Making an architecture using string art

Journey of Delhi Eye by KHMS

@ Math-Medley

Submitted by Aditi Bansal, K.R. Swathi, Ishita Banati, Shreeya Gupta

Kulachi Hansraj Model School, Ashok Vihar, Delhi, India

Contents

S.No. Content

Principal’s Desk
What is String Art?
Meet our team
The Challenge
Our Model- Delhi Eye
Our Journey- Some experiments
Mathematics Explored
Acknowledgements

Principal’s Desk

The impact of mathematics and creativity is intrinsic. It brings education to the front lines and in the prevailing discourse is expected to be a major tool for incorporating the knowledge in the society using hands-on. $E:\IT_projects\ICT_globalisation\photographs\princi.gif$

I am glad that my students K. R. Swathi, Ishita Banati, Aditi Bansal and Shreeya Gupta are a part of this novel initiative- Math Medley. It is a matter of great pride and joy for me that my students are participating in such an event wherein they get an opportunity to get create as well as innovate using string art. Mathematics is as powerful as a language.

I once again, thank DAV, Gurgaon for having organised such a competitive event, which not only facilitates competitiveness, creativity and teamwork but also helps students to build up their capabilities and strengths. I look forward to many such events in future.

Wishing success in every endeavour in this and the other forthcoming projects.

Ms. Sneh Verma

Principal, Kulachi Hansraj Model School

What is String Art?

Our Research

String art, or pin and thread art, is characterized by an arrangement of colored thread strung between points to form geometric patterns.

A stretched thread in string art represents a line segment.
Threads are arranged in such a way that they appear to form curves, representing a parabola

String art has its origins in the 'curve stitch' activities

Meet our Team:

Our project focuses on building and enhancing several aspects in the model- Beautification, mathematical concepts, realisticness, significance and many more.

Our team of four includes:

Aditi Bansal
K.R. Swathi
Ishita Banati
Shreeya Gupta

Following are the jobs which had been allotted to the team :

Aditi Bansal

My Job: To make and present the model, do the artwork and cater to the beautification.

My qualities: Good speaking skills, creative and a perfectionist!

Ishita Banati

My Job: To analyse all progress and compile them in form of written drafts.

My qualities: Efficiency in writing, command over language and love for maths!

K. R. Swathi

My Job: To coordinate all the activities done by the team, provide all technicaL support.

My qualities: love for computers and maths, leadership, commitment and never-say-die attitude!

Shreeya Gupta

My Job: model making, construction of architecture and beautification.

My qualities: always been creative, storehouse of ideas and desire to learn!

The Challenge

We had worked earlier with string art in 2-D form, but the real challenge was to bring this art form into 3-Dimension.

One of the major challenges that we faced in our journey was making an architectural structure using string art, that not only looks visually appealing, but also stores a number of mathematical concepts in it.
We also had to adhere to all specifications by making a model in a 24 * 24 inch base and 18 inches height.
Above all, we four students had so many ideas, that it was essential to finalise an idea and work upon it.

Planning and implementation go hand in hand. Before action, it is vital for us to plan our steps and act accordingly.

The various ideas discussed by us include:

To make an architectural structure using 3 icosihenagons lifted to a specific height.
To make 3-D geometric figures using curves and parabolas.

Our Model: Delhi Eye

We had worked earlier with string art in 2-D form, but the real challenge was to bring this art form into 3-Dimension.

One of the major challenges that we faced in our journey was making an architectural structure using string art, that not only looks visually appealing, but also stores a number of mathematical concepts in it.
We also had to adhere to all specifications by making a model in a 24 * 24 inch base and 18 inches height.
Above all, we four students had so many ideas, that it was essential to finalise an idea and work upon it.

Planning and implementation go hand in hand. Before action, it is vital for us to plan our steps and act accordingly.

The various ideas discussed by us include:

To make an architectural structure using 3 icosihenagons lifted to a specific height.
To make 3-D geometric figures using curves and parabolas.

Our model has various components:

Giant wheel for having a look at whole Delhi
Cafeteria
Merry-go-round for kids
Parking area

Our Journey- Some Experiments

Let’s peep into our journey towards achieving our objective of making “Delhi Eye” through the initiative “ MATH MEDLEY”.

