considered.