# Schwarz-Christoffel: piliero en rivero (a pillar on a river)

## TL;DR

This paper discusses conformal Schwarz-Christoffel transformations mapping the complex upper half plane to polygonal regions, focusing on coupling upper and lower half-plane maps and applying this to fluid motion analysis.

## Contribution

It introduces a method for coupling maps of the upper and lower half-planes in Schwarz-Christoffel transformations with a clear angle definition.

## Key findings

- Effective coupling of upper and lower half-plane maps
- Application to fluid motion modeling
- Clarification of complex angle definitions

## Abstract

La transformoj de Schwarz-Christoffel mapas, konforme, la superan kompleksan duon-ebenon al regiono limigita per rektaj segmentoj. Cxi tie ni priskribas kiel konvene kunigi mapon de la suba duon-ebeno al mapo de la supera duon-ebeno. Ni emfazas la bezonon de klara difino de angulo de kompleksa nombro, por tiu kunigo. Ni diskutas kelkajn ekzemplojn kaj donas interesan aplikon pri movado de fluido. ------- Schwarz-Christoffel transformations map, conformally, the complex upper half plane into a region bounded by right segments. Here we describe how to couple conveniently a map of the lower half plane to the map of the upper half plane. We emphasize the need of a clear definition of angle of a complex, to that coupling. We discuss some examples and give an interesting application for motion of fluid.