Audrey Nasar - Symmetry Card Game - G4G15 February 2024

Summary

Lud Nasser, a math professor and illustrator at the Fashion Institute of Technology, introduces 'Symmetry Cards,' a deck designed to teach symmetry groups. The cards cover rosette symmetry groups, including rotation and reflection symmetries. Nasser explains the cyclic (C1-C6) and dihedral (D1-D6, D Infinity) groups, using illustrations of characters interacting with objects to demonstrate symmetry. The deck, structured like a standard playing card set, includes 52 cards and two wild cards, with games designed to teach symmetry concepts.

Takeaways

• 🎨 The speaker, Lud Nasser, is a math professor at the Fashion Institute of Technology (FIT) in New York City and also an illustrator.
• 📐 Nasser teaches courses that blend math with fields such as illustration, animation, fine arts, graphic design, and fashion design.
• 🃏 Nasser created a deck of cards called 'Symmetry Cards' to teach and introduce symmetry groups, specifically rosette symmetry groups.
• 🔄 Rosette symmetry groups include two types of symmetries: rotational symmetry and reflection symmetry.
• ⚙️ Rotational symmetry refers to shapes that look the same after being rotated by a certain angle, while reflection symmetry refers to shapes that remain unchanged when reflected along a line.
• ♻️ The two symmetry groups in rosettes are cyclic (only rotational symmetry) and dihedral (both rotational and reflection symmetry).
• 🔢 The deck has 52 cards and 2 wild cards, structured similarly to a standard deck of playing cards, with 13 ranks per color, corresponding to symmetry groups C1 to C6, D1 to D6, and D Infinity.
• 🎲 Nasser describes two games designed to teach symmetry using the cards, including a memory game where players match cards with the same symmetry group.
• 🦋 An example of matching involves finding figures with the same symmetry, such as a butterfly and an upright base, both classified as D1 symmetry (one reflection line and 360° rotation).
• 📚 Nasser has printed three editions of the Symmetry Cards and hints at a fourth edition in development.

Q & A

What is Lud Nasser's profession?

Lud Nasser is a math professor at the Fashion Institute of Technology in New York City, as well as an illustrator.

What types of courses does Lud Nasser teach?

Lud Nasser teaches math courses related to his students' fields of study, including illustration, animation, Fine Arts, graphic design, and fashion design.

What is the name of the course that covers symmetry groups?

The course that covers symmetry groups is called 'Geometry and the Art of Design'.

What are the two types of symmetries in rosettes?

The two types of symmetries in rosettes are rotation symmetry and reflection symmetry.

What is the difference between cyclic and dihedral symmetry groups?

Cyclic symmetry groups are shapes with rotation symmetry only, while dihedral symmetry groups are shapes with both rotation and reflection symmetries.

What does the notation 'C5' represent in the symmetry cards?

The notation 'C5' represents a cyclic symmetry group with an order of rotation of five.

What does the notation 'D2' signify?

The notation 'D2' signifies a dihedral symmetry group with two reflection lines and a rotation symmetry of order two.

How many cards are in the symmetry deck Lud Nasser created?

The symmetry deck consists of 52 cards and two wild cards.

What is the structure of the symmetry deck?

The structure of the symmetry deck is identical to a standard deck of playing cards, with four colors and 13 ranks per color.

What is the significance of the numbers in the symmetry groups C1 to C6 and D1 to D6?

The numbers in the symmetry groups C1 to C6 and D1 to D6 correspond to the order of rotation symmetries and, in the case of dihedral groups, also equal the number of reflection lines.

How can the symmetry cards be used to play games?

The symmetry cards can be used to play games like a memory game where pairs are found based on the same symmetry group.

What is the next step Lud Nasser mentioned regarding the symmetry cards?

Lud Nasser mentioned that he has printed the Third Edition of the symmetry cards and hopes to have a fourth edition after editing.

