What are wallpaper patterns | Mathematics in the arts

Summary

In this educational video, Dr. Diana Song Song delves into the fascinating world of wallpaper patterns, a mathematical study of patterns that can be translated across a plane in multiple directions. She introduces viewers to the concept by starting with a motif and demonstrating how it can be transformed through reflection, rotation by 120 and 240 degrees, and translation to create intricate designs. Song Song encourages viewers to explore the work of graphic artist Maurice Cornelius Ashmir, who uses mathematical principles in his art, blending translations with transformations to create visually stunning patterns. The lesson concludes with an invitation to create one's own patterns and to explore further through research, with a reminder to subscribe for more enlightening content.

Takeaways

• 📚 The lesson is about the study of mathematics, specifically focusing on wallpaper patterns.
• 🔍 Wallpaper patterns are defined as patterns that can cover a plane and be mapped onto themselves through translation in more than one direction.
• 🎨 Examples of wallpaper patterns include gift flappers, which are a type of pattern that can be created using specific mathematical transformations.
• 🖌️ To create a wallpaper pattern, one typically starts with a motif and then applies various transformations such as reflection, rotation, and translation.
• 🔄 The process involves reflecting the motif vertically, rotating it by 120 and 240 degrees, and translating the figure to create a repeating pattern.
• 🔢 The transformations can be in multiple directions, and the angle between the translation vectors is 120 degrees for the given example.
• 🤔 The video encourages viewers to think about the transformation process and to create their own wallpaper patterns.
• 👨‍🎨 Maurice Cornelius Ashmir is mentioned as a graphic artist who uses fabrics and math to create different artworks, which can be studied for inspiration.
• 🎨 Ashmir's artwork demonstrates how patterns can evolve, with translations and changes in size creating a sense of symmetry and progression.
• 📘 The lesson concludes with an invitation for viewers to do their own research and to subscribe to the channel for more educational content.
• 🔔 Viewers are reminded to hit the bell button for notification updates to stay informed about future videos.

Q & A

What is the main topic of Dr. Diana Song's video?

The main topic of Dr. Diana Song's video is the study of wallpaper patterns in mathematics.

What are wallpaper patterns according to the video?

Wallpaper patterns are designs that cover a plane and can be mapped onto themselves through translation in more than one direction.

What is the first step in creating a wallpaper pattern?

The first step in creating a wallpaper pattern is to start with a motif.

What are some of the operations that can be performed on a motif to create a wallpaper pattern?

Some operations that can be performed on a motif to create a wallpaper pattern include reflection, rotation, translation, and glide reflection.

What is a motif in the context of wallpaper patterns?

A motif in the context of wallpaper patterns is the basic unit or element from which the pattern is generated through various transformations.

How many directions can translations occur in a wallpaper pattern?

In a wallpaper pattern, translations can occur in more than one direction.

What is the significance of the angle between the translation vectors in wallpaper patterns?

The angle between the translation vectors, such as 120 degrees mentioned in the video, is significant as it contributes to the symmetry and overall structure of the wallpaper pattern.

Who is Maurice Cornelius Ashmir and how is he relevant to the video?

Maurice Cornelius Ashmir is a graphic artist known for creating different artworks using fabrics and math. His work serves as an example of applying the concepts of wallpaper patterns in art.

What is an example of transformation that Maurice Cornelius Ashmir uses in his artwork?

In Ashmir's artwork, an example of transformation is the progression from a bird motif to a fish motif, with changes in the translation vector's size to create a sense of symmetry.

What does Dr. Diana Song suggest viewers do to learn more about creating their own wallpaper patterns?

Dr. Diana Song suggests that viewers look at Maurice Cornelius Ashmir's website and artworks to get ideas and inspiration for creating their own wallpaper patterns.

How can viewers stay updated with Dr. Diana Song's channel for more videos on patterns and mathematics?

Viewers can subscribe to Dr. Diana Song's channel and hit the bell button for notification updates to stay updated with more videos on patterns and mathematics.