Explore the Two-Torus T²: A Visual Guide and Explanation

  • Thread starter waterfall
  • Start date
  • Tags
    Picture
In summary, the conversation discusses the difficulty in finding a picture of a two-torus T² on the internet and the suggestion to search for a standard torus instead. The standard embedding of T^2 in R^3 is also mentioned, along with a request for videos showcasing complex topologies like 6 dimensional Calabi-Yau being ricci-flat. A link to a picture of the standard embedding of T^2 in R^3 is provided.
  • #1
waterfall
381
1
Hi, I can't find any picture of a two-torus T² in the net after much searching. Does anyone have a link or can draw what it looks like? Thanks.
 
Physics news on Phys.org
  • #4
oh. so it's just a donut.. I was thinking of many dimensional donuts...

if anyone has links to videos which show clearly how complex topologies like 6 dimensional Calabi-Yau can be ricci-flat, pls share it so it can be appreciated visually... thanks.
 
  • #5
The standard embedding of T^2 in R^3 is of course not flat. You need to consider it as a product of circles in R^4 for that.
 

1. What is a Two-Torus T²?

A Two-Torus T² is a mathematical concept that represents a two-dimensional surface with the shape of a doughnut. It is formed by taking a square and connecting the opposite sides, creating a tube-like shape.

2. How is a Two-Torus T² different from a regular torus?

A Two-Torus T² differs from a regular torus in the way it is constructed. While a regular torus is formed by taking a circle and revolving it around an axis, a Two-Torus T² is formed by connecting opposite sides of a square. This results in a different shape and topology.

3. What are some real-life applications of the Two-Torus T²?

The Two-Torus T² has various applications in mathematics and physics. In mathematics, it is used to study complex functions and differential equations. In physics, it is used to model the behavior of particles in a magnetic field. It also has applications in computer graphics and game development.

4. How is the Two-Torus T² visualized?

The Two-Torus T² can be visualized in different ways, such as a flat square with opposite sides connected, a torus with a hole in the center, or a circular graph with two holes. In this visual guide, we will be using a flat square with opposite sides connected to demonstrate the properties of the Two-Torus T².

5. What is the significance of understanding the Two-Torus T²?

Understanding the Two-Torus T² can provide insights into higher-dimensional spaces and topology. It also has various applications in mathematics and physics, making it an important concept for scientists and researchers. Additionally, it helps us better understand the complex and fascinating nature of the universe we live in.

Similar threads

Replies
4
Views
2K
Replies
19
Views
3K
  • Topology and Analysis
Replies
12
Views
4K
  • Differential Geometry
Replies
2
Views
3K
  • Quantum Physics
Replies
1
Views
623
  • Differential Geometry
Replies
4
Views
8K
  • Linear and Abstract Algebra
Replies
14
Views
630
Replies
22
Views
2K
Replies
4
Views
837
  • Introductory Physics Homework Help
Replies
14
Views
1K
Back
Top