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Euclid's straight lines
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
2015 (English)In: Normat, ISSN 0801-3500, Vol. 60, no 4, 145-169 p.Article in journal (Refereed) Published
Abstract [en]

We raise two questions on Euclid's Elements: How to explain that Propositions 16 and 27 in his first book do not follow, strictly speaking, from his postulates (or are perhaps meaningless)? and: What are the mathematical consequences of the meanings of the term eutheia, which we today often prefer to consider as different?

The answer to the first question is that orientability is a tacit assumption. The answer to the second is rather a discussion on efforts to avoid actual infinity, and having to (in some sense or another) construct equivalence classes of segments to achieve uniqueness.

Place, publisher, year, edition, pages
2015. Vol. 60, no 4, 145-169 p.
Keyword [en]
Euclid, Euclidean geometry, straight lines, axiom, postulate, projective space, orientablity
National Category
Geometry
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-248861OAI: oai:DiVA.org:uu-248861DiVA: diva2:801064
Available from: 2015-04-08 Created: 2015-04-08 Last updated: 2017-12-04Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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