### AxLam Example: Questions about Triangles

AxLam Example : Questions about Triangles Consider the humble, mighty triangle: a connected shape with 3 vertices, 3 sides, and 3 angles. We will experiment with AxLam models for describing and computing with triangles individually and in groups, at several levels of mathematical rigor. On this road we touch briefly on some fundamental aspects of mathematics and information, while staying intuitively grounded in the triangle simplex. In a computer-assisted modeling paradigm, it is natural to proceed constructively. An intuitive way to start modeling triangles is using the lengths of the 3 sides of the triangle. In any programming or data language, we might quickly write down an ADT, record or class containing three numeric sides, looking something like: class TriangleSidesRecord (sideA : Number, sideB : Number, sideC : Number) This structure is sufficient to begin computing with Triangles. However, when we examine the semantics of this simple record structure, we quickly find m