Is this one connected curve, or two? Bet you can’t explain why...
Go to to get started learning STEM for free. The first 200 people get 20% off an annual premium subscription.
One of the most fundamental properties of geometry is connectedness: when a shape is a single continuous entity. But how do you define this idea precisely so that you can apply it even to extremely bizarre shapes in very strange spaces?
=Chapters=
0:00 - The Topologist’s Sine Curve
1:54 - The goal of this video
3:06 - Path-Connectedness
6:56 - A new definition?
7:37 - Topology basics
10:27 - A snag
12:04 - Connectedness 2.0 and the Topologist’s Sine Curve
15:48 - Who’s right?
17:38 - The Ordered Square
19:32 - The connection between the definitions
21:18 - The underappreciated art of crafting definitions
22:16 - Brilliant ad
===============================
CREDITS
The songs used in this video are (in order of first appearance) “Dream Escape“, “Checkmate“, “Rubix Cube“, and “Twinkle in the Night“.
The song “Rubix Cube“ comes courtesy of
===============================
Want to support future videos? Become a patron at
Thank you for your support!
===============================
The animations in this video were mostly made with a homemade Python library called “Morpho“. If you want to play with it, you can find it here:
1 view
101
16
1 month ago 00:05:17 1
The Ultimate Email Extractor in 2024: YellowPages Scraper 🌎
1 month ago 00:02:22 1
Верное исполнение романса Сергея Рахманинова “Здесь хорошо“. Исполняет Юрий Гуляев, 1978 год
1 month ago 00:03:55 1
Pokemon GO Joystick, Teleport, Auto Walk - How to Get Pokemon GO Spoofer iOS & Android 2024 FREE
1 month ago 00:36:25 1
Decree x40 “Beloved Surya“ by Elizabeth Clare Prophet
1 month ago 00:12:05 1
ZenBusiness Review 2024: What Makes It Stand Out?
1 month ago 00:20:33 1
Movie “Wicked” Sign of the End Time
1 month ago 00:04:14 1
Paramore: Decode [OFFICIAL VIDEO]
1 month ago 00:03:07 1
Delta Executor iOS iPhone Android NO KEY - Roblox Script Executor Mobile NEW UPDATE 2024
1 month ago 00:00:00 1
🔴 LIVE Прославление | Церковь Божия Music | #cogmosmusic
1 month ago 11:55:00 1
13 minutes ago! First Largest US Naval Base Bombarded by Russian MIG 29 Arma3
1 month ago 11:54:56 1
1 minute ago, the plane carrying the US President and 10 Ministers was shot down by 3 Russian MIG-29
1 month ago 00:31:06 1
Whistleblow Uncovers Covid Scam
1 month ago 00:03:04 1
Bach, Organ Sonata No. 4 in E minor (BWV 528) 3. Un poco Allegro.
1 month ago 00:00:32 1
…but the people are retarded
1 month ago 00:02:36 5
Jingle Bells | Christmas Song | Super Simple Songs
1 month ago 00:02:59 1
Monster Girl Quest Paradox Part 3 OST - Ending 4-3
1 month ago 00:12:48 1
The Brand New STIHL MS400.1! WHY is this CHAINSAW different?
1 month ago 00:04:12 2
Stuart Townend - Christ Be In My Waking
1 month ago 00:05:32 1
Queen - Bohemian Rhapsody (Live at Rock Montreal, 1981) [HD]
1 month ago 00:08:10 1
AI Agents Will Create MILLIONAIRES in 2025 – Are You Ready
1 month ago 00:04:49 1
Play To Earn🔥This New Play to Earn Game is About to Make a Lot of People RICH
1 month ago 00:05:53 1
FIVE TINNED FISH YOU MUST TRY
1 month ago 00:06:39 1
TRAINS ADDON MCPE with 5 Powerful Train Engines in Minecraft Bedrock #minecraftpe #minecraft
1 month ago 00:01:17 1
Pathfinder: Wrath of the Righteous - Official Game of the Year Edition Trailer