<P> In this thesis, we mainly study geodesics on various two dimensional surfaces.
All the background material needed throughout the thesis is provided, including
an explanation of the theory of geodesics. We will calculate geodesics using two
numerical methods: Euler's method and Runge-Kutta method of fourth order.
Using Maple, we will test the accuracy of the numerical methods on a test case
surface, the Poincare half plane. Later, we proceed to investigate several interesting
surfaces by numerically calculating geodesics. From the investigated
surfaces, we will draw similarities between the human cerebral cortex and certain
surfaces. The human cerebral cortex is the most intensely studied part of
the brain and it is believe that their exists a relation between the function and
structure of the cortex. Geodesic analysis can possibly be an essential tool in
better understanding the cortical surface as it is in many disciplines of science
to understand the nature of physical based problems. </P> / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/21295 |
| Date | 04 1900 |
| Creators | Burazin, Andrijana |
| Contributors | Lovric, Miroslav, Mathematics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
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