Two mathematicians meet on a plane

Line (geometry) - Wikipedia

two mathematicians meet on a plane

The only reason you would say "older" when referring to THREE people (you would typically use "oldest") means that two of them must be twins. You want to show that all 3 planes are NOT parallel by considering the plane's normals. Also consider the intersections: The lines that the planes meet at should . Suppose we have four nondegenerate chained two-dimensional Consequently , any two of these planes intersect in a line (if two were to meet in a.

The traditional treatment of geometry was being pressured to change by the new developments in projective geometry and non-Euclidean geometryso several new textbooks for the teaching of geometry were written at this time. A major difference between these reform texts, both between themselves and between them and Euclid, is the treatment of parallel lines. According to Wilhelm Killing [8] the idea may be traced back to Leibniz.

Wilson edited this concept out of the third and higher editions of his text.

two mathematicians meet on a plane

The main difficulty, as pointed out by Dodgson, was that to use them in this way required additional axioms to be added to the system. The equidistant line definition of Posidonius, expounded by Francis Cuthbertson in his text Euclidean Geometry suffers from the problem that the points that are found at a fixed given distance on one side of a straight line must be shown to form a straight line.

Perspective -- from Wolfram MathWorld

This can not be proved and must be assumed to be true. Cooley in his text, The Elements of Geometry, simplified and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.

The three properties above lead to three different methods of construction [12] of parallel lines.


Draw a line through a parallel to l. Line m has everywhere the same distance to line l. Take a random line through a that intersects l in x. The second sentence of the puzzle should be "is the same as the number of windows you can see in this building" and he points. The responder says at this point s he still does not know the ages.

Then person says "the oldest has blue eyes. You forgot to put in the crucial bit of dialogue after the second question.

Parallel (geometry)

Might as well do it this way. It never occurred to me that a building always has the same number of windows at each floor Not nit-picking, just curious The Empire State building has windows and floors, and is not divisible by It's also doubtful that you should rule out having two 6-year-olds because of the word "oldest".

two mathematicians meet on a plane

Even with twins, one is generally born first. Moreover it's quite possible to have two 6-year-olds that are not twins.

Well, first off, let's list all the possible combination of ages and their sum: The only reason you would say "older" when referring to THREE people you would typically use "oldest" means that two of them must be twins. So, you now have three possibilities left: