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.

Ultrasonic Sensors:

Ultrasonic sensors work by sending out a sound wave at a frequency above the range of human hearing.  The transducer of the sensor acts as a microphone to receive and send the ultrasonic sound. It uses a single transducer to send a pulse and receive the echo.  The sensor determines the distance to a target by measuring time lapses between the sending and receiving of the ultrasonic pulse.

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 Servo Motor is connected with Arduino 3.3v. The Black Pin of Servo Motor is connected with Arduino GND (Ground). The Orange Pin of Servo Motor with Arduino Pin 8. VCC of Ultrasonic Sensor is connected with Arduino 5v. The Trig of the Sensor is connected with Arduino Pin 7. The echo of the Sensor is connected with Arduino Pin 6.GND of the Sensor with Arduino GND.

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 Ultrasonic Sensor, Arduino, and a Servo Motor. It is programmed using the Arduino code.

Code:

#include<servo.h>
Servo myservo;
int angle = 0;
int anglestep = 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);
}

Pins are defined for the Trigger and Echo. The Trigger and Echo pins of the HC-SR04 Ultrasonic Sensor are connected with the Arduino’s pins 6 and 7 respectively. Variables for the duration and the distance are defined. Create a servo object for controlling the servo motor. Define the pin of the servo motor attached. A function for calculating the distance measured by the Ultrasonic sensor for each degree is defined.

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

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

 

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.

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.

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.

+

 

 

Rajju Ganit and how we are surprised to learn about ancient mathematics

Rajju ganit (string geometry, cord geometry) aims to teach practical geometry more understandably.

The useful new things students would learn as part of string geometry or Rajju Ganit are

  • Conceptual clarity.
  • Measurement of angles
  • Simplified geometry
  • Measurement of the circle
  • The theory of approximation.
  • Trigonometry.
  • Applications to real life.

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.

As a part of the learning session through Rajju Ganit, Children used a rope to draw a circle, measure the circumference of the circle, and find the value of Pi.

The circumference of the circle is equal to the length of its boundary. This means that the perimeter of a circle is equal to its circumference. The length of the rope that wraps around the circle’s boundary perfectly will be equal to its circumference. The below-given figure helps you visualize the same. The circumference can be measured by using the given formula:

Circumference of a circle = 2πR =  π D

where ‘r’ is the radius of the circle and π is the mathematical constant whose value is approximated to 3.14 or 22/7. The circumference of a circle can be used to find the area of that circle.

For a circle with radius ‘r’ and circumference ‘C’:

  • π = Circumference/Diameter
  • π = C/2r = C/d
  • C = 2πr

Similarly using the rope, a circle and a square of the same area can be constructed and observed.

Squaring the circle can be done easily using the Rajju ganit method.

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 heart of Makey Makey is its circuit board that connects to a computer via a USB cable. Building circuits that can be used like a joystick or a keyboard key allows users with no coding experience to use Makey Makey to learn, experiment, and invent.

Makey Makey paves the way for “Integrative STEM Education”. “Integrative STEM education” refers very specifically to instructional approaches that intentionally situate the teaching and learning of science, technology, engineering, and /or mathematics concepts and practices in the context of hands-on engineering, designing, and making.

The Makey Makey kit includes the Makey Makey board, a USB cable, seven alligator clips, six connector wires, and an instruction sheet.

Working of Makey-Makey:

  • Plug in the USB of Makey Makey to the computer.
  • Connect to Earth-Connect one end of an alligator clip to “Earth” on the bottom of the front side of Makey Makey.
  • Hold the metal part of the other end of the alligator clip between your fingers.
  • While you are still grounded, touch the round “Space” pad on the Makey Makey. A green light should appear on the Makey Makey, and the computer will “think” the spacebar was pressed. Also, complete the circuit by connecting another alligator clip to “Space.
  • Experiment by turning various items, objects, or substances into a computer key.

Using Makey Makey with scratch:

Scratch is a programming language where interactive stories, games, and animations can be created. The Chase game is an example of a program made using the Makey Makey. The game is played with the arrow keys and the notes can be remixed for an array of versions.

