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.

Outlines

00:00

📚 Introduction to Wallpaper Patterns

Dr. Diana Song Song introduces the final topic of the mathematics of patterns series, focusing on wallpaper patterns. Wallpaper patterns are defined as those that can cover a plane and be mapped onto themselves through translation in multiple directions. The video provides an example of creating a wallpaper pattern starting with a motif, followed by various transformations such as reflection, rotation by 120 and 240 degrees, and translation. The process involves creating a pattern that can be translated in more than one direction, with the angle between the translation vectors being 120 degrees. The lesson encourages viewers to explore the creation of their own wallpaper patterns and to visit the website of Maurice Cornelius Ashmir, a graphic artist known for his mathematically inspired artworks using fabrics.

05:00

🎨 Exploring Art and Patterns

The second paragraph delves into the artwork of Maurice Cornelius Ashmir, highlighting his use of mathematical concepts in his fabric art. The summary showcases the transformation of patterns from simple translations to more complex designs where elements like birds morph into fish. The artwork demonstrates a play on symmetry and translation vectors that change in size, contributing to the overall aesthetic of the piece. The lesson concludes with a reminder to enjoy the learning experience and a prompt for viewers to do their research on the topic. Dr. Song Song also encourages viewers to subscribe to her channel and enable notifications for future videos.

Keywords

💡Wallpaper Patterns

Wallpaper patterns are a type of two-dimensional design that can be tiled across a plane without gaps or overlaps. They are characterized by their ability to be mapped onto themselves through translation in multiple directions. In the context of the video, wallpaper patterns are the main topic, and the script discusses how they are created and used in art and design. Examples from the script include the creation process of a wallpaper pattern starting with a motif and applying transformations such as reflection, rotation, and translation.

💡Motif

A motif is a recurring element or theme that serves as the basis for a pattern or design. In the video script, the motif is the starting point for creating a wallpaper pattern. It is the fundamental design element that is manipulated through various transformations to produce the final pattern. The script mentions starting with a motif and then applying different operations like reflection and rotation to it.

💡Translation

Translation in the context of wallpaper patterns refers to the process of sliding the motif or pattern a certain distance in a straight line without changing its orientation. This is one of the key operations used to create the repeating nature of wallpaper patterns. The script illustrates translation by explaining how a motif is moved in different directions to cover the plane.

💡Reflection

Reflection is a transformation that involves flipping a motif or pattern over a line, creating a mirror image. In the script, reflection is one of the methods used to manipulate the motif and create the wallpaper pattern. The example given involves reflecting the motif vertically to generate a new part of the pattern.

💡Rotation

Rotation is another transformation technique used in wallpaper pattern design. It involves turning the motif around a fixed point by a certain angle. The script provides an example where the motif is rotated by 120 degrees and 240 degrees to create different segments of the pattern, demonstrating how rotation contributes to the symmetry and repetition in the design.

💡Glide Reflection

Glide reflection is a combination of reflection and translation that is used in pattern design. It is a transformation where a motif is reflected across a line and then translated parallel to that line. The script mentions gliding the resulting pattern to produce a new pattern, which is a way to extend the design and create a continuous, repeating pattern.

💡Graphic Artist

A graphic artist is a professional who creates visual art works, often for commercial use. In the script, Maurice Cornelius Ashmir is mentioned as a graphic artist who has used mathematical concepts and fabric to create different artworks. His work serves as an example of how mathematical principles like wallpaper patterns can be applied in the field of art and design.

💡Symmetry

Symmetry refers to the property of a pattern or design where it can be divided into parts that are mirror images of each other. In the context of the video, symmetry is an important aspect of wallpaper patterns, as they often exhibit symmetrical properties through their transformations. The script describes how the artwork by Maurice Cornelius Ashmir has a sort of symmetry, even though two parts of the design are not identical.

💡Transformation

Transformation in the context of pattern design refers to the process of altering a motif through operations like translation, rotation, reflection, and glide reflection to create a new pattern. The script explains how different transformations are applied to the motif to generate a wallpaper pattern, emphasizing the creative process behind pattern design.

💡Vector

In mathematics and design, a vector is a quantity that has both magnitude and direction. In the script, the term is used to describe the direction of translations in the wallpaper pattern. The angle between translation vectors is mentioned as 120 degrees, which is crucial for understanding how the pattern tiles the plane without gaps.

