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Visualizing trigonometric ratios using scratch program

~ Soundhariya, Sandhiya.B

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively. Using scratch, the visualization of trigonometric ratios is comprehendible.

Let us have a look at the right-angled triangle drawn using the scratch shown below. Trigonometric ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle in terms of the respective angles.

The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on the angle. We can alternatively find the values of these trig ratios. Also, only the base and perpendicular will interchange for the given right triangle in that case.

Concerning θ, the ratios of trigonometry are given:

Sine: Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle to the hypotenuse.

cosine: The cosine angle is defined as the ratio of the side adjacent to that angle to the hypotenuse.

Tangent: The tangent angle is defined as the ratio of the side opposite to that angle to the side adjacent to that angle.

Cosecant: Cosecant is a multiplicative inverse of sine.

Secant: Secant is a multiplicative inverse of cosine.

Cotangent: Cotangent is the multiplicative inverse of the tangent.

The above ratios are abbreviated as sin, cos, tan, cosec, sec, and tan respectively in the order they are described. So, for Δ ABC, the ratios are defined as:

sin θ = (Side opposite to θ)/(Hypotenuse) = AB/AC

cos θ = (Side adjacent to θ)/(Hypotenuse) = BC/AC

tan θ = (Side opposite to θ)/(Side adjacent to θ) = AB/BC = sin ∠C/cos ∠C

cosec θ = 1/sin θ = (Hypotenuse)/ (Side Opposite to θ) = AC/AB

sec θ = 1/cos θ = (Hypotenuse)/ (Side Opposite to θ) = AC/BC

cot θ = 1/tan θ = (Side adjacent to θ)/(Side opposite to θ)= BC/AB

Unit Circle and Trigonometric Values:

Unit circles can be used to calculate the values of basic trigonometric functions- sine, cosine, and tangent. The following diagram shows how trigonometric ratios can be represented in a unit circle.

Degrees to radians:

In geometry, both degree and radian represent the measure of an angle. One complete anticlockwise revolution can be represented by 2π (in radians) or 360° (in degrees). Therefore, degree and radian can be equated as:

2π = 360° And π = 180°

Hence, from the above equation, we can say, 180 degrees is equal to π radian.

Usually, in general geometry, we consider the measure of the angle in degrees (°). Radian is commonly considered while measuring the angles of trigonometric functions or periodic functions. Radians are always represented in terms of pi, where the value of pi is equal to 22/7 or 3.14.

Trigonometric ratios of some special angles:

In the trigonometric ratios table, we use the values of trigonometric ratios for standard angles 0°, 30°, 45°, 60°, and 90º. It is easy to predict the values of the table and to use the table as a reference to calculate values of trigonometric ratios for various other angles, using the trigonometric ratio formulas for existing patterns within trigonometric ratios and even between angles. The trigonometric ratios of 45° using scratch are shown below.

In right Δ PQR, if ∠P and ∠Q are assumed as 30° and 60°, then there can be infinite right triangles with those specifications but all the ratios written above for ∠P in all of those triangles will be the same. So, all the ratios for any of the acute angles (either ∠P or ∠Q) will be the same for every right triangle. This means that the ratios are independent of the lengths of the sides of the triangle.

The trigonometric ratios of 30° and 60°simulated using the scratch program are shown below.

The trigonometric ratios of 90° and 0° using scratch programming are shown below.

Trigonometrical Ratios of 0 degrees are commonly called standard angles and the trigonometrical ratios of these angles are frequently used to solve particular angles. In ∆ABC is a right-angled triangle. If the length of the side BC is continuously decreased, then the value of ∠A will keep on decreasing. Similarly, the value of ∠C is increasing as the length of BC is decreasing. When BC = 0, ∠A = 0 , ∠C = 90° and AB = AC.

Trigonometric Ratios Table:

Attached the scratch link: https://scratch.mit.edu/projects/754205615

The summarization of the value of trigonometric ratios for specific angles is in the table below:

Some of the applications of trigonometric ratios are:

  • Measuring the heights of towers or big mountains
  • Determining the distance of the shore from the sea
  • Finding the distance between two celestial bodies
  • Determining the power output of solar cell panels at different inclinations
  • Representing different physical quantities such as mechanical waves, electromagnetic waves, etc.

