Is prior experience necessary to perceive the Kanizsa triangle illusion? We know the Kanizsa Triangle. 


Kanizsa Triangle

I was socialized in a "western" world, where I learned mathematics for about 13 years; I have designed products surrounding me using geometric forms and so forth.

I wonder if somebody would see the triangle who never or rarely saw a triangle before?
It's a difficult question to answer. My educated guess is that the appearance of the triangle, and illusionary contours in general, would persist, even in individuals who have never seen a triangle before in their lives. I think they would perceive the illusionary contours, but it might just not make sense to them, as the shapes may be unfamilair to them. In other words, they would not associate the form with something meaningful. The reason why I expect previous experience with geometrical shapes is unimportant for illusiuonary contours to be perceived is two-fold:


Illusionary contours are generated in the secondary visual cortex (V2), which is a low-level part of the visual system. It performs relatively simple processing such as the coding of orientations, contours and the perception of background and foreground (Anzai et al., 2007). Such low-level processing is, expectedly, largely innate. 
The neural representations of illusionary contours have been shown in a variety of species. Admittedly, most electrophysiological evidence comes from primates (e.g., Heydt, 1984), but illusionary contours have even been shown to be recognized by cuttlefish (Zylinsk et al., 2012). Hence, given the fact that relatively uncomplicated species like cuttlefish are able to successfully perceive illusionary contours, I doubt that prior experience in the geometry of the illusionary contour is a critical factor in perceiving it. 


References
- Anzal et al., Nature Neurosci (2007); 10: 1313 - 21
- Heydt, Science (1984); 224(4654): 1260-2
- Zylinsk et al., Proc Biol Sci (2012); 279(1737): 2386–90