ABSTRACT
This chapter describes aspect-perception with an eye to mathematics. It shows that aspect-perception at work in mathematics, chosen in part for their differing features to illuminate the breadth of aspects. The chapter presents the classical and conceptual issue of the irrationality of square roots, bringing out aspects geometric and algebraic, ancient and modern. It also presents circularity in the development of the calculus having to do with the derivative of the sine function, retraces features of the concept in ancient mathematics, and considers possible ways out of the circularity, thus drawing out new aspects. The chapter provides a basic circularity in textbook developments of calculus is brought to the fore, and this logical node is related to the ancient determination of the area of the circle. It also provides a 'new' result 'found' by the author, but one sees that creativity is belied to a substantial extent by context.
