3-fold

3-fold

3-fold is a term that can refer to various concepts across different fields, including mathematics, origami, and general usage. This article explores the different contexts in which the term "3-fold" is used.

Mathematics

In mathematics, a 3-fold is a type of algebraic variety that has a dimension of three. Algebraic varieties are fundamental objects of study in algebraic geometry, and a 3-fold is specifically a variety that locally resembles a 3-dimensional Euclidean space.

Examples

• Calabi–Yau manifold: A special type of 3-fold that is important in string theory.
• Fano variety: A type of 3-fold with ample anticanonical bundle.

Origami

In the art of origami, a 3-fold refers to a folding technique where a piece of paper is folded into three sections. This technique is often used to create complex designs and structures.

Techniques

• Valley fold: A basic fold where the paper is folded towards the folder.
• Mountain fold: A basic fold where the paper is folded away from the folder.

General Usage

In general usage, "3-fold" can describe anything that is tripled or has three parts. For example, a 3-fold increase means that something has increased to three times its original amount.

Related Pages

• Algebraic variety
• Calabi–Yau manifold
• Fano variety
• Origami
• Valley fold
• Mountain fold