This chasing game was coded from scratch and used the Makey Makey kit as a joystick controller.

Reflection from Sri Bhavani:
From the Makey Makey hands-on projects with children, they have learned about conducting and non-conducting materials. Current doesn’t flow in an open loop. They learned the open-loop and closed-loop of a circuit. x,y coordinates while moving the sprite.

Piano using Makey Makey.

Area of the circle using the derivatives of the rectangle in GeoGebra.

Area of circle:

The area of a circle is the region covered or enclosed within its boundary. It is measured in square units. The area covered by one complete cycle of the radius of the circle on a two-dimensional plane is the area of that circle.

 

Area of circle formula:

Let us take a circle with a radius r from the center ‘o’ to the boundary of the circle. Then the area for this circle, A, is equal to the product of pi and the square of the radius. It is given by; 

Area of a Circle, A = πr2 square units

Here, the value of pi, π = 22/7 or 3.14, and r is the radius.

Deriving the area of the circle:

The area of a circle can be visualized & proved using two methods, namely

  • Determining the circle’s area using rectangles.
  • Determining the circle’s area using triangles.

Using the area of a rectangle:

The circle is divided into equal sectors, and the sectors are arranged as shown in fig. 3. The area of the circle will be equal to that of the parallelogram-shaped figure formed by the sectors cut out from the circle. Since the sectors have equal areas, each sector will have an equal arc length. The blue coloured sectors will contribute to half of the circumference, and the yellow-coloured sectors will contribute to the other half. If the number of sectors cut from the circle is increased, the parallelogram will eventually look like a rectangle with length equal to πr and breadth equal to r.

The area of a rectangle (A) will also be the area of a circle. So, we have

  • A = π×r×r
  • A = πr2

Let’s see the practical execution of the area of the circle using the derivatives of the rectangle in GeoGebra.

Step 1: By using a slider operation, create a number slider (n) with the following values.

  • Set Min – 1; Max- 100 and increment as 1.

Step 2: By using a slider operation, create a radius slider (r) with the following values.

  • Set Min – 4; Max- 10 and increment as 0.1.

Step 3: Plot a point A and draw a circle with radius r by keeping A as the center.

Step 4: Plot a point B anywhere on the circle.

Step 5: Give input as Rotate (B,360°/n, A).

Step 6: Now point B’ appears.

Step 7: Draw a segment between B and B’.

Step 8: Plot the midpoint C and draw a segment connecting the center and point C.

Step 9: Give the following set of inputs:

  • List1=Sequence (Rotate(B,j(360°)/n,A),j,0,n).
  • List2=Sequence (circularsector (A, Element (List1, j), Element (List1,j+1)),j,1,n,2).
  • List3=Sequence (circularsector (A, Element (List1, j), Element (List1,j+1)),j,2,n,2).
  • List4=Sequence(circularsector((jf,0), (jf+f/2,g)(jf+(-f)/2,g))),j,0,n/2-1).
  • List5=Sequence (circularsector((jf+f/2,g),(jf+0,0),(jf+f,0))),j,0,n/2-1).

Step 10: Now we can observe the sectors getting formed and listed as per the input.

Step 11: Colour the sectors accordingly and insert the text for the area of the rectangle.

Step 12: By moving the number slider we observe the desired output. i.e., Area thus formed by the sectors forms a rectangle.

https://www.geogebra.org/calculator/sczjra48

Trigonometric Functions Graph of Sin𝛉 and Cos𝛉 using GeoGebra

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

Trigonometric Functions

There are six basic trigonometric functions used in Trigonometry. These functions are trigonometric ratios. The six basic trigonometric functions are sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. The trigonometric functions and identities are the ratio of sides of a right-angled triangle. The sides of a right triangle are the perpendicular side, hypotenuse, and base, which are used to calculate the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas.

Unit Circle and Trigonometric Values

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

Trigonometric Functions Graph

The graphs of trigonometric functions have the domain value of θ represented on the horizontal x-axis and the range value represented along the vertical y-axis. The graph of Sinθ passes through the origin and the graph of Cosθ does not pass through the origin. The range of Sinθ and Cosθ is limited to [-1, 1].

