## A session with Last School Children

On the 28th of July, the STEM Land team visited Last School for a session with them. The facilitating team Prabhaharan, Arun, and Illamkathir along with the last school children worked on RTL tools, seven segment displays, Cast puzzles, and the homopolar motor.

The session started with a few minutes of meditation. The team started the session with the Radical transformational leadership tool that helped children identify the universal values they stand for. Then the team helped the children identify their socialized fears and how courage is not the absence of fear, but the ability to act despite fear.

Later, we learned about the Seven segment Display and its primary uses. Our team explained how to use a multimeter and analyze the SSD and showed a demo. With that reference, the children worked on it and completed it.

Later, the working of the homopolar motor was demonstrated to the children. A Homopolar motor is one of the simplest motors built because it uses direct current to power the motor in one direction. The magnet’s magnetic field pushes up towards the battery and the current that flows from the battery travels perpendicular to the magnetic field. Students had a great time making it.

The whole session was engaging, encouraging, and enlightening. It was a great learning for everyone and we thoroughly enjoyed working with them.

Students from Last School requested to come to STEM Land on Saturdays to learn programming like Scratch and Python.  We will start such sessions soon.

## SET Theory Game

A set is a collection of objects or groups of objects. These objects are often called elements or members of a set. For example, a set of all squares.

A set can be understood playfully using a set game that constitutes 3 components. The three components are

• Colour
• Shape
• Size

It comprises:

Colour: Blue, yellow and green

Shape: Square, triangle, and circle

Size: small, medium, and large.

In total, there are 27 pieces which include

9 triangles (x3 colours, x3 shapes):

The three blue triangles are small, medium, and large.

The three yellow triangles are small, medium, and large.

The three green triangles are small, medium, and large.

9 squares (x3 colours, x3 shapes):

The three small blue squares, medium, and large.

The three small yellow squares, medium, and large.

The three small green squares, medium, and large.

9 circles (x3 colours, x3 shapes):

The three blue circles are small, medium, and large.

The three yellow circles are small, medium, and large.

The three green circles are small, medium, and large.

This set game can be used by children for a better understanding of set theory concepts.

Set Operations:

The four important set operations that can be performed using this set game are:

• Union of sets
• Intersection of sets
• Complement of sets
• Difference of sets

Union of sets:

The union of two sets is a set containing all elements that are in A or B (possibly both). The union of sets can be denoted using the symbol ‘U’. Symbolically, we can represent the union of A and B as A U B.

For example, A = Set of blue colour triangles and B = a Set of Green colour triangles.

Then the union will be all the triangles which are in blue and green.

The intersection of sets:

The intersection of two sets A and B is the set of all those elements which are common to both A and B. The intersection of sets can be denoted using the symbol ‘∩’. Symbolically, we can represent the intersection of A and B as A ∩ B.

For example, A = Set of blue colour objects and B = a Set of all triangles.

Then the intersection will be the triangles which are in blue.

Compliment of sets:

The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. The complement of set A can be denoted using the symbol A’.

For example, A = Set of blue colour circles and U = Set of all circles

Then the complement of A, A’ will be circles which are in yellow and green.

Difference of sets:

The difference between sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as “ A minus B”.

For example, A = Set of all green colour objects and B = Set of all squares.

Then the difference between A and B, A-B will be set of all green colour objects except squares.

Fundamental Properties of Set operations that can be observed:

The operations such as union and intersection in set theory obey the properties of associativity and commutativity. Also, the intersection of sets distributes over the union of sets.

Similarly, the set theory game can be used for understanding three sets and their operations.

## LAST SCHOOL STUDENTS VISIT STEMLAND

On the 14th of July students from the Last school, Auroville visited STEMLAND. The forty students accompanied by the teachers enjoyed their afternoon session by exploring STEMLAND.

