Abstract:
Visual images are frequently utilized to elucidate concepts in general mathematics and
geometry; however, their application in mathematical analysis remains uncommon. This paper
demonstrates how visual imagery can enhance the proof of certain theorems in mathematical
analysis. It emphasizes the importance of visualization in the learning and understanding of
mathematical concepts, particularly within mathematical analysis, where diagrams are seldom
employed. The paper focuses on the reasoning processes used by mathematicians in proving
selected fundamental theorems of mathematical analysis. It provides illustrative examples
where visual images are instrumental in performing specific subtasks within proof development
and in completing the proofs. The proofs discussed include the sum of the first n natural
numbers, the sum rule of integration, the mean value theorem for derivatives, the mean value
theorem for integrals, and Young’s Inequality. This paper underscores that visual images serve
not only as persuasive tools but also as bridges between symbolic representations and realworld understanding.
