Scratch cartesian circle_s pdf

**To draw a circle using Cartesian coordinate system**

**1.**

**2.**

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.

where ‘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 ;**

- 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;**

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