 

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Smart dustbin using Arduino

The smart dustbin is built on a microcontroller-based platform Arduino Uno board which is interfaced with the Servo motor and ultrasonic sensor. An ultrasonic sensor is placed at the top of the dustbin which will measure the stature of the dustbin. The threshold stature is set at a particular level. Arduino will be programmed in such a way that when someone will come in front of the dustbin the servo motor will come into action and open the lid for the person to put the waste material into the dustbin. The lid of the dustbin will automatically open itself upon the detection of a human hand.

Servo Motor:

SERVO MOTOR is an electromechanical device that produces torque and velocity based on supplied current and voltage. It can push or rotate an object with great precision. Servo Motor SG-90 is used. It will perform its angular rotations when a signal will be provided by the microcontroller. The servo motor rotates approximately 180 degrees (90 in each direction).

Infrared sensor:

IR SENSOR is a radiation-sensitive optoelectronic component with spectral sensitivity in the infrared wavelength. It is used for object detection.

Connections: –

The Red Pin of the Servo Motor is connected to Arduino 3.3v. The Black Pin of the Servo Motor is connected to Arduino GND (Ground). The Orange Pin of the Servo Motor with Arduino Pin 8. VCC of the sensor is connected with Arduino 5v.

The Smart Dustbin as you can see in the picture above is built using Cardboard. This is a custom-made Smart Dustbin equipped with HC-SR04  Sensor, Arduino, and a Servo Motor. It is programmed using the Arduino code.

Code:

#include<Servo.h>
Servo myservo;
int angle = 0;
int angle step= 50;

void setup(){
myservo.attach(8);
pinMode(2,INPUT_PULLUP);
}
void loop() {
if(digitalRead(2) == HIGH){
myservo.write(180);
}
else{
myservo.write(-180);
delay(3000);
}

Once there is no one in front of the  Sensor the Smart Dustbin Lid remains closed.

The smart dustbin is a carefully designed solution that solves the social issue of waste disposal.

 

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Sri Aurobindo 150th celebration talks with Aurovilians: Sanjeev

As part of the 150th Sri Aurobindo’s birth Anniversary, On the 24th of August 2022, Dr.Sanjeev Ranganathan had a live talk with the Aurovillians in Savitri Bhavan.

Dr. Sanjeev Ranganathan is the executive of the Isai Ambalam school, Sri Aurobindo International Institute of Educational Research (SAIIER), and RTL Academy. He received his Ph.D. in Electronics from Columbia University in New York City. He is motivated by his growth as a human being and supports the same in others.

Sanjeev is the recipient of the Lewis Winner award for best paper at ISSCC. He also volunteered for Asha for Education in various capacities and interacted with over 100 NGOs in India working on education. He has worked at Silicon Labs, NXP, ST-Ericsson, and Aura Semiconductor and has built chips used by over a billion people.

He addressed the Aurovillians with his inspiring talk by quoting his life instances with the guidance of Mother and Sri Aurobindo. While volunteering for Asha for Education he perceived Education’s purpose is not to just fit in something but also about standing out. It brought him to Auroville in 2000. He started working on alternative education. He focused on how are we going to support the next generation to do something unique.

He organized education conferences to have accelerated learning. He wanted to create a place for people to learn, experience, and contribute. He explored tribal villages and he did Vipassana, a 10-day silent meditative course that gave him a great feel about the right things to do. He also had a spiritual experience while doing his meditation and saw every being connected. All of us are connected. Once we stop judging people, life becomes easy and amazing.

Sanjeev is passionate about developing critical thinking skills with children and helping them learn and connect with their deepest selves. He believes that this can be achieved by deep meaningful educational experiences for both facilitators and children in the schools, at STEM Science Technology Engineering Mathematics centers, and Aura Auro Design, a technology business he coordinates. In time he created Aura Auro/STEM Land that allows youth to learn, grow, work, and teach as a research project and then a sub-unit of SAIIER.

He always followed the ideologies of Mother and Sri Aurobindo in his endeavors. At Auroville he was introduced to Radical Transformational Leadership which has tools, templates and distinctions used to create whole systems transformational solutions. These tools helped him explore what the root of his existence was and how he need to let it synthesize his life to let it manifest.

With the guidance of Mother and Sri Aurobindo, he continues to progress and help others progress in the beautiful journey of life.

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LOGIC GATES USING ARDUINO UNO

A basic gate is defined as a component with one or more inputs and one output.  The inputs and outputs are all digital.

There are three fundamental gates and a total of seven basic logic gates (plus several derivatives). The gate will set its output to either zero or one, based on the state of the input signals.  It uses the rules of Boolean algebra to determine the output condition. The relationship between the input and output logic levels on a gate can be best illustrated using what is known as a truth table.