Let’s see the practical execution of the trigonometric function graphs of Sinθ and Cosθ using GeoGebra.

Steps for trigonometric function graphs of Sinθ:

  • Plot two points A and B and draw a unit circle (radius=1cm).
  • Mark a point C on the circle and measure angle BAC. Rename the angle as a.
  • Change the settings of the x-axis by giving the distance as π/2.
  • Draw a line segment between points A and C.
  • Now give the input as Segment (C, (x(C),0)).
  • A line drawn from C to the x-axis and point C changes with the angle change can be seen.
  • Now click on settings and change the line style and colour.
  • Now give input as f(x)=sin(x),0<=x<=a.
  • A sine wave has drawn as per the given range can be seen.
  • Now plot a point on the curve end D.
  • Now, to see the change between 0 degrees to 360 degrees, give the input a     Dynamic coordinate (D, a, y(C)).
  • We can see the graph is drawn for every change in angle of BAC and a sine function graph simultaneously.
  • Random point E appears along with the curve.
  • Now give the input as Segment (E, (x(E),0)).
  • Now click on settings and change the line style and colour.
  • By clicking on the animation icon, the desired output can be visualized.

The figure shows the sine wave obtained using GeoGebra. It can be observed that the graph of Sinθ passes through the origin.

https://www.geogebra.org/classic/cdkf3rme

Steps for trigonometric function graph of Cosθ:

  • Plot two points A and B and draw a unit circle (radius=1cm).
  • Mark a point C on the circle and measure angle BAC. Rename the angle as a.
  • Change the settings of the x-axis by giving the distance as π/2.
  • Draw a line segment between points A and C.
  • Now give the input as Segment (C, (x(C),0)).
  • A line drawn from C to the x-axis and point C changes with the angle change can be seen.
  • Now click on settings and change the line style and colour.
  • Now give input as f(x)=Cos(x),0<=x<=a.
  • A sine wave has drawn as per the given range can be seen.
  • Now plot a point on the curve end D.
  • Now, to see the change between 0 degrees to 360 degrees, give the input a Dynamic coordinate (D, a, y(C)).
  • We can see the graph is drawn for every change in angle of BAC and a sine function graph simultaneously.
  • Random point E appears along with the curve.
  • Now give the input as Segment (E, (x(E),0)).
  • Now click on settings and change the line style and colour.
  • By clicking on the animation icon, the desired output can be visualized.

The figure shows the Cosine wave obtained using GeoGebra. It can be observed that the graph of Cosθ does not pass through the origin.

https://www.geogebra.org/classic/bcqtxcjr

Angle sum property of a triangle using GeoGebra

A triangle has three sides and three angles, one at each vertex. The angle sum property of a triangle states that the sum of the angles of a triangle is equal to 180º. Whether a triangle is an acute, obtuse, or a right triangle, the sum of its interior angles is always 180º.

The angle sum property of a triangle is one of the most frequently used properties in geometry. 

The angle sum property is used to find the measure of an unknown interior angle when the values of the other two angles are known.

Let’s see the practical execution of the angle sum property of the triangle using GeoGebra.

Step 1:

  • Plot two points and draw a triangle using the polygon.
  • Let’s name it ABC.
  • Now find the midpoint of AC and BC by clicking on the midpoint or center icon.
  • That midpoint is named point D. 
  • By using a slider operation, create an angle slider (r) with the following values.
    • Set Min – 0 degree; Max- 180 degrees and increment as 10 degrees.
  • Now by using rotate around point operation, click on point D and set the degree of rotation to slider r and set it as clockwise direction and click ok.

   

                   

  • The same way create another slider operation for p and set the corresponding angle value as p.
  • By using the Angle measure operation measure the angles and label and colour them accordingly.
  • Give the input as the Sum of the angles and we can see the output as 180 degrees.
  • Now the slider can be moved and the angle sum property can be observed.  
  • Even point C can be moved to observe the angle sum property for different angle combinations.

Please find the link below:

https://www.geogebra.org/classic/u6eer35p