Project Draft

 Renu and Rabia

project draft

 Week 10 Reading Reflection on

Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving

by

Gwen L. Fisher

In this paper, Gwen L. Fisher describes how impossible triangles are used to create sculptures with beads and thread, using a technique called "cubic right angle weave"(CRAW). "The impossible triangle, also called the Penrose triangle, is a two-dimensional drawing that represents three straight beams with square cross sections, and the beams appear to meet at right angles"(p.100).

The impossible triangle

The impossible triangle was independently discovered by the mathematician Roger Penrose, and a graphic designer  M.C. Escher, who, in turn, used it in his art. The beaded version of an impossible triangle is quite possible and it is not very intuitive. The twist in the beadwork allows the impossible triangle to be constructed in 3D.

Here is the link for mathematical beading by Gwen L. Fisher,

Mathematical Beading by Gwen L. Fisher

I have found this video of making ear studs by beading

beading ear stud

"A highly unlikely polygon is a beaded polygon whose edges are rectangular beams with a quarter twist. For a highly unlikely polygon with an odd number of beams (e.g., the triangle), there is a single path on the face that travels around the polygon four times. When the polygon is a square, the path on the faces separates into four, distinct paths that each travel all the way around the polygon only once. Similarly, there are four paths for the edges."(p.102)

Stop

"To resolve the paradox of the impossible triangle, a highly unlikely triangle exhibits a quarter twist on each beam. The twist in the beadwork allows the impossible triangle to be constructed in 3D. The twist in the beaded version also destroys the optical illusion due to the curvature it introduces to the edges that appear straight in the 2D drawing."(p.100)

The author's reaction to making an impossible triangle struck me because we may feel that everything is impossible when we first see it. When we see an impossible triangle we may feel like creating it is a difficult task because it is how our brains interpret shapes. It seems like a puzzle that makes you confused about what is real and what is not where to start and where to end. When we relate it with art we get a solution.

Question

What makes the highly unlikely triangle different from regular triangles, and how does it mess with our brains?Do you feel it like easy to make?

Reference

Fisher, G. L. (2015). Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving. In Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture. Sunnyvale, CA, USA: beAd Infinitum.

 

 Kerala style Mat Making

Last day, in our class we discussed different kinds of braiding and I would like to show Kerala-style mat-making. This mat is especially used for newborn baby bathing. Susan gave me this material for making a mat but it was not working(first one). So I decided to go with A4 paper. I made long paper strips from A4 paper and braided this mat. My friends Aiswarya and Rabia helped me to make it beautiful. We can see different angles and patterns in this.

 WEEK 9

Artist interview: JoAnne Growney

By Sarah Glaz

Summary

This article is all about JoAnne Growney's Life, which integrates both math and poetry. The content is an interview conducted by Sarah Glaz in 2017 during the Bridges conference in Canada. JoAnne shares her experiences and insights into her journey through math and poetry. She shares about her childhood days, her inspiration to start writing poems, math, poetry and her blog. She writes poems based on her real-life experiences, environmental issues, scarcity of women in mathematics, and abortion, and connects them with math. She says that math and poetry are the best blend. JoAnne was part of the pioneering group of mathematicians who not only wrote poetry with strong links to mathematics but also enthusiastically supported the cause of making mathematical poetry a visible and respected part of the collective creative work of both poets and mathematicians. The interview and the ten poems authored by JoAnne presented in this article reflect on the various influences and events in JoAnne’s journey through a life that includes both mathematics and poetry.

JoAnne Growney

JoAnne Growney reads "Love Mathematics!" and "A Baker's Dozen"

Stop 1

This poem really made me stop and think about the issue of the scarcity of women in the STEM field. It is a long-standing issue. Even if we say that everything is in progress there is a small number of women representing these fields. The main reasons are educational biases, lack of role models, unconscious biases, unwelcoming workplace cultures, and family expectations. I hope there will be a change in the upcoming days. Jo Anne presents this issue connecting with math in a beautiful way of 5 🇽 5 syllable square poem.

Stop 2

Can a mathematician See Red?

Consider the sphere—

a hollow rounded surface

whose outside points

are the very same points

insiders see.

If red paint spills

all over the outside,

is the inside red?

The mathematician says, No,

the layer of paint

forms a new sphere

that is outside the outside

and not a bit inside.

A mathematician

sees the world

as she defines it.

A poet

sees red

inside.

This poem explains the perspectives of a mathematician and a poet on a seemingly simple object – a sphere. I think it is a true fact because everyone defines objectives by their own perception or profession. When I was working as a math teacher, we faced different situations. Sometimes, math teacher thinks about logic and reasoning and they try to find the solution. Language teacher sees it emotionally and artistically. By the end of the day, as JoAnne says everything connects and math and art are a perfect blend.

Question

"How can combining math and writing poems in school help us understand things better?"

