Karl Theodor Reye

Background

Karl Theodor Reye was born on June 20, 1838, in Ritzebüttel, Germany, the son of Amalia Augustina Beckmann and Georg Wilhelm Reye. Georg Reye had been born in Ritzebüttel and he lived there all his life, being a local businessman.

Education

Theodor attended school in Hamburg, being a pupil at the famous Johanneum. He then studied mechanical engineering at the Polytechnikum in Hannover before continuing his studies at the Polytechnikum in Zürich (this institution was later called the Eidgenössische Technische Hochschule or the Swiss Federal Institute of Technology). In Zürich, Reye was taught by Kurt Culmann (1821-1881), who had held the Chair of Engineering Sciences since the Polytechnikum was founded in 1855. He received his doctorate at Gottingen in 1861 with a dissertation on gas dynamics.

Career

After qualifying as a lecturer at Zurich in 1863, he remained there until 1870 as a Privaldozent in mathematical physics. Following a short stay in Aachen came his most productive years 1872-1909, when he was a professor of geometry at the University of Strasbourg. He remained in Strasbourg until after World War I, when he moved to Wurzburg.

In his younger years, Reye published works on physics and meteorology - for example, a book on cyclones (1872). The two-volume first edition of his Geomelrie der Lage appeared in 1866 and 1868. He remained faithful throughout his life to the synthetic geometry presented in this work. His interest in geometry had been stimulated by analytical mechanics, and Culmann, the founder of graphic statics, had drawn his attention to Staudt’s works on geometry. Staudt’s books were considered very difficult to read; Reye’s Geomelrie der Lage, the fifth edition of which appeared in 1923, was easily comprehended.

Reye treated in detail the theory of conics and quadrics and of their linear systems, that of third-degree surfaces and some of the fourth degree, as well as many quadratic congruences and aggregates taken from line geometry.

Reye was the founder of that portion of projective geometry that E. A. Weiss later called point-series geometry. In a series of writings, Reye treated linear manifolds of projective plane pencils and of collinear bundles or spaces. Later these investigations were easily interpreted multidimensionally by means of the geometry of Segre manifolds. Reye refused to speak of true geometry when dealing with spaces of more than three dimensions. He was satisfied to interpret multidimensional relations in P2 and P3, that is, he treated the geometries of lines and spheres in P3 as four-dimensional geometries.

In 1878 Reye published a short work on spherical geometry, the only one of his mathematical writings, besides the Geomelrie der Lage, to appear as a separate publication.

Achievements

• Reye's major achievement was in becoming the founder of a portion of projective geometry that later was called point-series geometry. His name is linked to the axial complex of a second-degree surface, and he generalized the polarity theory of algebraic curves and surfaces, introducing the concept of polarity. He is best known for his introduction of configurations in the second edition of his book, Geometrie der Lage (Geometry of Position, 1876).
  
  Reye also developed a novel solution to the following three-dimensional extension of the problem of Apollonius: Construct all possible spheres that are simultaneously tangent to four given spheres. The Reye configuration of 12 points, 12 planes, and 16 lines is named after him.
  
  Reye's work on linear manifolds of projective plane pencils and of bundles on spheres influenced later work by Corrado Segre on manifolds.

Works

More photos

• book

  • Lecons Sur La Geometrie De Position

    (Part 2)

    1882
  • Synthetische Geometrie der Kugeln und linearen Kugelsysteme: mit einer Einleitung in die analytische Geometrie der Kugelsysteme 1879
  • Geometry of position 1898
  • Lectures on The Geometry of Position 1898

Personality

Quotes from others about the person

• Karl Geiser writes: "In the autumn of 1918, Reye decided to return to the old Germany, hoping that he would be able to spend the last days of his life in peace and quiet. Unfortunately, the relocation created various difficulties, which, when an order was rescinded by a counter-order, turned into the most repugnant delays and eventually forced the eighty-year-old to carry out the complicated relocation without the help of his son for which he had hoped. At least he could settle down in the comfortable home in Würzburg, which a son-in-law had chosen for him. In May 1919 he was able to celebrate his golden wedding; but the shocks, disappointments and the agitation of the previous months had such a strong after-effect that he fell victim to them a few weeks after the anniversary."

Connections

While in Zürich, Reye married Marianne Sattler (1847-1933) in 1868. They had five children: Katharina (born 1869), Franciska (born 1871), Wilhelm (born 1873), Charlotte (born 1875) and Otto (born 1880).

Father:

Georg Wilhelm Reye

1799-1850

Mother:

Amalia Augustina Beckmann

1810-1857

Brother:

Auguste Reye

born 1831

Brother:

Wilhelm Reye

born 1833

Brother:

Julius Reye

born 1834

Brother:

Adolf Reye

born 1836

Brother:

Otto Reye

born 1840

Brother:

Arnold Reye

born 1841

Sister:

Amilie Reye

born 1845

Sister:

Antoine Reye

born 1845

Sister:

Emilie Reye

born 1847

Wife:

Marianne Sattler

1847-1933

Daughter:

Katharina Reye

born 1869

Daughter:

Franciska Reye

born 1871

Son:

Wilhelm Reye

born 1873

Daughter:

Charlotte Reye

born 1875

Son:

Otto Reye

born 1880

collaborator:

Elwin Christoffel

Both Christoffel and Reye considered it their patriotic duty to assist in making the University of Strasbourg a German university.

colleague:

Joseph Wolfgang von Deschwanden

Reye had been an assistant to Deschwanden (1819-1866), the professor of descriptive geometry, and taught descriptive geometry at Zürich after Deschwanden became ill.

teacher:

Georg Riemann

While undertaking research at Göttingen, Reye had attended inspiring lectures on partial differential equations by Bernhard Riemann.

teacher:

Kurt Culmann

1821-188, in Zürich, Reye was taught by Kurt Culmann (1821-1881), who had held the Chair of Engineering Sciences since the Polytechnikum was founded in 1855.

References

• Dictionary of Scientific Biography volume 11
  1975
• Lectures on the geometry of position. By Dr. Theodor Reye
  2005