Circle in Life

look at these pictures

We can see the circle in every where;

the clock, the wheels, the children toys, the engine, ..

can you imagine the world without the circle!

off course no cars can work, no engines, no clocks, no bycicles, no rings, ....

I think the world may stop!!!!!!

we use this shape in all sides of life

in Home, School, Work, Bus, Car.

Watch this video

Puzzles & Brain Teasers:
A number of children are standing in a circle. They are evenly spaced and the 5th child is directly opposite the 19th child. How many children are there altogether?
the wright answer is below at the end of the post

let's see how can we messure the circumference and the area of the circle:

circumference-to-diameter ratio for a circle is constant as the size of the circle is changed (as it must be since scaling a plane figure by a factor increases its perimeter by ), and also scales by . This ratio is denoted (pi), and has been proved transcendental.

Knowing , the area of the circle can be computed either geometrically or using calculus. As the number of concentric strips increases to infinity as illustrated above, they form a triangle, so

This derivation was first recorded by Archimedes in Measurement of a Circle (ca. 225 BC).

If the circle is instead cut into wedges, as the number of wedges increases to infinity, a rectangle results, so

the answer of the puzzle is 22

what is the circle?

The Circle!
is a set of points which have the same distance from a fixed point.
the same distance called Radius
the fixed point called the Center
watch this video for more information



*Center
A point inside the circle. All points on the circle are equidistant (same distance) from the center point.
Radius
The radius is the distance from the center to any point on the circle. It is half the diameter.
Diameter
The distance across the circle. The length of any chord passing through the center. It is twice the radius.
Circumference
The circumference is the distance around the circle. See Circumference of a Circle.
Area
Strictly speaking a circle is a line, and so has no area. What is usually meant is the area of the region enclosed by the circle. See Area enclosed by a circle .
Chord
A line segment linking any two points on a circle. See Chord definition
Tangent
A line passing a circle and touching it at just one point. See Tangent definition
Secant
A line that intersects a circle at two points. See Secant definition
Pi
In any circle, if you divide the circumference (distance around the circle) by it's diameter (distance across the circle), you always get the same number. This number is called Pi and is approximately 3.142. See Definition of pi.
Relation to ellipseA circle is actually a special case of an ellipse. In an ellipse, if you make the major and minor axis the same length, the result is a circle, with both foci at the center. See Ellipse definition
study the following examples:

Example 1:
The radius of a circle is 2 inches. What is the diameter?

Solution:

d = 2.r

d = 2 · (2 in)

d = 4 in
Example 2:
The diameter of a circle is 3 centimeters. What is the circumference?

Solution:

C = pi . D

C = 3.14 . (3cm)

C = 9.42cm

Example 3:
The radius of a circle is 2 inches. What is the circumference?
Solution:
d = 2r

= 2 · (2 in)

= 4 in

C = pi . d

= 3.14 · (4 in)

= 12.56 in

Example 4:
The circumference of a circle is 15.7 centimeters. What is the diameter?

Solution:

C = pi . d

15.7 cm = 3.14 · d

15.7 cm ÷ 3.14 = d

= 15.7 cm ÷ 3.14

= 5 cm
Summary:
The number pi is;

the ratio of the circumference of a circle to the diameter. The value of is approximately 3.14159265358979323846...The diameter of a circle is twice the radius. Given the diameter or radius of a circle, we can find the circumference. We can also find the diameter (and radius) of a circle given the circumference. The formulas for diameter and circumference of a circle are listed below. We round to 3.14 in order to simplify our calculations.

exercises:

1.
The diameter of a nickel is 2 centimeters. What is the circumference?

The circumference of a bicycle wheel is 50.24 inches. What is the diameter?

The circumference of a compact disc is 28.26 centimeters. What is the radius?

The diameter of your bicycle wheel is 25 inches. How far will you move in one turn of your wheel?

send your answers as a comments with your e-mail address, to get your results

******* with my best wishes ********