The arrangements were done by the STEMLAND team. There were 8 stalls which include

1. Mindstorms
2. Games and puzzles
3. Science projects
4. Makey-Makey
5. Arduino
6. Electronics
7. Scratch programming
8. 3-D printing.

Mindstorms:

Mindstorms is a hardware and software structure that develops programmable robots based on Lego building blocks. Each version includes computer Lego bricks, a set of modular sensors and motors, and Lego parts from the Technic line to create the mechanical systems. The system is controlled by the Lego bricks.

Games and puzzles:

Logic and strategy games were present. They include Abalone, Gobblet, Quads magnetic, Aadu Puli (Puli Meka), Linja, Quarto, Quoridor, Othello and Eternals were put on view to play. Puzzles like Rubik’s cube, Cast puzzles, and holograms were displayed to solve and play with.

Science Projects:

Science projects based on concepts were exhibited. The exhibits include

• Magnetic levitation
• Electromagnetism
• Acid-base indicator
• Dc electric motor model
• Crank’s model
• Lungs- diaphragm model
• Magnetism- properties.
• DIY microscope
• DIY headphone
• Series and parallel connection
• Lights color – arithmetic model.

These models were made using the Arvind Gupta toys which are made of scrap materials.

Makey – Makey:

Makey Makey is an invention kit by the MIT media lab. With Makey Makey, everyday objects are transformed into touchpads empowering students to interact with computers as creative tools. The computer becomes an extension of their creativity, fostering imaginative play and discovery.

“Makey Makey” is a play on words – students having the ability to Make their Keyboards (“Ma-Key”). The mundane and boring keyboard is replaced by any object that conducts electricity – pie pans, Play-Doh, bananas, and even potted plants – the list goes on.

The projects can be coded by scratch and use the Makey Makey kit as a joystick controller.

Arduino:

Arduino is an open-source hardware and software that can be used for designs. It is a microcontroller and microcontroller kit for building digital devices. It can be programmed and built using the Arduino software. Exhibits include a Distance measurement kit, Automated street light was displayed.

Electronics:

The field of electronics is a branch of physics and electrical engineering that deals with the emission, behavior, and effects of electrons using electronic devices. Projects like Automatic street light controller and automated sound sensor control model, Automatic dustbin were displayed.

Scratch programming:

Scratch is a visual programming language that allows students to create their own interactive stories, games, and animations. As students design Scratch projects, they learn to think creatively, reason systematically, and work collaboratively.

3-D printing:

A machine allows the creation of a physical object from a three-dimensional digital model, typically by laying down many thin layers of a material in succession. The models are designed using software called Tinkercad and converted to the printing g code to feed to the machine using Ultimaker CURA software. This paves for creative models.

The visit session was facilitated by Dr.Sanjeev Ranganathan and the team of STEMLAND. The session started with a few minutes of concentration meditation and a few words about what we stand for, a casual talk on the similarities and differences between the last school and STEMLAND. Students had to choose any two stalls they can spend time on. Some of them wanted to explore all the activities.

Students and facilitators had a great time exploring. Few of them made hands-on projects using the kits provided. They played strategic games and got fascinated by them. It was a pleasure to have them in STEMLAND. The team had wonderful learning, growth, and fun having them.

## BHARATHA TIRTHA II- International conference on Indian knowledge systems by IIT Kharagpur.

BHARATHA TIRTHA II- International conference on Indian knowledge systems was organized by IIT Kharagpur. Dr. Sanjeev Ranganathan, founder of STEMLAND was invited to present and he presented on the topic of Rajju ganit (string geometry, cord geometry).

He demonstrated briefly the concept of squaring the circle can be done using the Rajju ganit method. Using the rope, a circle, and a square of the same area can be constructed and observed.

There are two main new features:

(1) The cord replaces the entire compass box.

(2) Empirical methods are admitted in geometry contrary to the philosophy of formal math and using instead the philosophy of approximation.

