By our eyes our brain can perceive only a very litle part of the universe and on that part Euclidean Geometry is the best fitting geometry till now. Yes our brain can also perceive non Euclideanness when he observe the geometry of some objects like a curved surface as the syrface of ball or a surface of a cylinder or cone, that this obviously not Eucledean; but if a cobsider a very small part and you are just a tiny insect on that surface, you will imagine it as Euclidean as your perseption there limited to a small part like on the surface of the earth we everywhere imagine its a flate Euclidean surface.

What is a straight line, for example? Is it a product of our brain? Or some experimental data are participated in the formulation of notion "straight line"?

Hi Anatoly,

There are some observations that support the view that Euclidean geometry is a purely mathematical construct that is absent in the physical world.

There is, for example, the observed prolonged lifetime of fast moving muons, see B. Rossi, D.B. Hall, Phys. Rev. 59(3), 223-228 (1941). This supports the view that if we describe 4D spacetime with a flat manifold, then it's a Minkowski spacetime, not an Euclidean spacetime.

That same view is also supported by the null-result of the Michelson-Morley experiment, see A.A. Michelson, E.W. Morley, Am. J. Sci. 34, 333-345 (1887). 

Other observations support the view that even our three spatial dimensions do not form a 3D Euclidean space, e.g. the observed deflection of light by the gravitational field of the sun, see F.W. Dyson, A. S. Eddington, and C.R. Davidson, Philos. Trans. R. Soc. Lond. A 220, 291–333 (1920).

There are other observations as well, but these are some famous examples.

Marcoen

Dear Sirs,

I among them who suppose geometry, math, physics in some part is a certain madness.. Remember picture "The Sleep of Reason Produces Monsters" by Francisco Goya. It is about all us at researchgate and not only us :) :) :)

But I am physicist... Of course bad physicist. But I just want to understand this madness, maybe due to boredom or for other reason. Did you get me?  

Euclidean geometry arises naturally in Mathematics itself as the geometric structure of the sets of pairs of real numbers (or of triples of real numbers).