The last book XIII of Euclid's Elements deals with the regular
solids which therefore are sometimes considered as crown of
classical geometry. More than two thousand years later around 1850
Schl fli extended the classification of regular solids to four and
more dimensions. A few decades later, thanks to the invention of
group and invariant theory the old three dimensional regular solid
were involved in the development of new mathematical ideas: F.
Klein (Lectures on the Icosa hedron and the Resolution of Equations
of Degree Five, 1884) emphasized the relation of the regular solids
to the finite rotation groups. He introduced complex coordinates
and by means of invariant theory associated polynomial equations
with these groups. These equations in turn describe isolated
singularities of complex surfaces. The structure of the
singularities is investigated by methods of commutative algebra,
algebraic and complex analytic geometry, differential and algebraic
topology. A paper by DuVal from 1934 (see the References), in which
resolutions play an important rele, marked an early stage of these
investigations. Around 1970 Klein's polynomials were again related
to new mathematical ideas: V. I. Arnold established a hierarchy of
critical points of functions in several variables according to
growing com plexity. In this hierarchy Kleinls polynomials describe
the "simple" critical points."
General
Imprint: |
Vieweg+teubner Verlag
|
Country of origin: |
United Kingdom |
Release date: |
June 1986 |
First published: |
1986 |
Authors: |
Klaus Lamotke
|
Dimensions: |
244 x 170 x 12mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
236 |
Edition: |
1986 ed. |
ISBN-13: |
978-3-528-08958-0 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
Algebraic geometry
|
LSN: |
3-528-08958-X |
Barcode: |
9783528089580 |
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