Some other interesting topics that were presented at the conference were trigonometry in Ancient India and how that led to many discoveries and applications.

Jyotpatti: Trignometry in India

Trigonometry in India is called Jyotpatti.” Ja” means chord in a circle and “Jia” means string in a bow. Mathematicians used this to find the relation between the arc of a circle and the chord of a circle. The sine function is ubiquitous in all disciplines. It is very important to study the application part of sine and cosine functions.

Bhaskara’s metaphor for sine and cosine:

Bhaskar Acharya is a 12th-century astronomer and mathematician. He brought in the importance of science in astronomy, and the application of it is beautifully brought out with a nice simile.

He says that,

Just as fabric(pata)is made up of crisscrossed threads Likewise the spherics or science of astronomy is crisscrossed with sine and cosine functions.

Sines and cosines are everywhere in astronomy:

Interestingly, sines and cosines from the earliest times were formally a part of astronomy rather than a separate discipline of mathematics, it is because applications in astronomy fall all over the place.

The main phenomenal applications such as

1. Ascensional differences between planets. (Spherical trigonometry)
2. Epicyclic orbital corrections to planetary longitudes.
3. Zenith distances and the length of the shadows.

Arcs and chords: The origins of trigonometry in India:

In the 17th century, a famous mathematician named Nityananda Sarvasisiddhantaraja explicitly links the advantage of looking at half chords.

Mathematicians paid more attention to what a chord concerning a given arc is, What is half of the chord of double the arc, and the right-angled triangle which is used for mathematics and computes various line segments concerning half of the chord made computations much easier for astronomers.

Technical terminology introduced bow and bow string:

The evolution of trigonometry in India:

Practitioners needed to compute:

1. Half chords and other line segments in right triangles using the geometry of polygons inscribed in a circle.
2. Tables of Rsines are computed for various values of R.
3. Linear(or occasionally second-order) interpolation is used to determine non-tabulated values.

Addressing these led to brilliant discoveries and the results from the middle.

Mathematicians like Brahmagupta, Aryabhatta, and Varahamihra have given the tables of sine and their geometric dimensions of it.

## The Possible Missing Ingredients in Engineering Higher Education

The Possible Missing Ingredients in Engineering Higher Education – Mastering Self, Agency to Shift Disempowering Norms and Socialization, and Mastering Technical Skills

Context and Autoethnography

• We are youth who completed our engineering bachelors from rural colleges.At the end of our bachelor’s, we found that we lacked skills and any specific guidance on meaningful employment or life.
•  This research paper represents our experience in Becoming and Being a Shifu (Master) program (BnB Shifu) is a 1-year residential program where we experienced being our full potential and developing the five minds of the future not addressed in college.
• Autoethnography offers a way of giving strength and voice to personal
experience to extend social understanding of being.
• We feel that the autoethnography methodology based on our reflections is appropriate for this paper as we are addressing the lack of reflection in youth and our education system. We hope the multiple (five) reflections reduce the weakness of autoethnography of not being general enough.

## Vaughn cube

Vaughn cube is for children who find visualization easier rather than memorizing the multiplication tables.

Elements of Vaughn cube:

• Numbers.
• Pictures.
• Colours.

Construction of Vaughn cube:

• 4 sides = 4 walls.

Each wall has a specific color.

• Numbers are arranged as follows:

Odd numbers- Diagonal.

Even numbers- In the middle.

• Pictures-Specific arrangement based on the sound they make.

For eg: Tuna- T, and n.

Nose -N and s.

Working with Vaughn cube:

• Create a room as shown in the image with the numbers marked.
• Ask children to practice the objects along with their position on which number the object comes.
• Make it clear for children to see that it is the same object between 3 to 4 and 4 to 3.
• Let children study the base picture and introduce the different words.
• It’s important for the children to know the orientation of the room as they will remember objects based on their location rather than the numbers they are in between. This is how the mind castle works.
• There are different charts for tables 3,4 5, etc.

