Epic Circles - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it as an intuitive introduction to circle inversion and as a worked example of using inversive geometry on tangent-circle and Pappus chain problems.
Recommended by 2 people across 2 different months, 2014 to 2021.
What it is
A 26-minute Numberphile video in which Simon Pampena walks through Pappus chains, circle inversion and related circle geometry, building up to how inversion makes tangent-circle problems easy. It is an extended, visual explainer with hand-drawn constructions.
What people said
Recommends Alice Ryhl · 2014-05 · Mathematics Stack Exchange · on “Problem of a circle tangent to three other circles”
If the figure, is in fact correct, the following video might have some ideas for an alternate solution: [this video]
Recommends Arthur · 2021-05 · Mathematics Stack Exchange · on “Definition of inversion in a circle”
I think you also want $OPP'$ collinear. Numberphile [this video] made a video about it a while ago, maybe check that out if you want some intuition?
Cites u840903 · 2014-04 · Mathematics Stack Exchange · on “Why isn't my Pappus chain lining up?”
TL;DR Why isn't my Pappus chain lining up? Visualisation: [LINK] Proof: [LINK] Code: [LINK] I saw a [this video] and I decided to create an animated visualisation of it. It looks nice and pretty [LINK] until you study it [LINK] . Shouldn't the midpoint of the circles creating the chain line up? I'm not sure if I have a programming problem or a maths problem, but since I'm a far better programmer than I'm a mathematician I'm guessing I'm having a maths problem. To be honest, I'm no mathematician at all. I didn't know what a Pappus chain was three days ago. If there's an error with my calculations they are probably here [LINK] : 60: var val = (i * i * s * s + pulse) / 2; 61: var x = i * pulse * s /
Cites Matt · 2018-09 · Mathematics Stack Exchange · on “What can we do with inversive geometry?”
I've recently been introduced to inversive geometry [LINK] . This seems like it would be a very pretty area of study. Many sources that I have found seem a little old, however. I have two related questions: The wiki page (linked above) suggests that there are various problems in geometry which are known to be solvable using inversive geometry. What are examples of these? I have found one very exciting one explained by Numberphile here [this video] . Are there more? My looking around in various places suggests that inversive geometry is not such an active area of research at the moment. Is this true? Has it been superseded by other geometries, i.e. projective geometry? Are there any authoritative