Counting On Frameworks: Mathematics To Aid The Design Of Rigid Structures (dolciani Mathematical Expositions)
by Jack Graver /
2001 / English / DjVu
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Consider a scaffolding that is constructed by bolting together rods
and beams. The ultimate question is whether the structure is strong
enough to support the workers and their equipment. This is the
problem that motivates the area of mathematics known as rigidity
theory. The purpose of this book is to develop a mathematical model
for the rigidity of structures. In fact the author develops three
distinct models in which the structure under consideration is
modelled as a framework. These models are the degrees of freedom
model and two models based on quadratic equations and linear
equations respectively. The author shows that all three of these
models agree except for a very small class of specially constructed
frameworks. This is a theory with significant practical
applications and will be of interest to a wide range of people
including those studying graph theory or mathematical modelling.
Consider a scaffolding that is constructed by bolting together rods
and beams. The ultimate question is whether the structure is strong
enough to support the workers and their equipment. This is the
problem that motivates the area of mathematics known as rigidity
theory. The purpose of this book is to develop a mathematical model
for the rigidity of structures. In fact the author develops three
distinct models in which the structure under consideration is
modelled as a framework. These models are the degrees of freedom
model and two models based on quadratic equations and linear
equations respectively. The author shows that all three of these
models agree except for a very small class of specially constructed
frameworks. This is a theory with significant practical
applications and will be of interest to a wide range of people
including those studying graph theory or mathematical modelling.