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highway systems require more than building
sturdy roads. To achieve efficient movement
of people and goods, scientists and engineers
deploy a wide range of mathematical techniques.
Operations Research (OR) was developed by
the military. Its goal was to develop a mathematical
framework for solving complex logistics problems.
Through techniques called mathematical programming,
optimization, and others, engineers can design
highway networks that balance transportation
efficiency with resource constraints.
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One
of the first traffic problems:
Leonhard Euler (Swiss,
1707-1783) introduced a famous math
problem called the Seven Bridges of Königsberg
– how do you cross over all seven
bridges without crossing over any bridge
more than once?
To analyze this problem, Euler introduced
graph theory, which represents connected
elements (like places connected by bridges),
as lines and points (edges and vertices)
and provides mathematical tools to solve
key problems. Through graph theory Euler
proved that it is impossible to not cross
any bridge more than once. Today, graph
theory is an important mathematical technique
for designing networks of all kinds including
networks of highways. |
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