A **Möbius strip** (or **Möbius band**) is a fascinating mathematical surface with only **one side** and **one edge**. It was discovered independently by German mathematicians **August Ferdinand Möbius** and **Johann Benedict Listing** in 1858. ### **Key Properties of a Möbius Strip:** 1. **Non-orientable Surface**: Unlike a regular strip, it has no distinct "inside" or "outside." 2. **One-Sided**: If you start drawing a line along the surface, you’ll eventually return to your starting point without lifting the pen, covering "both sides." 3. **One Boundary Edge**: It has only one continuous edge, unlike a normal loop, which has two. 4. **Twist Effect**: It is made by taking a rectangular strip, giving it a **half-twist (180° twist)**, and then joining the ends. ### **How to Make a Möbius Strip:** - Take a long strip of paper. - Twist one end **halfway** (180°). - Tape the ends together. ### **Interesting Experiments:** - If you cut a Möbius strip **lengthwise down the middle**, instead of falling apart, it becomes a **longer twisted loop** (not another Möbius strip). - If you cut it **one-third of the way from the edge**, you get **two interlinked rings**—one Möbius strip and a longer twisted loop. ### **Applications:** - Used in **conveyor belts** (to ensure even wear on both "sides"). - Inspires designs in **mathematics, art, and engineering**. - Appears in **topology** (the study of geometric properties preserved under deformations). `Concepts:` `Knowledge Base:`