💡Tiling

Tiling refers to the process of covering a surface with a pattern that repeats in a regular, continuous manner. Wallpaper patterns are a type of tiling that can be extended infinitely in all directions. The script discusses how the transformations applied to the motif result in a pattern that can tile a plane, which is a fundamental concept in the study of patterns.

Highlights

Introduction to the final topic of the study: wallpaper patterns.

Wallpaper patterns are defined as patterns that cover the plane and can be mapped into itself by translation in more than one direction.

Examples of wallpaper patterns include gift flappers.

Creating a wallpaper pattern begins with a motif and involves various transformations such as reflection, rotation, and translation.

Demonstration of creating a wallpaper pattern through reflection, rotation by 120 and 240 degrees, and translation.

Explanation of the process of creating a pattern by reflecting a motif vertically and then rotating and translating it.

Introduction of the concept of translations in more than one direction for wallpaper patterns.

Illustration of how the angle between translation vectors in a wallpaper pattern is 120 degrees.

Invitation to the audience to participate in finding out the transformation process from one example to another.

Mention of Maurice Cornelius Ashmir, a graphic artist known for his artworks using fabrics and math.

Examples of Ashmir's artwork showcasing translations and transformations in patterns.

Discussion on the progression of patterns from birds to fish and the changing translation vector sizes.

Ashmir's artwork demonstrating the concept of symmetry in patterns.

Encouragement for viewers to create their own wallpaper patterns and to explore the provided website.

Conclusion of the lesson on math as a pattern with a hope that the audience enjoyed the lesson.

Call to action for viewers to subscribe to the channel and hit the bell button for notification updates.

Transcripts

hi everyone this is dr diana song song

and we're still continuing our study of

mathematics

of patterns we are now on our last topic

and that

is wallpaper patterns

let us now go to our last pattern

wallpaper

patterns wallpaper patterns

are patterns that covers the plane and

can be mapped into itself by translation

in more than one

direction okay so these are examples of

wallpaper patterns

for example also your gift flapper

they are wallpaper patterns

how to make a wallpaper pattern um

you always start with a motif so let's

say

this motif and then you reflect

but you can do different different

things you can

do reflection you can do rotation by a

certain thing

it's up to you this is just an example

the point is you always start with a

motif in this particular example we

reflect this motif

vertically to obtain this and then using

this

figure we rotate it by 120 degrees and

240 degrees to produce

this one and then you now translate this

figure okay and

you glide the resulting pattern to

produce

this one and then you just continue

doing this and then you get a pattern

so these are examples of

wallpaper patterns so you start you

started with this

motif and then what happened you

reflected

it um you have

vertical so from here

you have vertical translation and

similarly you have

120 and 240 degrees

floating shot and then from this

you now do

so this is just reflection here right

you have two directions remember for

wallpaper patterns

you can have translations in more than

one direction so in this direct

you have two directions this direction

and

this direction we're in the angle

between these two vectors

are is 120

okay so for our next example

we have this motif and then what

happened

here you have 120 degree

rotation and then i leave it up i will

division

to you to find out how it

went from here to here okay

um this is another example everything

just started with uh

okay and then from here

where is that okay i will leave it as an

exercise for you to think about what

happened from

here to here okay you can make your

own wallpaper pattern um i want you to

look at

uh website in order to do this

okay who is this maurice

cornelius ashmir he is a

graphic artist who the

hooded different art

artworks using um fabrics in math so

these are

examples okay so it's like you have

translations but then as

you progress let's see you progress

from here but then the bird became fish

and then

it looks as if he is just

translating right but then the

translation vector it becomes smaller

and smaller and then it becomes bigger

and bigger again

so that this art has a sort of

symmetric because these two are not

symmetric but

yeah anyway so these are also

um some of his famous artwork so

it's like a flat

correct but then look at that the

patterns are

this is the bigger version this is the

smaller version

okay and it's like our lists are those

steps it's like i just said

with a flat but anyway so

um that concludes our lesson

in math as a

pattern so i hope you enjoyed this

lesson

and okay you can all do your res for

this lesson

thank you for watching my video for more

videos like this don't forget

to subscribe to my channel and don't

forget also to hit the bell button for

notification updates

see you on the next video