MATH 3560: History of Mathematics (UNSW): Lecture 16

MATH 3560 - History of Mathematics

MATH 3560: History of Mathematics (UNSW). Taught by Professor N. J. Wildberger, this course provides an overview of the history of mathematics, in 17 lectures; meant for a broad audience, not necessarily mathematics majors. Starting with Greek mathematics, Professor N. J. Wildberger discusses Hindu, Chinese and Arabic influences on algebra; the development of coordinate geometry, calculus and mechanics; the course of geometry from projective to non-Euclidean in the 19th century; complex numbers and algebra; differential geometry; and topology. This course roughly follows John Stillwell's book 'Mathematics and its History' (Springer, 3rd ed).

Lecture 16 - Differential Geometry

Differential geometry arises from applying calculus and analytic geometry to curves and surfaces. This video begins with a discussion of planar curves and the work of C. Huygens on involutes and evolutes, and the related notions of curvature and osculating circle. We discuss involutes of the catenary (yielding the tractrix), cycloid and parabola. The evolute of the parabola is a semi-cubical parabola. For space curves we describe the tangent line, osculating plane, principle normal and binormal.

Go to the Course Home or watch other lectures:

Lecture 1a - Pythagoras' Theorem

Lecture 1b - Pythagoras' Theorem (cont.)

Lecture 2a - Greek Geometry

Lecture 2b - Greek Geometry (cont.)

Lecture 3a - Greek Number Theory

Lecture 3b - Greek Number Theory (cont.)

Lecture 04 - Infinity in Greek Mathematics

Lecture 5a - Number Theory and Algebra in Asia

Lecture 5b - Number Theory and Algebra in Asia (cont.)

Lecture 6a - Polynomial Equations

Lecture 6b - Polynomial Equations (cont.)