• Introduce all the images in the Vaughn cube and ask children what they are along with the sounds.
• Make children practice the names of the objects and see if they can identify the sounds while saying the names of the objects.

Eg: Tuna-t,n

Deciphering the sounds and numbers:

Map the numbers from 0-9 with the sounds.

• 1 looks like t.
• N written sideways as z looks like 2.
• M written sideways looks like 3 especially small m.
• Cursive r has a hidden 4 in it.
• L is logged the bar on top of 5.
• Ch written with c inside h looks like a 6.
• Cursive k has a 7 inside it.
• Cursive f looks like an 8.
• P reversed looks like a 9.
• Practice making children map the numbers with the sounds for all the objects.
• See if children can say the numbers instead of the object name between the two numbers/on top of the number in the room.

Vaughn cube can help children learn multiplication as well as division effectively by visualizing.

## A Session with Mr. Thiyaragaraja Kumar

An enthusiast researcher Mr. Thiyaragaraja Kumar visited STEM land on 20th June 2022 to exhibit the projects made by him and to inspire young minds.  He is an inspiring, energetic, curious person who makes projects, and teaches and guides children to invent projects. He plans to take project-based learning for the children.

The projects include a wireless charging unit, a quiz breaker, and sun-directed solar panel motor drive equipment. The wireless charging unit works based on the principle of mutual induction. The Quiz breaker model is based on relays. It finds its Industrial usage mainly in industry automation and helps in finding the valve tripping or if there is any fault. Using this model, faults in the high boiler plants can be easily found and repaired accordingly.

The sun-directed solar panel motor drive model was interesting and inspiring. It works based on the principle of movement of the sun.  this exhibit was presented at the Japan conference in 2015. According to the movement of the sun the solar cell panel moves which is driven by the motor using an LDR. This model gained more attention than other models.

He had a session with our team and explained the working methodology of the exhibits. He also enlightened the people on the topics of BCD, the Fibonacci series, Pascal’s triangle (Mahameru), Mehruprasta, Base10 calculations, Base16, and Base20 calculations.

He threw light on various number systems like the Roman number system, Greek number system, Mayon number system, and Egyptian number system. He also elucidated the shortcuts in simplification, Vedic math which is used in quantitative aptitude.

The whole session was inciting, encouraging, and enlightening. Mr. Thiyagarajan enjoyed sharing his exhibits, got fascinated with the framework of STEM land, and wanted to support us in encouraging children to invent more projects.

Reflections from the team:

1. The session was inspiring. We learnt more facts and it was interesting too.
2. It motivated us to make more projects on automation.
3. It was interesting. The BCD chart was good. The Sun directed solar panel equipment was stunning. It stirred up to do more research on it.

## Boyle’s Law

Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant. Boyle’s law was put forward by the Anglo-Irish chemist Robert Boyle in the year 1662.

For a gas, the relationship between volume and pressure (at constant mass and temperature) can be expressed as

P (1/V)

where P is the pressure exerted by the gas and V is the volume occupied by it. This proportionality can be converted into an equation by adding a constant, k.

P = k*(1/V) PV = k

The pressure v/s volume curve for a fixed amount of gas kept at constant temperature is illustrated below.

Experiment using Thinktac kit:

This gas law describes how the pressure of a gas tends to increase as the volume of the container decreases. We use a syringe and balloon to understand the phenomenon.

Steps:

• Take a syringe of 60 ml capacity and remove its plunge.
• Take a small balloon.
• Blow a small amount of air into the balloon and hold at its neck tightly with your fingers.
• Insert the balloon through the syringe’s open end and remove it to check whether the balloon can enter freely inside the syringe or not.
• Now, tie a tight single knot at the balloon’s neck. Ensure that there is no air leakage.
• Insert the balloon into the syringe to the tip. Insert the plunger back to close the open end.
• Initially, push and set the plunger at the 30 ml reading on the syringe, with the tip of the syringe open. Now, tightly close the tip of the syringe with your finger.
• Press the plunger hard as much as possible and observe what happens to the balloon inside.
• After you reach the optimum level, release the plunger and continue to observe.
• Now, pull the plunger and set it at the 30 ml reading on the syringe again, with the tip of the syringe closed.
• Now, pull the plunger to the open end of the syringe and observe what happens to the balloon.

