This document discusses circles and how to form circles using a compass robot. It defines what a circle is, listing its key parts like the center, radius, and diameter. It presents the standard equation for a circle centered at the origin (x2 + y2 = r2) and one centered at a point (h,k) ((x - h)2+(y - k)2= r2). The methodology section describes the materials needed for a compass robot, which uses a motor, batteries, and other components to form circles by moving a nail attached to a rubber band.

1. {
COMPASS
ROBOT
FORMING
CIRCLE

2. INTRODUCTION
Peoples hatred to Mathematics is already starting in
early ages......
Mathematics is really a process. Learning it should be in
connected progress......
Pre-calculus is one of the many classifications of
mathematics:
• Analytic Geometry
• Series
• Mathematical Induction
• Trigonometry
Analyzing and understanding are the things that need to
consider in solving an equation.....

3. OBJECTIVES
Define circle and it’s parts;
Illustrate the different parts of circle
Understand the standard equation
of circle; and
Show examples using the formula
aligned in circles

4. EXPECTED OUTPUT
Learn more about circles;
Identify the different parts of the circle;
Arrange the equation based on the standard
equation; and
Solving the problem/ equation using the
formula.

5. DEFINITION OF TERMS
Circle- the set of points in a plane equidistant
from a fixed point.
Center- the fixed point of the circle.
Radius- a line from the center to any point on a
plane.
Diameter- segment that goes through the center
of the circle, with both endpoints on the edge of
the circle.
Domain- the set of all first coordinates.
Range- the set of all second coordinates.

6. REVIEW
OF
RELATED
LITERATURE

7. Based on Circle Posamentier and Salkind
A circle is a simple closed shape in Euclidean geometry.
A circle is a simple closed curve which divides the plane
into two regions: an interior and an exterior.
In everyday use, the term "circle" may be used
interchangeably to refer to either the boundary of the
figure, or to the whole figure including its interior; in
strict technical usage, the circle is only the boundary and
the whole figure is called a disk.

8. A circle is all points in the same
plane that lie at an equal distance
from a center point. The circle is
only composed of the points on the
border.
Base on the basic Information about
circles
By MatteBoken

9. A circle is the set of all points equidistant
from a given point. The point from which all
the points on a circle are equidistant is called
the center of the circle, and the distance from
that point to the circle is called the radius of
the circle. A circle is named with a single
letter, its center
Spark Notes

10. A robot is a computational unit capable of
sensing the positions of other robots in its
surrounding, performing local computations
on the sensed data, and moving towards the
computed destination.
Giuseppe Prencipe

11. The robot compass has no identity, no
memory of past actions, no common sense of
direction and distance. Besides, robots execute
the same deterministic algorithm, are unable
to communicate directly, and can only interact
by turning on the switch.
Stapel, Elizabeth

12. In "primative" terms, a circle is the shape formed in
the sand by driving a stick (the "center") into the
sand, putting a loop of string around the center,
pulling that loop taut with another stick, and
dragging that second stick through the sand at the
further extent of the loop of string. The resulting
figure drawn in the sand is a circle

13. METHODOLOGY
INSTRUMENT
COMPASS ROBOT FORMING CIRLCE:
Materials:
• Battery
• Candle Glue
• Glue gun
• Ruler
• Pencil
• Rubber Band
• Nail
• 5V DC motor gearbox
• 2AA Batteries Holder
• Switch
• Wire

14. STANDARD EQUATION OF A CIRCLE CENTERED AT
THE ORIGIN
A circle with an equation x2 + y2 = r2 has center at the
origin (0,0) and radius r, where r > 0.
Example:
For instance, x2 + y2 = 32 is an equation of the circle centered at the
origin with radius 3. Its graph is shown below.

15. Standard Equation of a circle
centered at (h,k)
A circle with an equation (x - h)2+(y - k)2= r2
has center at (h,k) and radius r, where r > 0
Example:
The equation can be written as (x - 1)2 + ( y - 0)2 = 12.
It is clear h = 1, k = 0, and r = 1.
Hence, the center of the circle is at (1,0) and its radius is 1