Reference

Glaz, S. (2019). Artist interview: JoAnne Growney. Journal of Mathematics and the Arts, 13(3), 243–260. https://doi.org/10.1080/17513472.2018.1532869

 Week 9 Activity

Fibonacci Poem

 It is a small poem about my son, Aloshy who is in India. I try to explain my emotions by using the Fibonacci series, 

1 1 2 3 5 8 13  

Aloshy, 

Cute 

My Aloshy, 

He is cute 

Sometimes he is little shy 

I love him even before he born here 

Aloshy, my darling, sweet and charm, captured my heart's eternal tie 

In my dreams, you shine, my dear, forever cherished, never apart.

I know you are far away from here

But you caught my eye 

You my sunshine 

Be mine 

Love  

you 

Activity 2

PH4 poems

 

 

 

Activity Clap Hands

We tried this activity with my roommates and Rabia's Kids. It was really an awesome activity and everyone took it as a challenge. First, each of the groups was confused with deciding the steps after that it was with remembering the sequence and pattern. Then Zainab memorised everything by telling the names of each step. It was a good idea. Then everyone followed it. This is good for teaching multiplication tables where we can clap as many times as in a table for 2,3 and 4. For table 2, for the first round give 2 claps, then 4 jumps, etc..

 WEEK 8 

Reflection on

Dancing Mathematics and the Mathematics of Dance 

by Sarah Marie Belcastro and Karl Schaffer

In this journal article, the authors, who are both into math and dance, explain how math is connected to dance. They point out that counting steps and noticing shapes in dance involve math, and deeper connections exist where math inspires and solves dance problems. They share their experiences in modern dance and other styles, showing how math is present in the rhythm and patterns of movements. They discuss how different dance traditions, like ballet and Bharatya Natyam, use math in their unique ways, such as creating lines and symmetry. The authors explore how symmetries in dance can interact with each other. They focus on four specific symmetries: translation, mirror reflection, 180-degree rotation, and glide reflection. By combining these symmetries in pairs, they create what's known as the Klein four group or Z2 ⊕Z2. They illustrate this concept using three dancers, showing that a mirror reflection of the first dancer leads to the position of the second dancer, a 180-degree rotation of the second dancer corresponds to the third dancer, and this is equivalent to applying a glide reflection to the first dancer. The authors note that similar outcomes occur when combining any pair of symmetries from the original list, always resulting in one of the four symmetries mentioned.

The authors share how they've blended math and dance in various performances. Karl and Erik Stern's show combines math discussions with dances exploring basketball physics and tap dance rhythms. Sarah-marie's ballet trio, "Crystalline Meringue," uses symmetries, while "Swirly Suite I" incorporates binomial coefficients. Karl, Scott Kim, and Barbara Susco's "Trio for Six" involves finger geometry and illusions.

                                                        

 Karl's recent dance, "Fragments," explores war's fragmentation using tangram pieces, leading to a math question about polyhedra. The article also discusses the influence of mathematical patterns on rhythm in dance.

dance by Dr Schaffer and Mr stern

Stop 1

"Each dance tradition has its own characteristic way of using mathematical concepts. For example, classical Western ballet and Bharatya Natyam both use a strong sense of line. However, as Karl’s teacher Kathryn Kunhiramen pointed out to him, in Bharata Natyam the dancer’s lines end—they are cut off by abstract or representational mudras made by flexing the hands. This situates the dancer “in the world,” rather than extending beyond it into the “world of the gods.” In contrast, the ballet dancer’s lines extend toward infinity, symbolizing an endless extension over the natural world."(p.16)

Ballet

Bharatanatyam

This paragraph is really interesting to me because it talks about how different dance styles use the idea of lines in unique ways. For instance, in Bharata Natyam, the lines created by dancers end with hand gestures, keeping them connected to the real world. In contrast, in classical ballet, a dancer's lines extend endlessly, suggesting a connection to the infinite and the natural world. As a math teacher and reader, it's cool to see how these dance styles express mathematical ideas in their own cultural and artistic ways. It's a reminder that math isn't just numbers; it can be found in various forms of art and expression.

Stop 2

The second stop is about the Klein group which I mentioned above. When we integrate math into art forms these types of abstract concepts can be easily understood by students. As a math teacher, this integration of group theory with dance not only makes the subject more engaging but also emphasizes the broader applicability of mathematical concepts beyond traditional problem-solving contexts. It encourages students to see mathematics as a dynamic and creative tool that can be used to understand and appreciate various forms of art and expression.

Question

How can educators effectively integrate mathematical concepts, with dance in higher grade levels to foster a deeper appreciation for both disciplines and enhance students' analytical and creative skills? Do you have any experience in this?

Reference

Belcastro, S. M., & Schaffer, K. (2011). Dancing Mathematics and the Mathematics of Dance. Math Horizons, 18(3), 16-20. Taylor & Francis, Ltd. on behalf of the Mathematical Association of America. https://doi.org/10.4169/194762111X12954578042939