Simulating Gates with an Arduino:

All of the Boolean algebra functions performed by the basic logic gates can also be emulated on an Arduino. With that in mind, a logic gate emulator that will emulate six of the seven basic gates has been constructed. It doesn’t include the NOT gate because it only has one input whereas the other gates have two.

Project on logic gates using Arduino Uno board consists of 8 LEDs and 8 resistors for the LEDs and two resistors for the pushbutton switches. The LEDs are connected for the logical output and the pushbutton switches are used for the logical input. The positive terminals of the LEDs are connected to the respective terminals of the Arduino board. The negative terminals are connected to the ground of the Arduino.

The green LEDs are for the logic outputs and the red LEDs are for the input.

The dropping resistors for the LEDs are all 220 ohms.

The two pulldown resistors for the pushbutton switches are 2.2k each.

First, define some Boolean variables to represent the logic states of both the two inputs and six outputs. Next, define some integers to represent the connections to the Arduino from the LEDs and push buttons.

It displays logic states on the serial monitor, so in the Setup routine, initialize the monitor at 9600 bps. The rest of the Setup is used to define the LEDs as outputs and pushbuttons as inputs.

In the Loop, it starts by reading the state of the two pushbuttons, and then displaying the results on the two Red LEDs marked “A” and “B”.

The actual Boolean math consists of the following four characters:

  • NOT =!
  • AND = &
  • OR = |
  • XOR = ^

We use the NOT function (!) to create the NOR, NAND, and XNOR gates.

After determining the Boolean results they are sent to both the serial monitor and the LEDs.  Following a short delay the whole Loop repeats.

Load the sketch and give it a try. Cycle through all four combinations of the two pushbuttons and observe the LED statuses, as well as the status on the serial monitor.

This would be a great training tool for testing our knowledge of digital logic.

Arduino gates using code

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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.

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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.

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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.

Conference_Paper_presentation


 

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Sanjay Tumati reflection

The last week’s reflection covered the similarity between teaching adults and children. Here we will cover a few differences as they pertain to language skills.

 

  1. The biggest difference I noticed was the language. Since I am not a Tamilian, my Tamil language skills are zero to non-existent. Thus I am reduced to communicating in English or in broken Tamil. Adults, by and large are more comfortable than children in their command of English and thus I am able to make myself understood more easily with them when it comes to explaining concepts like connectivity, voltage, current flow, voltage division, LED drops etc.

 

  1. The one kid with whom I was most effective was from Nepal and was fluent in Hindi which I am as well. 80% of the instruction regarding subtle concepts was delivered in Hindi as his command of English was found inadequate to understand what I was trying to communicate. Now, during sleepovers in Isai Ambalan, I find that I am most effective with his younger brother as I lapse into Hindi in spite of myself.

 

  1. It is all very well to insist that the children learn how to communicate in English, given that English is a global and indispensable language worldwide.
    1. However, I cannot wait for the child to become fluent in English before we start explaining subtle concepts.
    2. Neither can I reasonably insist on instructing in English regardless of whether he/she understands it or not. The concepts are hard enough to understand even in one’s mother tongue. Why make it harder than it is?
    3. It has to be understood that I get a few hours a week with a child, much less than what is spent in school. I trust that these few hours of interacting in a non-English language will not significantly impact the child’s grasp of English in an adverse way

 

  1. If I am to be effective in working with children, then it is imperative that I improve my command of the Tamil language or else this is a non-starter at worst and will quickly stagnate at best.

 

  1. Another option is to train the youth in electronics and they can pass this on to the kids. So this means I do not work with kids directly and work with the youth on this. However, this may not always be feasible since
    1. the youth may not be interested in Electronics or in teaching Electronics (they may well want to teach something else)
    2. The supply pool of youths interested in electronics is smaller than the supply pool of children interested in electronics

 

  1. The best solution appears to be a mix of the two. Keep improving Tamil language skills while also training the youth in circuits.

 

  1. The big bottleneck in improving Tamil language skills is the availability of time. In between working for Aura, working with Youths in the Shifu program, Sleepovers, morning electronic classes (will not be there in May), evening electronics lab (now reduced to 3 days a week), personal work, daily meditation, daily exercise, organizing Vipassana one-day course and group sits, organizing Vipassana courses (to come) it is not clear where the time to learn Tamil will come from.

 

  1. A solution certainly exists for this problem, but I have not found it yet. This will require some creativity, some application to Vipassana (reduce time spent in sleep, reduce time being wasted), RTL (sourcing inner capacities, what do I care about, how much do I care about it, what I am willing to give up for it?)

