Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces. The concept of multidimensionality is pervasive in mathematics, has come to play a pivotal role in physics, and is a common element in science fiction.
Ludwig spent most of his life in Switzerland. He was born in Grasswil (now part of Seeberg), his mother's hometown. The family then moved to the nearby Burgdorf, where his father worked as a tradesman. His father wanted Ludwig to follow in his footsteps, but Ludwig was not cut out for practical work.
In contrast, because of his mathematical gifts, he was allowed to attend the Gymnasium in Bern in 1829. By that time he was already learning differential calculus from Abraham Gotthelf Kästner's Mathematische Anfangsgründe der Analysis des Unendlichen (1761). In 1831 he transferred to the Akademie in Bern for further studies. By 1834 the Akademie had become the new Universität Bern, where he started studying theology.
After graduating in 1836, he was appointed a secondary school teacher in Thun. He stayed there until 1847, spending his free time studying mathematics and botany while attending the university in Bern once a week.
A turning point in his life came in 1843. Schläfli had planned to visit Berlin and become acquainted with its mathematical community, especially Jakob Steiner, a well known Swiss mathematician. But unexpectedly Steiner showed up in Bern and they met. Not only was Steiner impressed by Schläfli's mathematical knowledge, he was also very interested in Schläfli's fluency in Italian and French.
Steiner proposed Schläfli to assist his Berlin colleagues Carl Gustav Jacob Jacobi, Peter Gustav Lejeune Dirichlet, Carl Wilhelm Borchardt and himself as an interpreter on a forthcoming trip to Italy.
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Explores orthogonality, eigenvalues, and diagonalization in linear algebra, focusing on finding orthogonal bases and diagonalizing matrices.
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E2. It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has also metrical properties induced by a distance, which allows to define circles, and angle measurement. A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane.
In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen. The convex regular 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. He discovered that there are precisely six such figures.
The great Swiss mathematician Ludwig Schläfli (1814-1895) left after his death more than three hundred and fifty notebooks. They include mathematical studies and new results, as well as works about classical mathematical texts and a priori more surprising ...