C\'omo obtener curvas con formas predeterminadas a partir de circunferencias

TL;DR

This paper introduces methods to generate algebraic curves with predetermined shapes from circles using classical algebraic techniques like blow-up and blow-down.

Contribution

It demonstrates how to produce both known and new algebraic curves from circles through reciprocal algebraic transformations.

Findings

Successfully generated various algebraic curves from circles.

Identified new algebraic curves with specific shapes.

Applied classical algebraic geometry methods effectively.

Abstract

We produce several algebraic curves, some well--known, some new, out of circles, by means of two classical (mutually reciprocal) algebraic methods: blow--down and blow--up.