~Sanjay

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Shifu students visiting Savitri Bhavan

Being and Becoming Shifu program provides opportunities for students to explore and integrate in Auroville. As part of it we visited Savitri Bhavan last Friday and Dhanalakshmi shared about Sri Aurobindo and Mother and also about Savitri Bhavan and the art gallery.

Following are our reflections  after the visit.

Saranya
It was a wonderful visit and I really came to know about Sri Aurobindo’s and Mother.
I specifically came to know about Sri Aurobindo’s 3 madness.
First madness, it is my firm faith that all the virtue, talent, the higher education and knowledge and the wealth God has given me, belong to Him. I have the right to spend only so much as is necessary for the maintenance of the family and on what is absolutely needed…

The second madness has recently taken hold of me; it is this: by any means, I must have the direct experience of God.

The third madness is this: whereas others regard the country as an inert piece of matter and know it as the plains, the fields, the forests, the mountains and the rivers, I know my country as the Mother, I worship her and adore her accordingly.

Mano
We went to Savitri Bhavan and learned about Sri Aurobindo’s life journey and mother’s life journey and learned how mother’s participation in paintings and how she thaught it to others. By looking at the paintings I have recaptured the stories of “Savitri”. Then learned about Savitri Bhavan’s architectural importance and how much people are interested on architecture design.

Sandhiya

My name is Sandhiya I stand for progress as happiness and love for myself and others. Visit to Savithri Bhavan was new to me . I have heard of it but I learnt about the history of Savithri Bhavan, mother, Sri Aurobindo and the interconnections between them only after the visit. Some of the incidence in that story was hard to believe but was inspiring. I felt grateful to be a part in Auroville. I learnt that art of keeping mind calm is a step to reach my goal and meditation is important to calm myself. In addition I also learnt that everyone is having their own perspective of looking at things and I should respect them.

Kathir
I learned Sri Aurobindo life journey and how he and Mother joined together and build Auroville. I get inspired from sri Aurobindo transformation of his spiritual journey and the involvement, dedication he had on that, also the different aspects of life he has been through
I have read Sri Aurobindo’s quote in savitri bavan
“The first principle of true teaching is nothing can be taught” it inspired me.

Sundar
I was excited to the structure and construction of the Savitri Bhavan and learned about Savitri and Sri Aurobindo’s history. The major part of the visit is the painting of the Savitri. On watching the photos inside of my mind was creating a movie about the Savitri related to the order of pictures.

Sri Bhavani

My name is Sri Bhavani. I stand for love and equality for myself and others. From this visit, I have learned about the life journey of Sri Aurobindo and Mother. How much Savitri is important to Sri Aurobindo and Mother. The way Mother portrayed Savitri in the form of paintings made me think of art can communicate effectively.
What did I learn about myself is that I should always compete with the person who is highly skilled than me so that I can learn from them.

Poovizhi

I learnt that it is not always necessary to think a lot to complete a task or solve  problem. Instead calm my mind and concentrate. Earlier I did not know that mother gave the sketches of the paintings and directed the person who painted Savitri. I found Savitri Bhavan as a place for creativity and inspiring.

 

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Shifu Graduation 2022 Feb 2nd

One year Shifu program was completed successfully. We had a small graduation program for them. In the celebration, the Shfuans shared their experience for one year with everyone. We invited all the supporters to the Shifu program.  Once the Shifuan shared their experiences the mentors also shared their experience on mentoring them. They also shared about their skill competency and inner capacity that they acquired during one year program.

Attendees Reflections:

These are some reflections on who attended the celebration.

Attendees 1 “It was wonderful to witness and share the graduating individuals who have gone through the program, listen to what they valued, and what made them wholesome in their own ways and confident too — to be able to present to a group! Very touching and impressive!“

Attendees 2 “Dear Shifuians, Sanjeev, mentors and support team,
I just wanted to say how inspired I was yesterday and I was sorry I had to leave before the program ended. I could see what a game-changer the Shifu program is. I was touched by the Shifuian reflections, how in touch your all are with the greatness that is inside you, and how you are stretching in self-mastery and skill. Shiva put it beautifully when he said you are now our mentors. Shine on and best wishes for your respective paths ahead.“

Attendees 3 “Was happy to attend the ceremony yesterday. Great work.“

Attendees 4 ” I am grateful for being invited to the graduation ceremony. It was a beautiful and genuine program.“