{"id":{"repo_id":"csusb","oai_identifier":"oai:scholarworks.lib.csusb.edu:etd-project-1142"},"canonical_url":"https://search.dev.ndltd.org/etd/csusb/oai:scholarworks.lib.csusb.edu:etd-project-1142","repository":{"repo_id":"csusb","name":"CSUniversity San Bernardino","base_url":"https://scholarworks.lib.csusb.edu/do/oai/"},"display":{"title":"Hyperbolic transformations on cubics in H²","abstract":"The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).","abstract_html":"The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).","abstract_has_math":false,"creators":["Marfai, Frank S."],"institution":null,"degree_name":"Master of Arts in Teaching, Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-01-01T08:00:00Z","date_published":"2003-01-01T08:00:00Z","updated_at":"2026-07-24T01:53:22Z","subjects":["Henri Poincaré 1854-1912","Hyperbolic Geometry","Hyperbolic Differential equations","Möbius transformations","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd-project/142","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Marfai, Frank S."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Teaching, Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Henri Poincaré 1854-1912","Hyperbolic Geometry","Hyperbolic Differential equations","Möbius transformations","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd-project/142"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation)."]},{"key":"dc:title","label":"Title","values":["Hyperbolic transformations on cubics in H²"]}]}],"canonical_facts":{"dc:creator":["Marfai, Frank S."],"dc:description.abstract":["The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation)."],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd-project/142"],"dc:subject":["Henri Poincaré 1854-1912","Hyperbolic Geometry","Hyperbolic Differential equations","Möbius transformations","Mathematics"],"dc:title":["Hyperbolic transformations on cubics in H²"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Teaching, Mathematics"]},"updated_at":"2026-07-24T01:53:22Z"}