APOLLONIUS PROBLEM - A Problem From Euclidean Plane Geometry скачать в хорошем качестве

APOLLONIUS PROBLEM - A Problem From Euclidean Plane Geometry

CAN YOU DRAW EIGHT CIRCLES TANGENT TO THREE GIVEN CIRCLES ? In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga (c. 262 BC – c. 190 BC) posed and solved this famous problem in his work Ἐπαφαί (Epaphaí, "Tangencies"); this work has been lost, but a 4th-century AD report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them, a pair of solutions for each way to divide the three given circles in two subsets (there are 4 ways to divide a set of cardinality 3 in 2 parts). #Apollonius #Problem Subscribe: BRAIN EXPLODERS Link:    / brainexploders   Watch the video and Learn Something Extraordinary... 00:00 | Introduction 00:16 | How many required circles can be constructed 01:19 | General Statement of Apollonius Problem 01:42 | What if all the circles are of infinite radius? 02:01 | Some simple cases 04:09 | How to find a reference circle such that inverse of 2 given circles in it, become concentric? 04:28 | What is Radical Axis 05:47 | Resizing 06:33 | First Approach - Change the radii such that any two circles become tangent 07:44 | Second Approach - Resizing the circles such that one of the circle becomes a point 08:06 | With the help of inversive geometry, we can find the solutions in pairs. 08:51 | How to draw orthogonal circle Get early access and support the channel on Patreon Link:   / brainexploders   Suggested Book: Title: Problems and Solutions in Euclidean Geometry (Dover Books on Mathematics) Link: https://amzn.to/36ut8HZ A challenge for you in the last of this videos of the playlist Exploders Contest, can you solve that questions? Watch the videos, Take your time & give your answer in the comment section, if your answer is correct, we'll announce your name in our next YouTube video of this playlist - Exploders Contest: Season 2 Link:    • EXPLODERS CONTEST: Season 2   Exploders Contest: Season 1 Link:    • EXPLODERS CONTEST: Season 1   This is the channel to feature this type of questions suggested by the people. Join us on another platforms: Instagram: @Brain_Exploders Facebook: @BrainExploders Twitter: @BrainExploders Telegram: @Brain_Exploders ___Show your support to us. ________THANKS FOR WATCHING #Brain_Exploders _______________Next video will come soon.