A difference equation is a mathematical equation that describes how a geometric or numerical quantity changes over time. There are many different synonyms for this term, including recurrence relation, iterative equation, discrete dynamical system, and discrete-time dynamical system. Each of these phrases refers to the same basic concept, which is the way that a given quantity changes in discrete intervals rather than continuously over time. Whether you are dealing with a simple linear equation or a complex system of non-linear equations, the principles underlying difference equations are fundamental to many different areas of mathematics and science. By understanding these concepts, you can gain powerful insights into how geometric systems behave over time, and how to model these behaviors with precision and accuracy.