Over de oorsprong van de meetkunde

In de blog: De zwarte doos reacties: 1 pdf print
  1. De vroeg-Griekse visie van Pythagoras
  2. De invallen van Descartes
  3. Husserl, die een nieuwe beschrijving van Descartes gebruikt

Via deze visies zal ik ook mijn eigen inzichten trachten te ontvouwen, die enigszins geïnspireerd is op Wittgenstein: wiskunde is een beschrijving, een model van zaken. in de leer van Pythagoras is een punt gedefinieerd als een 'eenheid' met positie. Cruciaal: met 1 punt ben je echter niets, positie is immers bepaald relatief ten opzichte van andere punten. Een 'eenheid' betekent hier dat een punt een unieke positie heeft, of dat elk 'punt' met dezelfde positie dezelfde functie uitvoert als dat punt. Euclides doet iets vergelijkbaars, en opent zijn beroemde Elementen met deze definitie: "a point is that without parts" "We can say: location-grammar applies to the word 'point' but not object-grammar." (link) "Geometry is a study, not of objects, but of relationships." descartes: http://www.fi.uu.nl/ctwo/WiskundeD/ MateriaalDomeinenWiskundeD/AnalytischeMeetkundeVwo/docs/Descartes.pdf


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