Date	Activity	Memories
9.12.15	Our first meeting: we did a research on the internet and a lot of brainstorming on the framing of idea. Keeping in view the specifications of the 3D Model, we shortlisted 3 ideas namely making an architecture using 3 icosihenagon using string art, 3D designing of bridges and designing an amusement place.
10.12.15	Since all the ideas were beautiful, so we decided to poll. Maximum votes were for designing an amusement place. So, we decided to procure the materials as per the requirements. We decided upon having a cafeteria, a merry-go-round, and a giant wheel.
11.12.15	Swathi and Shreeya cut the wood pieces in the carpenter's room of our school, did painting and created frames for their final model. we learnt a new technique called Regmar, which meant smoothening the edges of the cut wooden pieces, and to paint the model using special equipments.
12.12.15	We had decided the model, and now it was time to finalise the string art used. Since the Giant wheel is indeed, a giant structure, we had to use a stiff and turgid string art to give support, as well as aesthetic sense. Thus, we decided to make an icosihenagon, a 21-sided polygon using string art.
13.12.15	We utilised our Sunday in doing a research on internet and created the rough draft on the paper of various string art designs. We all were connected on Google Drive and Picasa web album and discussed ideas.
14.12.15	We started practising making icosihenagons on paper. After some foiled attempts, we finally learnt to make the 21-sided polygon. Interesting observations were made while making icosihenagons using straight line segments. We found out that the number of pegs left after wrapping the thread each time forms an AP.
15.12.15	We again reached the carpenter’s den, to get the ready, dry pieces of wood, and started off with our work. We also learnt to use the special wood-cutting machine to cut small blocks of wood. We nailed, hammered and fixed the model. It was a thrilling experience.
16.12.15	We nailed the wooden pieces as per the design of the model, and started making our model. We also simultaneously started jotting down all the mathematical concepts used in our model.
17.12.15	Aditi and Shreeya started with creating string art on the frames of the architecture using strings. It was indeed challenging, yet fun.
18.12.15.	We did the final assembly of our model and checked if all our artwork is in place.
19.12.15	We started preparing for our final presentation. Ishita and Swathi started off with the report and the powerpoint presentation.
20.12.15	We prepared our final report to be presented on the 22nd.
21.12.15	We rehearsed for our final presentation. We took out printouts of reports, ppts, and made a checklist of items to be taken with us on the final event.

MATHEMATICS Explored

While designing the ‘Delhi Eye’ Giant wheel, following mathematical observations were made:

Making of icosihenagon: Icosihenagon is a polygon with twenty-one edges and twenty-one angles. When made using string art, it proves to be a very stiff and turgid piece, and looks very beautiful, too.

Stage 1	Stage 2	Stage 3
Stage 4	Stage 5	Stage 6
Stage 7	Stage 8	Stage 9

Observations for central angles and area of sectors from each angle.

Wrapping leaving (no.of pegs)	Central Angle (ϴ)	Area of sector (ϴ/360° * π r2) (in inch2)
no peg	17.1°	9.5456
1 peg	34.2°	19.0912
2 pegs	51.3°	28.6368
3 pegs	68.4°	38.1824
4 pegs	85.5°	47.7280
5 pegs	102.6°	57.2376
6 pegs	119.7°	66.8192
7 pegs	136.8°	76.3648
8 pegs	153.9°	85.9104
9 pegs	171.0°	95.4560

It is observed that the degree of the central angle after leaving successive number of pegs is increasing by a constant of 17.1°.

We also observed that the area of the sector is also increasing with a common difference of 9.5456 inch2 . Both these measures are found to be in Arithmetic Progression.

After the completion of stages 1, 2 and 3, we find out that the second mark comes after 12 pegs from the first one, and the third peg also comes 12 pegs after the second one. A similar pattern is found to be observed up to the 21st mark.

Stage 3 Stage 4

While designing the Cafeteria of our amusement park, we made the following mathematical observations:

When straight lines are joined together, they form a curve-like appearance. This curve is a parabola.
Parabolas made in different angles form different type of curves. It was interesting to observe that the smaller the angle, the steeper the curve. As the angle expands, so does the parabola.

Acknowledgement

They say that it’s the journey that matters, not the final destination. Even we believe the same. There are several people, who accompanied us through the journey, and thus, made it more memorable.

Thank you, Madam Principal Ms. Sneh Verma, for giving us an opportunity to participate in a collaborative, competitive and enjoyable environment, and representing the school in this event.

A special thank to Ms. Rashmi Kathuria, for being the most consistent form of inspiration for us. Thank you for being the great source of motivation.. We all couldn’t have accomplished the task without your guidance. Your vision helped give the structure to our ideas.