Outlines

00:00

📚 Introduction to Symmetry Cards

Lud Nasser, a math professor and illustrator at the Fashion Institute of Technology in New York City, introduces symmetry cards, a deck designed to teach symmetry groups. He explains that despite FIT being a fashion school, it's more of an art school where he teaches math courses related to students' fields of study such as illustration, animation, Fine Arts, graphic design, and fashion design. Nasser teaches a course called 'Geometry and the Art of Design' where he covers symmetry groups. He created the cards to teach rosette symmetry groups, specifically focusing on rotation and reflection symmetries. He gives an overview of these symmetries and explains how they can be used to categorize rosettes into cyclic (rotation only) and dihedral (both rotation and reflection) groups. The cards feature characters interacting with objects, with the object's symmetry being the focus of classification. The deck is structured like a standard deck of cards, with 52 cards and two wild cards, divided into four colors representing different symmetry groups from C1 to C6, D1 to D6, and D Infinity.

Keywords

💡Symmetry Cards

Symmetry Cards are a deck of cards designed to introduce and teach symmetry groups. They are used as a tool in educational settings, particularly in courses related to art and design, to visually represent different types of symmetries. In the script, the professor uses these cards to explain concepts of symmetry to students studying fields like illustration, animation, and fashion design.

💡Rotation Symmetry

Rotation Symmetry refers to the property of a shape that allows it to look the same after being rotated by a certain angle. It is a key concept in the study of symmetry groups. In the script, the professor demonstrates this by showing a 'Z' rotated 180 degrees and still appearing the same, indicating it has a rotation symmetry of order two.

💡Reflection Symmetry

Reflection Symmetry, also known as line symmetry, is when a shape can be divided into two identical halves by a line (the axis of symmetry). The script uses the example of the letter 'A' being reflected along a vertical line to illustrate this concept.

💡Rosette Symmetry Groups

Rosette Symmetry Groups are mathematical concepts that deal with patterns that repeat in a circular arrangement. These are the focus of the professor's course and the cards. The script mentions that these groups are divided into cyclic (rotation only) and dihedral (both rotation and reflection) symmetries.

💡Cyclic Symmetry

Cyclic Symmetry is a type of symmetry where a shape has only rotational symmetry without reflection. The script explains that cyclic groups are denoted by 'C' followed by a number, which indicates the order of rotation symmetry. For instance, a C5 would represent a shape with a rotation symmetry of order five.

💡Dihedral Symmetry

Dihedral Symmetry includes both rotational and reflectional symmetries. It is represented in the script by the notation 'D' followed by a number, which corresponds to the number of rotational symmetries and reflection lines. An example given is D2, indicating two reflection lines and a rotation symmetry of order two.

💡Symmetry Groups

Symmetry Groups in mathematics are classes of geometrical figures that are invariant under a given group of symmetry operations. The script discusses teaching these groups using the symmetry cards, which are divided into ranks corresponding to different symmetry groups like C1 to C6, D1 to D6, and D Infinity.

💡Illustration

Illustration is a form of visual art used to entertain, educate, or decorate. The script mentions that the professor teaches at a fashion school that is more akin to an art school, and the students studying illustration are among those who benefit from understanding symmetry in their artwork.

💡Memory Game

The Memory Game mentioned in the script is a suggested use for the Symmetry Cards, where pairs of cards are matched based on having the same symmetry group. This game serves as an interactive way to reinforce the understanding of symmetry concepts.

💡Finite Figures

Finite Figures are shapes that can be completely enclosed within a finite boundary. The script uses the concept to explain that all finite figures have at least a rotational symmetry of order one, as they can be rotated 360 degrees and look the same.

💡Standard Deck of Playing Cards

A Standard Deck of Playing Cards is a set of 52 cards used for various games. The script notes that the Symmetry Cards are structured similarly to allow for the use of symmetry concepts in traditional card games, thus blending educational content with familiar gameplay.

Highlights

Lud Nasser is a math professor at the Fashion Institute of Technology in New York City and also an illustrator.

He teaches math courses related to fields of study such as illustration, animation, Fine Arts, graphic design, and fashion design.

Nasser teaches a course called Geometry and the Art of Design, covering symmetry groups.

He created symmetry cards to teach rosette symmetry groups.

The two types of symmetries in rosettes are rotation symmetry and reflection symmetry.

Rotation symmetry of order two is demonstrated by a Z being rotated 180 degrees.

The letter A has one reflection line, demonstrating reflection symmetry.

All finite figures have rotational symmetry of order one as they can be rotated 360 degrees and look the same.

Rosettes can be divided into two symmetry groups: cyclic (rotation symmetry only) and dihedral (both rotation and reflection symmetries).

