5000 Jahre Geometrie

Abstract

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Symmetric Matrices: Theory and Applications

“…this shows all other assertions but the last one. We see also that a form [α, β, γ] is properly equivalent with [α, β + 2α, α + β + γ] and analogously (by 25 Example 31 now shows that there are exactly two. 26 and any other descriptions of composition I know; An interesting account on this is also [4].…”

“…section 4) which represent the most simple non-linear algebraic varieties. In dimension two and three quadrics were investigated already in the Greek-Hellenistic antiquity (s. [25], sect.2.2.2, p.42 and sect.2.5.10, p.92). For instance, the notions "ellipse, parabola, hyperbola" were already used by Apollonios of Perge (262?-190 B.C.)…”

On the history of the Euclidean Steiner tree problem

“…5.1 Gauss' letter to Schumacher [1836] The extensive epistolary correspondence between the great mathematician and scientist, Carl Friedrich Gauss (1777-1855), and the Danish-German astronomer, Heinrich Christian Schumacher (1780-1850), published in a series of volumes in the 1860s, has been a valuable source for historians and mathematicians. Gauss' connection to the Steiner tree problem was discussed by Schreiber (1986), and the story has been told in a number of other papers and books (Cheng et al (2004), Cieslik (2004a), Cieslik (2004b), Du and Wu (2007), Gander et al (2008) and Scriba and Schreiber (2010)).…”

“…For some time this letter was believed to be the earliest source of the problem (Schreiber, 1986). Today we know that the Euclidean Steiner tree problem was posed and analysed even earlier, in 1811, by Joseph Diaz Gergonne (1771Gergonne ( -1859; this fact is mentioned briefly in a mathematics history book by Scriba and Schreiber (2010).…”

Geometrie der Zahlen. Ein Überblick

“…siehe etwa Scriba & Schreiber[129] 41 Und in Franken nennt man hier noch den seinerzeit in Würzburg und Erlangen ansässigen Lehrer Karl Georg Christian von Staudt als weiteren Schöpfer der projektiven Geometrie.…”