Filling water in the syringe:

• Take about 100 ml of water in a cut bottle container and the syringe with the balloon.
• Push the plunger till it reaches the balloon.
• Dip the tip of the syringe in the water and pull the plunger till the 60 ml reading fills the water.
• Hold the syringe with the syringe’s tip positioned upward as shown. Shake the syringe and adjust it to push air above the water level.
• Now, push the plunger slowly for the air above the water level to escape through the tip of the syringe.
• Push the plunger to remove the excess water into the container, till the plunger reaches the 40 ml reading on the syringe.
• Now, push and pull the plunger to the closed end of the syringe and observe what happens to the balloon.

Preparing the water balloon:

• Take another small balloon.
• Use the same 60 ml syringe and draw about 10 ml of water from the container.
• Empty the syringe before filling it with 10 ml of water.
• Now, insert the syringe’s tip into the mouth of the balloon and press the plunger to add water to the balloon’s neck.
• Pinch the balloon’s neck, at the point where the water is present, to prevent the air bubbles from entering the balloon.
• Now, twist the balloon’s neck, two times, and tie a knot tightly.
• Insert the balloon -filled with water into the syringe and close the syringe’s open-end by inserting the plunger.
• Position the plunger at the 30 ml reading on the syringe.
• Now, close the syringe’s tip and press the plunger to the maximum possible level. Release the plunger and then pull it to the open end of the syringe.

Observe the difference when the balloon filled with water is within a closed system of the syringe.

We observe in both cases, that when the pressure increases the volume decreases. Similarly, the volume increases when the pressure decreases.

## ARITHMETIC PROGRESSION USING VISUAL MATHEMATICS

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For example, the series of natural numbers: 1, 2, 3, 4, 5, 6… is an Arithmetic Progression, which has a common difference between two successive terms equal to 1 (2 -1). Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2.

This can be observed visually using a graph. If an arithmetic sequence is plotted in a graph lies on a straight line. There is a finite distance between points.

For plotting in a graph, the sequence is written as in the following table.

Sequence of numbers: 3,5,7,9, 11, …

 Term(x) Number of squares(y) Point(x,y) Formula /Pattern 1 3 (1,3) 3=2(1-1) +3 2 5 (2,5) 5=2(2-1) +3 3 7 (3,7) 7=2(3-1) +3 4 9 (4,9) 9=2(4-1) +3 5 11 (5,11) 11=2(5-1) +3 6 13 (6,13) 13=2(6-1) +3 7 15 (7,15) 15=2(7-1) +3 . . . . . . . . n . . tn=a+(n-1) d

The plotted point of an AP is shown below:

Notations in Arithmetic Progression:

In AP, we will come across some main terms, which are denoted as:

• First-term (a)
• Common difference (d)
• nth term. (an)

First Term of AP

The AP can also be written in terms of common differences, as follows;

where “a” is the first term of the progression.

a, a + d, a + 2d, a + 3d, a + 4d, ………., a + (n – 1) d

Common Difference in Arithmetic Progression

Suppose, a1, a2, a3, ……………. is an AP, then the common difference “d” can be obtained as;

d = a2 – a1 = a3 – a2 = ……. = an – an – 1

Where “d” is a common difference. It can be positive, negative, or zero.

The nth term of an AP

The formula for finding the n-th term of an AP is:

an = a + (n − 1) × d

where

a = First term

d = Common difference

n = number of terms

an = nth term

In the graph, the slope of the line formed by the arithmetic progression is equal to the common difference in Arithmetic progression.