The deck of symmetry cards is structured like a standard deck of playing cards with 52 cards and two wild cards.

The cards are divided into four colors, each with 13 ranks corresponding to symmetry groups C1 to C6, D1 to D6, and D Infinity.

The deck can be used to play games that teach symmetry.

A basic memory game is suggested where pairs are found based on the same symmetry group.

An example match in the game is a D1, where both shapes have one reflection line and one rotation.

Nasser provides a teaser for another game that teaches symmetry.

The Third Edition of the symmetry cards has been printed and is available for purchase.

Nasser invites attendees to come to his table to play the games and get a copy of the cards.

He encourages questions from the audience about the symmetry cards and their applications.

Transcripts

[Music]

my name is lud Nasser I'm a math

professor at the Fashion Institute of

Technology in New York City as well as

an illustrator and I'm going to talk

about symmetry cards uh which are a deck

of cards um that could be used to teach

um or to introduce symmetry groups uh so

fit is a a fashion school but it's

really more of an art school and I teach

math courses that are uh relate to that

relate to my students uh fields of study

which uh include illustration animation

Fine Arts um graphic design and uh

fashion design among other things um in

particular I teach a course called

geometry and the Art of design and in

this course we cover symmetry groups uh

so I created these cards u to teach

specifically rosette symmetry groups

which I'll give a brief overview of for

those who may not be familiar with them

um the two types of symmetries in

rosettes which are finite figures are

rotation Symmetry and reflection

symmetry you could see in the on the

left the Z is being rotated 180 degre

and it looks the same so that has

rotation symmetry of order two and the a

is being reflected uh along this uh

vertical reflection line so that has one

reflection line um it also has

rotational symmetry of order one because

it can be rotated 360 Dees and look the

same that's true for for all finite

figures and so um using these symmetries

we can divide rosettes into two symmetry

groups uh cyclic uh which are shapes

with rotation symmetry only um and then

dihedral which are shapes with both

rotation and reflection symmetries um if

you notice on the left the these are

what the cards look like um and so

specifically on the left you have a

character interacting with um an

everyday object uh in this case a flat

tire and the um so I go I guess I hope

that's not an everyday object but um in

the uh in the corners you see the hubc

cap repeated and that's what we're going

to be classifying according to its

symmetry group it has um order of

rotation of five um and so that would be

considered a C5 on the right uh the uh

the bone that's uh supposed to be thrown

here um is a a dihedral it has both uh

reflection um two reflection lines um

the horizontal and vertical as well as

rotation of order two uh so that's a D2

and in in both notations the N denotes

the number of rotation symmetries but

specifically with dihedral that's also

equal to the number of reflection lines

um so the deck is made up of 52 cards

and two wild cards it's divided into

four colors red blue orange and

yellow there are 13 ranks per color and

those correspond to the Symmetry groups

C1 to C6 D1 to D6 and D Infinity so

you'll notice the structure is identical

to a standard deck of playing cards

which means that you can use the cards

to play any game that you would play

with a with a standard deck um however I

have two games to introduce uh maybe

just one and I'll leave the other as a

teaser um so and these will be

specifically to teach symmetry so um you

could do a you know basic memory game uh

where you would turn the cards over and

you look for pairs in this case what

makes a pair is if the figure uh in the

corners has the same uh or falls in the

same symmetry group so this is an

example of a of a match uh specifically

a D1 because both of those shapes the

butterfly and the upright base have one

reflection line as well as one um

rotation which is that 360° rotation uh

so now is your turn um you've got four

cards down below and you've got the card

up on the right and can you tell which

one uh would be a match so if you said

the uh the pedals that's correct they're

both uh C2 in that they have a

rotational symmetry of order two and no

reflection lines and let's try one

more hopefully you said the radioactive

symbol um which is uh correct that's um

a D3 uh and that means that they both

have three reflection lines as well as

rotational symmetry of order three okay

and I'll just give a sneak preview to

the other game this is uh my favorite um

and you'll come see me at the table if

you want to play uh and that's an

example which we won't get to uh so next

steps I just printed the Third Edition

um I already have an edit so they'll

hopefully be a fourth and you can come

get a copy at the at the sales table if

you have more questions just ask thank

you