Model of the final stellation of the icosahedron

Johannes Max Brückner (5 August 1860 – 1 November 1934) was a German

geometer A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...

, known for his collection of polyhedral models.

Education and career

Brückner was born in Hartau, in the

Kingdom of Saxony The Kingdom of Saxony (german: Königreich Sachsen), lasting from 1806 to 1918, was an independent member of a number of historical confederacies in Napoleonic through post-Napoleonic Germany. The kingdom was formed from the Electorate of Saxon ...

, a town that is now part of

Zittau Zittau ( hsb, Žitawa, dsb, Žytawa, pl, Żytawa, cs, Žitava, :de:Oberlausitzer Mundart, Upper Lusatian Dialect: ''Sitte''; from Slavic languages, Slavic "''rye''" (Upper Sorbian and Czech: ''žito'', Lower Sorbian: ''žyto'', Polish: ''żyto' ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

. He completed a Ph.D. at

Leipzig University Leipzig University (german: Universität Leipzig), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December ...

in 1886, supervised by

Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...

and Wilhelm Scheibner, with a dissertation concerning

conformal map In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in ...

s. After teaching at a grammar school in

Zwickau Zwickau (; is, with around 87,500 inhabitants (2020), the fourth-largest city of Saxony after Leipzig, Dresden and Chemnitz and it is the seat of the Zwickau District. The West Saxon city is situated in the valley of the Zwickau Mulde (German: ' ...

, he moved to the gymnasium in

Bautzen Bautzen () or Budyšin () is a hill-top town in eastern Saxony, Germany, and the administrative centre of the district of Bautzen. It is located on the Spree river. In 2018 the town's population was 39,087. Until 1868, its German name was ''Budis ...

. Brückner is known for making many geometric models, particularly of stellated and

uniform polyhedra In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent. Uniform polyhedra may be regular (if also fa ...

, which he documented in his book ''Vielecke und Vielflache: Theorie und Geschichte'' (''Polygons and polyhedra: Theory and History'', Leipzig: B. G. Teubner, 1900). The shapes first studied in this book include the

final stellation of the icosahedron In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram. That is, every three inter ...

and the

compound of three octahedra In mathematics, the compound of three octahedra or octahedron 3-compound is a polyhedral compound formed from three regular octahedra, all sharing a common center but rotated with respect to each other. Although appearing earlier in the mathemati ...

, made famous by

M. C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for most of his life neglected in t ...

's print ''Stars''. Joseph Malkevitch lists the publication of this book, which documented all that was known on polyhedra at the time, as one of 25 milestones in the history of polyhedra. Malkevitch writes that the book's "beautiful pictures of uniform polyhedra ... served as an inspiration to people later". Brückner died on November 1, 1934 in

Honors and awards

Brückner was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in 1904, 1908, 1912, and 1928.. In 1930–1931 he donated his model collection to

Heidelberg University } Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, ...

, and the university in turn gave him an honorary doctorate in 1931.

Bibliography

* Die Elemente der vierdimensionalen Geometrie mit besonderer Berücksichtigung der Polytope, Jahresbericht des Vereins für Naturkunde zu Zwickau 1893 * Vielecke und Vielflache – Theorie und Geschichte, Teubner, Leipzig, 1900 * Über die gleicheckig-gleichflächigen, diskontinuierlichen und nichtkonvexen Polyeder. dans: Abhandlungen der kaiserlichen leopoldinisch-carolinischen deutschen Akademie der Naturforscher, vol. 86, p. 1–348, Halle 1906.

References

{{DEFAULTSORT:Brueckner, Johannes Max 1860 births 1934 deaths 19th-century German mathematicians Geometers Leipzig University alumni 20th-century German mathematicians Heidelberg University alumni People from Zittau