Sum of n terms of an arithmetic progression:

The sum of n terms of an AP can be easily found using a simple formula which says that, if we have an AP whose first term is a and the common difference is d, then the formula of the sum of n terms of the AP is

Sn = n/2 [2a + (n-1) d]

The proof of the sum of n terms can be visualized and derived using the area concept. This can be implemented and observed in GeoGebra.

Suppose we arrange the terms in the AP as shown in the figure we can calculate the area to find the sum of the first n terms in an AP.

This is can be done in two methods:

1.Using the area of the trapezium

2.Using the area of the rectangle.

1. Using the area of the trapezium:

When the terms in the AP are arranged as shown in the figure we can observe that it forms a trapezium. to find the sum of the first n terms in an AP the area of the trapezium can be calculated which gives the result of the sum of the first n terms.

2. Using the area of the rectangle:

Likewise, the terms in the AP can be arranged in such a way that the tilted arrangement and the regular arrangement of the terms form a rectangle as shown in the figure. To find the sum of the first n terms in an AP the total area of the rectangle can be calculated and divided into half to get the required area which gives the result of the sum of the first n terms.

Finding the equation of a line using the arithmetic progression:

Lets take the sequence 3,5,7,9,11…..The nth term is taken as x and its number of squares as y.

As we know tn can be expressed as tn=a+(n-1)d.

i.e., y=tn=a+(n-1)d

We know that a=3,common difference is 2. Substituting we get

y=3+(x-1)2

y=3+2x-2

y=2x+1 ———- > Equation of the line.

General equation of a line is y=mx+c.

Here we can observe that m= slope =2 = common difference.

c=1 = Intercept (A point at which the given line cuts the y axis).

In an arithmetic progression intercept means the value of sequence, when x=0.

This can be observed in the graph given below.

+

## A visit to AUROVILLE INSTITUTE OF APPLIED TECHNOLOGY

On 13th May 2022, our C3Streamland team visited AIAT as a part of the BVOC program. The team was led by Dr. Sanjeev Ranganathan. AIAT is situated in Thricurtamburam, Koot Road.

AIAT, a non-profit Industrial Training Centre, aims to create prosperity in rural areas through vocational education and self-empowerment.

AIAT was established in 2004 with the support of the German Government and the non-profit organization VFAVR (Association for Development of the Region around Auroville).

AIAT focuses on technical education as a holistic approach based on learning by doing, enabling youth to become independent thinkers and to be able to provide solutions.

AIAT’s two campuses have a favourable ambience for learning, experimenting, and for creative activities.  The Irumbai campus focuses on segments of Computer Science, Electronic and Electric, and Civil; at the Palmyra campus, the focus of training is more on manufacturing and production.

The visit gave us exposure to the newly constructed Electronics lab, Electrical lab, and ICTSmartroom. The facilitators guided the team and gave a demonstration about each and every lab present.

The latest constructed Electrical lab is fully equipped with the prescribed tools and machine list. Different types of motors like series, shunt with AC and Dc supply were present. Generators, coupling units and several equipments like fridge, washing machine, solar bike and its working were also demonstrated.

In the manufacturing lab, The Fitter trades Turning, Milling, and Sheet Metal are present. Workshop halls for Fitter, equipped with 6 lathe machines, a universal milling machine, and CNCC training facilities.

The welding workshops practice various types of welding technologies such as Arc, MIG, TIG, and Gas welding machines.

Pic: Electrical lab, Electronics lab, Palmyra campus.

The Electronic Machines includes solar system maintenance. In electronics lab the wide range of projects like solar table lamp, Bluetooth car, Automatic dustbin were displayed. LED tv, WIFI router, and several equipments were illustrated.

Overall, this visit gave a versatile knowledge about the hands-on projects and experiments. The team had a wonderful time learning and observing by visiting the campus.