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### Klein Bottles without Holes, or How to Crochet Through

After I crocheted Whitney Umbrellas, I got excited that I figured out how to crochet through an existing layer of fabric. I decided to use my skills to crochet “correct-er” Klein bottles. A Klein bottle is a cool mathematical surface with only one side, similar to the Möbius strip. Unlike the strip, the Klein bottle […]

### Crocheting Away My Pain

Putin became the 21st century Hitler. I call him Putler. I am an American. However, I was born in Moscow and lived my youth in the Soviet Union. I speak Russian, and I have friends in both Russia and Ukraine. The war in Ukraine is the biggest tragedy of my life. When Putler invaded Ukraine, […]

### Trying to Crochet the Impossible

I’ve been crocheting hyperbolic surfaces of constant curvature. The process is time-consuming, so while I am crocheting, I wonder about the mathematics of crocheting. Hilbert’s theorem says that I can’t embed a hyperbolic plane in 3-dimensional space. The proof is rather involved. But here, I have an explanation from the point of view of a […]

### Solomon’s Knot

I deleted my previous post about Solomon’s knot. The reason is simple. I made the mistake of trusting Wikipedia. I was sure that the linking number of Solomon’s knot was 2. Then Wikipedia said it was 0, so I fixed “the error” in my post. One of my readers corrected me. So, I rechecked it, […]

The Museum of Mathematics organizes a biannual conference in recreational mathematics called MOVES: Mathematics Of Various Entertaining Subjects. Being a math-recreatinalist myself, I attend all of them. The last one was held in August 2023 and was devoted to the mathematics of Fiber Arts. A few years ago, I wouldn’t have believed I had something […]

### Borders of Strips

Why would I complicate my life by crocheting colored borders onto different strips? Answer: I wanted to emphasize their borders. Do you recognize the objects in the picture? The leftmost one is a Möbius strip. I made it by crocheting a long rectangle. Then, instead of connecting the short sides to form a cylinder, I […]

A link is defined as two closed curves in three-dimensional space. The first picture shows an example of a link with one yellow curve and one blue. The linking number is a simple numerical invariant of a link. Intuitively, it represents the number of times that each curve winds around the other. For example, if […]

### Whitney Umbrellas

A Whitney umbrella is a cool surface I wanted to crochet. The umbrella continues to infinity, and there is no way I want to crochet the whole thing. I wanted to make a finite portion of a Whitney umbrella surrounding the most exciting point. The result is seen in the picture. Technically, I crocheted not […]