Geometry Quote by Arthur Cayley
“Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.”
About This Quote
Source Book: Elements of Geometry, 1850
Euclidean geometry is exactly true within its abstract space, even if physical space differs.
In simple terms: Euclidean geometry is perfectly true in its own abstract space.
Key Takeaway
Recognize the limits of physical intuition.
Themes
geometry
abstraction
philosophy
Mood
analytical
thoughtful
Type
philosophical
educational
When to use this quote
- teaching geometry
- philosophical debates
- science education
Key Concepts
Euclidean space
physical reality
mathematical truth
Questions to Reflect On
- How does abstraction aid scientific progress?
- When should we trust mathematical models?
A Different Perspective
Physical space may not match Euclidean assumptions.
![“Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we…” quote by Jean le Rond d'Alembert](https://sms4smile.com/quotes/img-quotes/0d9/jean-le-rond-d-alembert-26487_able_geometry-which-should-only-obey-physics_6945.jpg)
![“Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.” quote by Arthur Cayley](https://sms4smile.com/quotes/img-quotes/5dc/arthur-cayley-48537_euclid_euclid-avoids-it-the-treatment-of-the-in_1635536.jpg)
