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The Euclidean Distance Degree of Conics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The Euclidean Distance Degree (EDD) of a variety is the number of critical points of the squared distance function of a general point outside the variety. In this thesis we give a classification of conics based on their EDD, originally attributed to Cayley. We show that circles and parabolas have EDD 2 and 3 respectively while all other conics have EDD 4. We reduce the computation of the EDD to finding solutions of the determinant of a certain generalized matrix, called the hyperdeterminant of type 2 × 3 × 3. This determinant is computed using the celebrated Schläfli decomposition.

Abstract [sv]

The Euclidean Distance Degree (EDD) of a variety is the number of critical points of the squared distance function of a general point outside the variety. In this thesis we give a classification of conics based on their EDD, originally attributed to Cayley. We show that circles and parabolas have EDD 2 and 3 respectively while all other conics have EDD 4. We reduce the computation of the EDD to finding solutions of the determinant of a certain generalized matrix, called the hyperdeterminant of type 2 × 3 × 3. This determinant is computed using the celebrated Schläfli decomposition.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:074
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-252533OAI: oai:DiVA.org:kth-252533DiVA, id: diva2:1319483
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2019-06-04 Created: 2019-06-01 Last updated: 2019-06-04Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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