Connected Sum Of Tori Using Tikz-3dplot

Introduction

In the realm of topology, the connected sum of two tori is a fundamental concept that has been extensively studied. It involves taking two tori (doughnut-shaped surfaces) and "gluing" them together along a common circle. This operation results in a new surface, which is also a torus. In this article, we will explore how to create a 3D plot of a connected sum of two tori using the tikz-3dplot package in LyX.

Background

Tikz-3dplot is a powerful package in LaTeX that allows users to create 3D plots using Tikz. It provides a range of features, including the ability to rotate and zoom in on 3D plots. LyX is a document processor that allows users to create documents using a WYSIWYM (What You See Is What You Mean) approach. It is a popular choice among mathematicians and scientists due to its ease of use and flexibility.

Creating a Connected Sum of Two Tori

To create a connected sum of two tori, we need to define the coordinates of the two tori and then "glue" them together along a common circle. We can use the following code to create a connected sum of two tori:

\documentclass{article}
\usepackage{tikz-3dplot}
\begin{document}




















































































Introduction
In our previous article, we explored how to create a 3D plot of a connected sum of two tori using the tikz-3dplot package in LyX. In this article, we will answer some frequently asked questions about creating connected sums of tori using tikz-3dplot.
Q: What is a connected sum of two tori?
A: A connected sum of two tori is a topological operation that involves taking two tori (doughnut-shaped surfaces) and "gluing" them together along a common circle. This operation results in a new surface, which is also a torus.
Q: How do I create a connected sum of two tori using tikz-3dplot?
A: To create a connected sum of two tori using tikz-3dplot, you need to define the coordinates of the two tori and then "glue" them together along a common circle. You can use the following code to create a connected sum of two tori:
\documentclass{article}
\usepackage{tikz-3dplot}
\begin{document}

\tdplotsetmaincoords{60}{110}
\begin{tikzpicture}[scale=2,tdplot_main_coords]
\draw[thick] (0,0,0) circle (1);
\draw[thick] (1,0,0) circle (1);
\draw[thick] (0,0,0) -- (1,0,0);
\draw[thick] (0,0,0) -- (0,1,0);
\draw[thick] (0,0,0) -- (0,0,1);
\draw[thick] (1,0,0) -- (1,1,0);
\draw[thick] (1,0,0) -- (1,0,1);
\draw[thick] (0,1,0) -- (1,1,0);
\draw[thick] (0,1,0) -- (0,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (1,0,1) -- (0,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (0,1,1);
\draw[thick] (1,0,1) -- (1,1,1);
\draw[thick] (0,1,1) -- (1,1,1);
\draw[thick] (0,0,1) -- (1,0,1);
\draw[thick] (0,1,1) -- (1,1</code></pre>