# The Girl with the Hyperbolic Helicoid Tattoo - Numberphile | Summary and Q&A

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September 29, 2019
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Numberphile
The Girl with the Hyperbolic Helicoid Tattoo - Numberphile

## TL;DR

Mathematician explains the mathematical concepts behind her hyperbolic helicoid tattoo and explores different types of ruled surfaces.

## Key Insights

• 🫥 Helicoids are ruled surfaces made of straight lines that rotate about a central line, creating a helix-like shape.
• ✈️ Different types of ruled surfaces, such as planes and hyperbolic paraboloids, are commonly used in architecture.
• 👾 The mathematician's hyperbolic helicoid tattoo is created using the Poincaré disk model in hyperbolic space.
• 🫥 The tattoo can be manipulated by twisting and bending the central line, resulting in different shapes and curves.
• 🎥 Helicoids are not only ruled surfaces but also minimal surfaces, often found in films and other materials.
• 🥰 The mathematician has studied decomposing surfaces into helicoids and has found that they are prevalent in mathematics and art.
• 🥰 The mathematician's tattoo demonstrates the interactive nature of combining mathematics and art.

## Transcript

I wanted to tell you about the maths of my new tattoo, so I got recently a tattoo this is a hyperbolic helicoid. And so I was going to explain the math of helicoids and a little bit of hyperbolic space. So I actually went into the tattoo parlor with the line work and the shading and I had an artist who was kind enough to actually transfer that onto... Read More

### Q: What is a helicoid?

A helicoid is a type of surface that is constructed of straight lines that rotate about a central line at a constant rate, creating a helix-like shape.

### Q: What are ruled surfaces?

Ruled surfaces are surfaces made entirely out of straight lines. They can be found in architecture, as they allow for easy creation of straight objects that can be assembled to create curved surfaces.

### Q: How did the mathematician create her hyperbolic helicoid tattoo?

The mathematician used the Poincaré disk model in hyperbolic space to determine the shape of straight lines and then rotated them around a central line, resulting in a helicoid tattoo.

### Q: What is the significance of the North Pole and South Pole in the tattoo?

The North Pole and South Pole of the tattoo represent the points where the central line meets the sphere boundary of the Poincaré disk model. By manipulating the central line, the tattoo can be twisted and bent.

## Summary & Key Takeaways

• The mathematician explains the concept of helicoids, ruled surfaces made of straight lines, which can be combined with hyperbolic space to create mathematical tattoos.

• Different types of ruled surfaces, such as planes, hyperbolic paraboloids, and hyperboloids of revolution, are discussed, showcasing their prevalence in architecture.

• The mathematician demonstrates how she created her hyperbolic helicoid tattoo, using the Poincaré disk model and the concept of straight lines in hyperbolic space.