Entfernung und Zusammenhang

Constantin Carathéodory
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Constantin Carathéodory: Universität München

Chapter Kapitel IV in Vorlesungen über Reelle Funktionen, 1927, pp 191-229 from Springer

Abstract: Zusammenfassung Unter Entfernung von zwei Punkten P und Q des n-dimensionalen Raumes mit den Koordinaten 1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaGabaWdaeaafaqabeGabaaabaWdbiaadcfacaGG6aGaamiEa8aa % daWgaaWcbaWdbiaaigdaa8aabeaak8qacaGGSaGaamiEa8aadaWgaa % WcbaWdbiaaikdaa8aabeaak8qacaGGSaGaeyOjGWRaaiilaiaadIha % paWaaSbaaSqaa8qacaWGUbaapaqabaaakeaapeGaamyuaiaacQdaca % WG5bWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiaacYcacaWG5bWd % amaaBaaaleaapeGaaGOmaaWdaeqaaOWdbiaacYcacqGHMacVcaGGSa % GaamyEa8aadaWgaaWcbaWdbiaad6gaa8aabeaaaaaak8qacaGL7baa % aaa!4F3A! $$ \left\{ {\begin{array}{*{20}{c}} {P:{{x}_{1}},{{x}_{2}}, \ldots ,{{x}_{n}}} \\ {Q:{{y}_{1}},{{y}_{2}}, \ldots ,{{y}_{n}}} \\ \end{array} } \right. $$ versteht man den Ausdruck 2 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiaacI % cacaWGqbGaaiilaiaadgfacaGGPaGaeyypa0JaamyraiaacIcacaWG % rbGaaiilaiaadcfacaGGPaGaeyypa0ZaaOaaaeaacaGGOaGaamiEam % aaBaaaleaacaaIXaaabeaakiabgkHiTiaadMhadaWgaaWcbaGaaGym % aaqabaGccaGGPaWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaiikai % aadIhadaWgaaWcbaGaaGOmaaqabaGccqGHsislcaWG5bWaaSbaaSqa % aiaaikdaaeqaaOGaaiykamaaCaaaleqabaGaaGOmaaaakiabgUcaRi % abl+UimjabgUcaRiaacIcacaWG4bWaaSbaaSqaaiaaikdaaeqaaOGa % eyOeI0IaamyEamaaBaaaleaacaWGUbaabeaakiaacMcadaahaaWcbe % qaaiaad6gaaaaabeaaaaa!5B4A! $$ E(P,Q) = E(Q,P) = \sqrt {{{({x_1} - {y_1})}^2} + {{({x_2} - {y_2})}^2} + \cdots + {{({x_2} - {y_n})}^n}} $$ .

Date: 1927
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DOI: 10.1007/978-3-663-15768-7_5

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