Euclidean Triangles, Irrational Numbers, and the Purpose of Geometric Theories
 
What's the purpose of geometric theories? To explain the phenomena we experience? To teach us about the physical world? To give us tools that we can use to construct objects?

Do "irrational numbers" imply that numbers exist outside our minds - or do they imply a flaw with the orthodox theory of numbers?

Part three of an investigation into the foundations of geometry and mathematics.