|
Showing 1 - 4 of
4 matches in All Departments
Few people outside of mathematics are aware of the varieties of
mathemat ical experience - the degree to which different
mathematical subjects have different and distinctive flavors, often
attractive to some mathematicians and repellant to others. The
particular flavor of the subject of minimal surfaces seems to lie
in a combination of the concreteness of the objects being studied,
their origin and relation to the physical world, and the way they
lie at the intersection of so many different parts of mathematics.
In the past fifteen years a new component has been added: the
availability of computer graphics to provide illustrations that are
both mathematically instructive and esthetically pleas ing. During
the course of the twentieth century, two major thrusts have played
a seminal role in the evolution of minimal surface theory. The
first is the work on the Plateau Problem, whose initial phase
culminated in the solution for which Jesse Douglas was awarded one
of the first two Fields Medals in 1936. (The other Fields Medal
that year went to Lars V. Ahlfors for his contributions to complex
analysis, including his important new insights in Nevanlinna
Theory.) The second was the innovative approach to partial
differential equations by Serge Bernstein, which led to the
celebrated Bernstein's Theorem, stating that the only solution to
the minimal surface equation over the whole plane is the trivial
solution: a linear function."
Few people outside of mathematics are aware of the varieties of
mathemat ical experience - the degree to which different
mathematical subjects have different and distinctive flavors, often
attractive to some mathematicians and repellant to others. The
particular flavor of the subject of minimal surfaces seems to lie
in a combination of the concreteness of the objects being studied,
their origin and relation to the physical world, and the way they
lie at the intersection of so many different parts of mathematics.
In the past fifteen years a new component has been added: the
availability of computer graphics to provide illustrations that are
both mathematically instructive and esthetically pleas ing. During
the course of the twentieth century, two major thrusts have played
a seminal role in the evolution of minimal surface theory. The
first is the work on the Plateau Problem, whose initial phase
culminated in the solution for which Jesse Douglas was awarded one
of the first two Fields Medals in 1936. (The other Fields Medal
that year went to Lars V. Ahlfors for his contributions to complex
analysis, including his important new insights in Nevanlinna
Theory.) The second was the innovative approach to partial
differential equations by Serge Bernstein, which led to the
celebrated Bernstein's Theorem, stating that the only solution to
the minimal surface equation over the whole plane is the trivial
solution: a linear function."
Osserman erzahlt lebendig und anschaulich eine Geschichte der
Geometrie, von der Bestimmung der Erdgestalt und -grosse durch die
alten Griechen uber das Problem der Kartierung der Weltkugel bis
hin zur gekrummten Raumzeit, den Fraktalen und Buckyballs. Viele
wird uberraschen, dass in der Mathematik nicht nur analytisches
Denken zahlt, sondern dass Imagination, Phantasie und Kreativitat
viel wichtiger sind. Dies und die Schonheit der Mathematik schlagen
die Brucke zur Bildenden Kunst und Literatur, so nimmt Dante in
seiner Gottlichen Komodie das Riemannsche Universum vorweg - zudem
besteht eine frappante Analogie zwischen Dantes Gottlichem Licht
und dem Urknall. Auch menschliche Aspekte kommen nicht zu kurz:
Euler, Gauss und Riemann werden zum Beispiel als mathematische
Entsprechungen von Bach, Beethoven und Brahms vorgestellt.
An exciting intellectual tour through the ages showing how
mathematical concepts and imagination have helped to illuminate the
nature of the observable universe, this book is a delightful
narrative "math for poets". Osserman traces the mathematical
breakthroughs over the centuries and explains their significance.
40 illustrations throughout.
|
You may like...
The Expendables 2
Sylvester Stallone, Jason Statham, …
Blu-ray disc
(1)
R64
Discovery Miles 640
|