What are wallpaper patterns | Mathematics in the arts
Summary
TLDRIn 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
- đ The lesson is about the study of mathematics, specifically focusing on wallpaper patterns.
- đ Wallpaper patterns are defined as patterns that can cover a plane and be mapped onto themselves through translation in more than one direction.
- đš Examples of wallpaper patterns include gift flappers, which are a type of pattern that can be created using specific mathematical transformations.
- đïž To create a wallpaper pattern, one typically starts with a motif and then applies various transformations such as reflection, rotation, and translation.
- đ The process involves reflecting the motif vertically, rotating it by 120 and 240 degrees, and translating the figure to create a repeating pattern.
- đą The transformations can be in multiple directions, and the angle between the translation vectors is 120 degrees for the given example.
- đ€ The video encourages viewers to think about the transformation process and to create their own wallpaper patterns.
- đšâđš Maurice Cornelius Ashmir is mentioned as a graphic artist who uses fabrics and math to create different artworks, which can be studied for inspiration.
- đš Ashmir's artwork demonstrates how patterns can evolve, with translations and changes in size creating a sense of symmetry and progression.
- đ The lesson concludes with an invitation for viewers to do their own research and to subscribe to the channel for more educational content.
- đ 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
đ 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.
đš 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.
Mindmap
Keywords
đĄWallpaper Patterns
đĄMotif
đĄTranslation
đĄReflection
đĄRotation
đĄGlide Reflection
đĄGraphic Artist
đĄSymmetry
đĄTransformation
đĄVector
đĄTiling
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
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