Cartesian Coordinate System

Scratch cartesian circle_s pdf

To draw a circle using Cartesian coordinate system

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ccs

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pythagoreantheorem

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates. Considering two points x and y on the x-axis and y-axis which meet at (x,y), this produces a right angle triangle with base of length x and height y. Here we could implement Pythagorean theorem which states ; The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c). now applying to the above fig we get.

x,ywhere ‘r’ denotes the radius of the circle, which can be drawn by keeping either x or y a constant and varying the others value.

To run the script ;                                                                         Script ;

scScreenshotofcode

  • the step are defined to 40.
  • setting radius of the circle to r
  • defining x position to 0
  • defining y position to -r ( i.e.. To start the circle from the point (0,-r))
  • determines the centre of x and y.Pen down starts to draw
  • the first loop repeats for the number of steps i.e..40
  • y value is changed with respect to delta of y .
  • x is set to the modified equation of circle i.e.. x= √(r*r) – (y*y)
  • this draws only a semi circle starting from the point (0,-r) to the point (0,r)
  • hence we require a second loop to draw the other half of the semi circle.
  • the second loop repeats for the number of steps ie.40
  • y value is changed with respect to delta of – y.
  • y is set to the modified equation of circle i.e.. x= – √ (r*r) – (y*y)
  • this draws only a semi circle starting from the point (0,r) to the point (0,-r)
  • hence the other half of the semi circle is dawn.

Now this whole script is user defined to perform 3 concentric circles around each points (0,0) and (100,50)

The Drawn Circles;

 screenshotoutput

reference : http://en.wikipedia.org – image 2

A vibrant opening

We had a fun opening with the children of Isai Ambalam School putting up a mini fair with blindfold bursting of balloons, pick out the right items (and components), dropping the coin in a bucket of water to get to target in the center of the bucket, bun eater and a recent addition the finch robot game. One of the students was also displaying the scratch programs they had written for fun and to learn various mathematical concepts.

A short speech from Sanjeev was followed by the demonstration of SpeeDe our first project that detects the instantaneous speed (actually speed averaged over 6 cm) of an objects that falls through it. The project can help children understand the speed of objects dropping to the ground, the speed of a punch/kick, etc. The  arduino based project used a couple of modified laser pointers and print the speed in m/s & km/hr on a 16×2 display mounted on a frame. More about the project and step by step construction will be available soon under projects.

This followed lighting floating candles in a large bronze vessel with water. The kolam around the vessel made this an interesting affair as well and children and adults put in their candles into the water.

We wrapped up with samosas (from Ganesh Shree in Pondy), cookies, fruits and tea. The children who had diligently kept their stalls till then dived into the snacks as well. Back at school they were raving about the samosas. There is a little project they have undertaken to draw a pie chart for the samosas that they all ate using Scratch.

More photographs…

Inauguration

The adventure of Aura Auro Design begins on 2 Jan 2015 @ 10:30 a.m. at Saracon Campus in Auroville.

You are welcome to attend, but please RSVP sanjeev.r@auroville.org.in to help us make arrangements.

There is a small lamp lighting, followed with games with Isai Ambalam school children and samosas from Ganesh Shree in Pondicherry. You may also stay to play some board games. Once all visitors leave we start our work.

Fraction addition

Children demonstrating their understanding of fraction addition and the common mistakes they made when they kept forgetting the procedural step of taking LCM when in 5th grade they used to just add the numerators (the denominators were the same then).