Yao Zhang - Geometry

Geometry is a vital branch of mathematics that studies the properties and relationships of shapes, sizes, and spaces. It encompasses various subfields, including classical geometry and differential geometry. Classical geometry, rooted in the works of Euclid, focuses on the properties of flat surfaces and solids, including concepts such as points, lines, angles, and polygons. This foundational knowledge helps us understand the geometric aspects of the world around us.

Differential geometry extends these concepts to curves and surfaces in higher dimensions, utilizing calculus to study their properties. This field has profound implications in modern physics, particularly in the theory of relativity, where the curvature of space-time is described using differential geometric principles. Through the study of manifolds and Riemannian geometry, mathematicians and physicists analyze complex systems, enhancing our understanding of gravity and the fabric of the universe. Thus, geometry serves as a bridge between abstract mathematics and practical applications in science.