Geometric Bites

Function Composition: A Simple Way to Organise Your Mathematics Function composition is one of the most useful tools in mathematics. It allows us to combine several steps into a single process, keeping our work neat, organised, and easy to reuse. Rather than performing one operation after another by hand, composition lets us build those steps into a single function. Once you become comfortable with function composition, you never want to go back to doing everything manually. It reduces clutter, helps you work systematically, and allows you to achieve remarkable results with only a few lines of equations. What Is Function Composition? A function takes an input, performs an operation, and produces an output. Function composition takes this idea further: it links functions together so that the output of one becomes the input of the next. We write this as: (f ∘ g)(x) = f(g(x)) This means that g acts first, then f . The circle symbol ∘ simply means “do one funct...

Common Transformations in Geometry: A Beginner’s Guide In geometry, a transformation is a rule that changes the position or appearance of a shape or a set of points. Some transformations simply move a shape to a new location, while others may turn it, resize it, or reflect it. Understanding these ideas helps us describe movement and change in a clear mathematical way. This guide introduces the most common transformations: translation, rotation, scaling, reflection, shear, and projection. Each section includes a simple example to make the ideas easier to follow. 1) Translation — Moving A translation shifts every point of a shape by the same amount. Nothing about the shape itself changes — not its size, not its proportions, and not its orientation. Only its position is different. Example: Imagine a triangle on graph paper. If every point of the triangle moves 3 units to the right and 2 units up, the triangle looks exactly the same — it simply appears somewhere else on th...