A problem in Linear Algebra by Jim Hefferson: Euclid describes a plane as \a surface which lies evenly with the straight lines on itself". Commentators (e.g., Heron) have interpreted this to mean \(A plane surface is) such that, if a straight line pass through two points on it, the line coincides wholly with it at every spot, all ways". (Translations from [Heath], pp. 171-172.) Do planes, as described in this section, have that property? Does this description adequately define planes? The answer is ambiguous: Euclid no doubt is picturing a plane inside of R^3. Observe, however, that both R^1 and R^2 also satisfy that definition. So what about R^4 and beyond? Do planes in R^4 (and beyond) have the property stated above? Is this property a definition of planes in R^4 (and beyond)? Is it even a definition of planes in R^3?