ما هي مجموعة الأعداد الحقيقيه ( ح ) ؟

 The circle is the first geometric shape known on the surface of the globe, and it is a flat  geometric shape known in 

It consists of an infinite set of points that are called the circumference of a circle while the  point that is in the middle of the circle is called the center of the circle

In this article, we will learn what is the definition of a circle, what are the most important  characteristics of a circle, the equation of a circle, the circumference and area of the circle, and information Important, circuit elements and circuit rules, and we will get to know all of that and more in the mathematics genius blog

? What is the definition of a circuit

It is a round geometric shape in the center of the circle and away from the center of

 the circle  a group of points that represent the circumference of the circle and are

 called the  distance The radius of the circle is between the center of the circle and

 any point on the  surface of the circle, and it is denoted by the symbol (n) Each

 radius is equal in the circle and the circle is distinguished from the rest of the other

 geometric shapes such as the rhombus, parallel, square, oblique, rectangle and

 triangle

Circuit elements

1. The center of the circle: It is the point in the middle of the circle
2. Radius: is the distance between the center of the circle and any point on its surface, and it is symbolized by the symbol (r)
3. Hypotenuse: It is a straight piece connecting any two points on the surface of the circle
4. Diameter: is a chord that passes through the center of the circle and is equivalent to (2 r)
5. Central angle: It is the angle between any two diagonals in a circle
6. Peripheral angle: is the angle between any two chords in a circle
7. Tangential angle: It is the angle between the tangent and any chord in the circle
8. Pi (π): is one of the mathematical constants defined as the ratio of the circumference of a circle to its diameter, which is equivalent to 7/22 or 3.14
9. Area of a circle: It is the area enclosed between the circumference of a circle and is denoted by the symbol (m)
10. Circumference: the length of the outer line that borders the circle
11. Tangent: It is a straight line outside the circle so that it touches the circle at one point only.
12. A secant is a straight line of a circle across two points on its circumference.

 ? What are the characteristics of the circuit

• A circle has an infinite number of radii, all of equal length
• A circle contains only one center, and it is called the center of the circle
• The circle contains an infinite set of points
• The diameter is the longest chord in the circle
• If the radii of the two circles are equal, they will coincide
• The tendon does not have to pass the center of the circle because if it passes through the center it will be considered a diameter
• Any circumference of a circle is approximately three times the length of its diameter
• The arc depends on the radius and the angle opposite it
• The circle contains an unlimited number of diagonals

circumference of a circle

The perimeter of a circle in general is the distance around the two-dimensional shape or the

 circumference of a circle is the length of the distance around the circle that begins and ends at the same  point, and is measured in meters, cm, milli meters, or any unit of lengths measurement, so the  circumference of the circle is equal to the product The length of the diameter is in the constant  expression “π”, and in mathematical form, the circumference of a circle = Q ×. To calculate the circumference of a circle, there are several methods, the most important of which are

Using the diameter: This method is one of the easiest ways to find the perimeter of a circle, according to the law (C = d) where the symbol C is the circumference of the circle, the value of equals 3.14, and the symbol d is the diameter of the circle.

• Using the radius: The method for calculating the circumference of a circle by means of the radius of the circle depends on the first method, in which the value of the radius is first multiplied to obtain the diameter, d = 2 x r where r is the radius of the circle, or by adding the two values ​​of the radius Twice to get the diameter d = r + r, then we apply the law of the circumference of a circle using the diameter.
• Using area: These methods are one of the more complex methods similar to the first two methods, as the steps of the solution are increased by finding the radius, then the diameter, then the perimeter, as the law of the area of ​​a circle is A = π × r ^ 2, and with the presence of the area value we divide by the value π = 3.14 and then take the square root of the product, and then follow the steps in the first and second methods.

