Background
He spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. The family later moved to Bremen, where his father died early (in 1864).
(Excerpt from Analytische Geometrie der Ebene Das vorlieg...)
Excerpt from Analytische Geometrie der Ebene Das vorliegende Werkchen ist aus den Vorlesungen entstanden, die ich viele Jahre hindurch an der technischen Hochschule in Hannover gehalten habe, und es haben mir bei seiner Abfassung in erster Linie die Bedurfnisse des Technikers vorgeschwebt Mir scheint, da Bdie analytische Geometrie, wie sie an den technischen Hochschulen gelehrt wird, vor allem das Handwerkszeug liefern soll, mit dem man geometrische Verhaltnisse rechnend verfolgen kann. Ich habe daher beim Unterricht groBen Nachdruck darauf gelegt, zu zeigen, wie man. mit Hilfe der Koordinaten alle Konstruktionen, die man auf dem Papier mit Zirkel und Lineal ausfuhrt, auch rechnen kann, und wie man die Rechnung bei den verschiedenen Aufgaben am Zweck maBigsten einrichtet. Diesen Gegenstand behandelt der zweite Ab schnitt des vorliegenden Werkes, nachdem im ersten der Begriff des Vektors und die Gleichung der geraden Linie und des Kreises be sprochen sind. Der dritte Abschnitt behandelt die linearen Transformationen der Koordinatenoder geometrisch gesprochen die Ver schiebung und Drehung ebener Figuren, die ahnliche Anderung, die afline Anderung und endlich die perspektivische Anderung. Durch diese Transformationen werden die Kegelschnitte aus dem Kreise erzeugt, und das Studium cler linearen Transformationen gibt Veranlassung, die Grundeigenschaften der Kegelschnitte aus denen des Kreises abzuleiten. Der vierte Abschnitt behandelt die homogenen Koordinaten und geht damit vielleicht uber die nachsten Bedurfnisse des Technikers hinaus. Aber der hohere Standpunkt, zu dem man durch die homogenen Koordinaten aufsteigt, laBt die Dinge so viel einfacher erscheinen, da Bdie Muhe, die man darauf verwendet, sich reichlich lohnt. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
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mathematician physicist university professor
He spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. The family later moved to Bremen, where his father died early (in 1864).
In 1880, he received his Doctor of Philosophy in mathematics at Berlin, where he studied under Karl Weierstrass.
He was co-developer and co-eponym of the Runge–Kutta method (German pronunciation: ), in the field of what is today known as numerical analysis. In 1886, he became a professor at the Technische Hochschule Hannover in Hanover, Germany. His interests included mathematics, spectroscopy, geodesy, and astrophysics.
In addition to pure mathematics, he did a great deal of experimental work studying spectral lines of various elements (together with Heinrich Kayser), and was very interested in the application of this work to astronomical spectroscopy.
In 1904, on the initiative of Felix Klein he received a call to the Georg-August University of Göttingen, which he accepted. There he remained until his retirement in 1925.
(Excerpt from Analytische Geometrie der Ebene Das vorlieg...)
(Leopold is delighted to publish this classic book as part...)
(This book was digitized and reprinted from the collection...)