MathHistory2a: Greek geometry

The ancient Greeks loved geometry and made great advances in this subject. Euclid's Elements was for 2000 years the main text in mathematics, giving a careful systematic treatment of both planar and three dimensional geometry, culminating in the five Platonic solids.
Apollonius made a thorough study of conics. Constructions played a key role, using straightedge and compass.

This is one of a series of lectures on the History of Mathematics by Assoc. Prof. N J Wildberger at UNSW.

Category:

Education

Tags:

• MathHistory2a
• History
• of
• mathematics
• Wildberger
• course
• UNSW
• Euclid
• geometry
• Stillwell
• axioms
• parallel
• postulate
• constructions
• Apollonius
• conics
• pentagon
• ellipse
• parabola
• hyperbola
• eccentricity
• Richmond

[robotadventures]

hello professor I am excited to start watching this series. and i look forward to the others. i received a BA in civil engineering so are you know that is only up to around calculus. I have a question. Maybe you will explain it later and my terms are not correct. but. i always wonder.. circles and arcs are not real. they are just infinate polygons. is that correct?

[njwildberger]

@robotadventures What exactly is a circle? is an interesting and historically important question. I would not go so far as to say circles are not real. There are different things we can write down on a piece of paper, and then point to, and say--that is a circle. One example: the equation x^2+y^2=1. That equation somehow represents a circle. There are other ways too. But the circle as a particular kind of continuous curve is more problematic.

[grichard24]

Lock the door when class starts. Maybe those who are rudely tardy will get to class on time!

[andreirocks1992]

hehe... 21:14 "They mutually cut each other"... those lines don't just stand around and talk, they mean business :) :D

[bluetwinky]

To define a regular solid it is not enough to say that the faces are all regular polygons. We must also define the vertices as all being identical. To give an example (of a non regular solid) it is possible to build a solid with twelve faces which are all equilateral triangles sharing the same dimensions. Cundy and Rollet cite the work of Freudenthal and van der Waerden who describe 8 convex deltahedra, 5 of which are not regular.

[robotadventures]

Thank you Professor. Of course you know my question stems from "the one and the many" points touch they make a line, lines touch they make a plane, planes touch they make 3d objects, a curve is an illusion using infinity? Could you recommend someone to read? Or point out my error. I think i might not understand infinity or limits. Thank you again. @njwildberger

[yonglin426]

@grichard24 yea....my teacher tried that, didn't work

[172Break]

@grichard24 Totally agree.