Examples on the calculation of the circumference of a circle

Example 1 (a circle with a radius = 7 cm, find its perimeter)

Solution         Circumference = 2 x π x Radius

Circumference = 2 x 3.14 x 7 = 44 cm

The second example          (a circle with a diameter = 28 cm, find its perimeter)

Solution,           circumference of a circle = π x length of diameter

Circumference = 22/7 x 28 = 88 cm

Circle area

It is the area occupied by a circle in a two-dimensional plane, or the area covered by a complete turn of the radius on a two-dimensional plane, and is calculated from the equation:

                                             π x  r × r  =   A 

• A : the area of ​​a circle
• π: the number pi constant is roughly equal to 3.14.
• r: the radius of the circle

Circle space has simple practical applications that made our life easier. For example, the fencing needed to fence a circular field can be calculated by calculating the area of ​​the field, or the amount of fabric needed for a round table by calculating its area. Mathematicians observed through their mathematical operations the constant ratio between the circumference of a circle and its diameter, hence the famous discovery of the number.

                                  c / d  = π      

• C: the circumference of a circle
• d: the diameter of the circle, we can deduce from it

                                 C = π × 2 r

 ? What is the date of the number π

  It is the most mysterious, romantic and controversial mathematical puzzle

 throughout history, from ancient Babylon to Central Europe to the era of smart

 computers, mathematicians  sought to calculate this number, it is believed that the

 Babylonians and Egyptians are the first to search for this number about 4000 years

 ago, and the dated Egyptian papyrus showed

 Around 1650 BC, by a copyist called Ahmes, when the nine of the diameter of the

 circle is cut off and a square is drawn over the remainder, the equivalent area of ​​

the circle is formed.The Greeks came up with a method based on drawing a

 polygon inside a circle, finding its  area, and doubling the sides to the point where

 the polygon becomes a circle, and Bryson  calculated the area of ​​polygons that

 enclose the circle, and over the centuries scientists have  lived an argument about

 the possibility of finding a way to draw a square by the area of ​​a circle Then

 Archimedes came to invent another method based on the circumference of a circle

 and  not on its area, so he began by drawing a hexagon inside the circle, doubling

 the sides four  times, to finish with two polygons from 96 sides, to reach the conclusion:

Law of circle area

In China, the value used remained 3 until Liu Hui came, and discovered the same

 method of  calculating the circumference of regular polygons drawn inside the

 circle from 12 to 192  sides, and reached the value 3.14, which is the closest value.

 In the fifteenth century,  scholars Tzu Chung and his son Tsu Qeng arrived at the value:

The Hindu scholar Aryabana arrived at a value more accurate than that of

 Archimedes 3.14 = 20000/62832. As for the Arabs, the scholar Muhammad Ibn

 Musa al-Khwarizmi arrived  at the value of = 3 1/7, but the Arabs replaced it with a

 less accurate value The ratio of the circumference of a circle to its diameter

 remained without symbolic  significance until 1647 AD, to be calculated by the

 scientist William Utric, and in 1737 AD, the  scientist Leonard Eller used the

 symbol, and after painstaking effort scientists came to an   answer that the circle

 cannot be squared. With the advent of computers in the twentieth century and to

 this day, scientists have sought  to arrive at the value of the number, so they did

 not accurately determine the magic number.

  Equation of the circle

 The equation of a circle can be derived by drawing a right triangle inside it and

 then drawing a hypotenuse that passes through the center of the circle  The

 equation of the central circle when the center = (zero, zero) and after drawing a

 right  triangle inside it, we will get the equation of the circle  Central by applying the

 Pythagorean theorem, which states that the hypotenuse squared = the first side

 squared + the second side squared after its application  So the equation of the

 central circle   = x 2 + y 2 = radius squared The equation of the eccentric circle 

 when the center = (i.e. a non-zero number, that is, a non- zero number) and after

 drawing a right triangle inside it   We will obtain the equation of the eccentric circle

 by applying the Pythagorean theorem  which states that the hypotenuse squared =

 the first side  Squared + second side squared applied

 So the equation of the eccentric circle = (x - a) ² + (y - b) ² = (radius) ².