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Cassini Ovals As Elliptic Curves, Nozomi Arakaki
Cassini Ovals As Elliptic Curves, Nozomi Arakaki
Theses Digitization Project
The purpose of this project is to show that Cassini curves that are not lemniscates, when b does not equal 1, represent elliptic curves. It is also shown that the cross-ratios of these elliptic curves are either real numbers or represented by complex numbers on the unit circle on the conplex plane.
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
Theses Digitization Project
This project demonstrates how an elliptic curve f defined by invariance under two involutions can be represented by the locus of circumcenters of isosceles triangles in the hyperbolic plane, using inversive model.
Constructible Numbers: Euclid And Beyond, Joshua Scott Marcy
Constructible Numbers: Euclid And Beyond, Joshua Scott Marcy
Theses Digitization Project
The purpose of this project is to demonstrate first why trisection for an arbitrary angle is impossible with compass and straightedge and second how trisection does become possible if a marked ruler is used instead.
Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas
Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas
Theses Digitization Project
The purpose fo this project is to study ideals in polynomial rings and affine varieties in order to establish a connection between these two different concepts. Doing so will lead to an in depth examination of Groebner bases. Once this has been defined, step will be outlined that will enable the application of the Groebner Basis Algorithm to geometric problems.
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Theses Digitization Project
The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.