2014/06/01 by Ákos G. Horváth · 1 citation
Mathematics · Engineering · #Mathematics and Applications #History and Theory of Mathematics #Mechanics and Biomechanics Studies #Mathematics #Hyperbolic triangle #Euclidean geometry #Plane (geometry) #nobody #Hyperbolic geometry #Economic shortage #Order (exchange) #Mathematical analysis #Geometry #Computer science #Differential geometry
paper · doi:10.1556/sscmath.51.2014.2.1276
openalex publication_date 2014/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
More than two centuries ago Malfatti (see [9]) raised and solved the following problem (the so-called Malfatti’s construction problem): Construct three circles into a triangle so that each of them touches the two others from outside moreover touches two sides of the triangle too. It is an interesting fact that nobody investigated this problem on the hyperbolic plane, while the case of the sphere was solved simultaneously with the Euclidean case. In order to compensate this shortage we solve the following exercise: Determine three cycles of the hyperbolic plane so that each of them touches the two others moreover touches two of three given cycles of the hyperbolic plane .