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.
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?
@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.
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
hehe... 21:14 "They mutually cut each other"... those lines don't just stand around and talk, they mean business :) :D
andreirocks1992 1 month ago
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.
bluetwinky 1 month ago
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?
robotadventures 3 months ago
@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.
njwildberger 3 months ago
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
robotadventures 3 months ago
Lock the door when class starts. Maybe those who are rudely tardy will get to class on time!
grichard24 11 months ago 4
@grichard24 Totally agree.
172Break 11 months ago
@grichard24 yea....my teacher tried that, didn't work
yonglin426 6 months ago in playlist Math History