本文以孔恩(Thomas Kuhn)的典範轉移(paradigm shift)觀點追溯幾何史上的八種典範轉移-歐氏幾何、人是萬物的尺度、投影學、笛卡兒十字座標、磚花、對稱群、非歐氏幾何及碎形(fractal)-在造形設計上的影響。 由於碎形是晚近新創的理論，其學理與應用仍在持續發展中，因此，本文概述各個幾何典範轉移之後，側重在碎形的描述及新啟示的探索，這些新啟示包括「以新思維看」、「主觀定客觀」、「簡單蘊複雜」、「明確生難測」、「以電腦創新」等五大項，並認為躬逢此新典範伊始之際，探索新幾何是明智的抉擇。

By applying the ideas of Thomas Kuhn's 'paradigm shift' to geometry history, this paper chooses 'Euclidean Geometry', 'Measure of Human', 'Projection', 'Descartes' coordinate', Tessellation', 'Group Theory', 'Non-Euclidean Geometry' and 'Fractal' as paradigm shifts in the geometry history, and reviews their influences on the design of forms. Since fractal is a new theory, its indications and applications are still under development. This research paper focus on its indications and concludes that (1) 'seeing with new thinking', (2) 'making objective with subjective', (3) 'revealing complexity with simplicity', (4) 'having unpredictability with determinism', (5) 'applying computer to innovation' are five indications of fractal. Additionally, this paper considers that it is a good choice to explore this new geometry as one that has the opportunity to encounter the growing of this new paradigm shift of geometry.