Antes de Memmo, mis apuntes estaban dispersos en PDFs. Ahora, un espacio de trabajo lo reúne todo y veo exactamente lo que me queda por estudiar.
In this book, we present the topic of chains of circles — a subject within Plane Euclidean Geometry — in a complete and unified manner. These chains are generally classified into two main groups: (1) Pappus chains and (2) Steiner chains. While many results on these chains have been published since ancient times, including some with practical applications, they remain scattered across the literature. To date, no comprehensive and cohesive exposition has been compiled in a single volume.
This book aims to fill that gap by providing a thorough treatment of the topic, along with new research that leads to several important findings. Among these are an extension of the famous Archimedes formula to general chains, newly discovered properties of the chains, and their intriguing connections with conic sections — which serve as geometric loci of points related to the chains.
To benefit fully from the material, the reader should be familiar with the fundamentals of Euclidean plane geometry, similarity and inversion theory, conics, radical axes of circles, and related concepts. For convenience, Chapter 4 includes a summary of key facts that readers may reference while studying this material. Where details have been omitted or computations shortened, we provide sufficient hints, instructions, and references for the interested reader to reconstruct the full arguments. In addition, we pose a few new questions for readers who may wish to explore and publish further work on the subject.
Beyond inversion, the topics explored here include Descartes's Theorem for four mutually tangent circles (not meeting at a single point) and the classical Stewart's Theorem in triangle geometry. We also take the opportunity to correct an error that has persisted in the classical bibliography.
Contents:
Readership: Undergraduate students, graduate students, educators, engineers, and math enthusiasts with an interest in Euclidean geometry.
Antes de Memmo, mis apuntes estaban dispersos en PDFs. Ahora, un espacio de trabajo lo reúne todo y veo exactamente lo que me queda por estudiar.
Los resúmenes de Memmo son oro antes de los exámenes. No tengo que releer 800 páginas dos semanas antes, solo las partes importantes.
El chat de IA me ha salvado la noche antes de un examen más de una vez. Sigo preguntando hasta que lo entiendo, sin esperar a que un grupo de estudio responda.
Los cuestionarios aciertan exactamente lo que necesito saber. Memmo registra dónde me atasco, así que solo practico lo que vale la pena.
Las flashcards con repetición espaciada son magia. Memmo sabe cuándo estoy a punto de olvidar algo y me lo recuerda.
Los pódcasts de IA son mis favoritos. Los escucho de camino a la universidad y obtengo un resumen sin tener que sentarme frente a un ordenador.
Handbok i kvalitativa metoder
281 kr
Hållbar utveckling: en introduktion för ingenjörer och andra problemlösare
334 kr
Brymans Samhällsvetenskapliga metoder
390 kr
Projektledning
491 kr
Den orättvisa hälsan: om socioekonomiska skillnader i hälsa och livslängd
326 kr
Organizational Leadership
429 kr
Vetenskapsteori för nybörjare
196 kr
På väg mot läraryrket
172 kr
Det sociala livet i skolan: Socialpsykologiska perspektiv
253 kr
Betygsättningens didaktik
151 kr
Personality
402 kr
Studying Leadership
404 kr
Managing Innovation
477 kr
Introduktion till samhällsvetenskaplig metod
347 kr
The Psychology of Sex and Gender
698 kr
Evidens och kunskap för socialt arbete
207 kr
Introduction to Leadership
605 kr