Useful Tips

Circumference

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How was the mathematical constant pi found? Who did this? We will tell you how to independently find the value of pi, as well as learn about the original source of origin of this constant. Pi can be found by drawing any circle or sphere. We will tell you how to do it and what you need to draw. Read on to find out more.

Method 1 Basic Geometry of a Circle on a Plane

  1. 1 Remember the basics of the geometry of a circle lying on a plane. You need to know what a point, a plane and space are. You must know their definitions and characteristics.
    • What is a circle? The following information will help you better understand what a circle is and what characteristics it has.
    • Equidistant - a circle that maintains distance at equal intervals.
    • Circle - when all points of the figure are at the same distance from the center.
    • The following things apply to the circle, but are not part of it:
      • Center - a point located at the same distance from any point on the surface of a circle.
      • Radius - a segment located between one of the edges of a circle and its center.
      • Diameter - a segment passing from one point of a circle to another through its center.
      • A segment, area, sector - are inside the circle, but are not its parts.
      • A circle is a closed line defining the boundary of a circle.

Method 2 Creating a Formula

  1. 1 Find the circle formula. The diameter can be drawn from anywhere in the circle to any point through the center. If you fold three diameters, they will be almost the same length as the circle: three diameters + a small part of the diameter = circle. C = 3XD. Now you need to find the exact formula of the circle, since this definition is inaccurate and approximate. In ancient times, the circle formula was found in this way.
  2. 2 Thus, the approximate value pi = 3. But this is an inaccurate definition. Now we will tell you how to find the exact definition of pi.

Method 3 Finding the Exact Pi

  1. 1 You need 4 round containers or lids of different sizes. A sphere or ball is also suitable for this, but it will be a little more complicated with them.
  2. 2 Take inextensible thread and a measuring tape or ruler.
  3. 3 Draw a table as shown in the picture: circle / diameter / segment C / d.
    1. __________|________|__________________
    2. __________|________|__________________
    3. __________|________|__________________
    4. __________|________|__________________
  4. 4 Measure the circumference of each item by wrapping a thread around them. Mark the distance on the thread and attach the thread to the ruler. Record the length of the circle, i.e. its perimeter.
  5. 5 Align the thread and measure the part that you marked. Record the value found using the decimal system. The circumference must be measured very accurately by attaching the thread to the object being used.
  6. 6 Turn the used container, lid or sphere upside down, find the center of the lid or container on its bottom. This is necessary for measuring the diameter.
  7. 7 Measure the length of the line extending from one edge of the lid to the other through its center. Record the value.
    • By measuring the radius and multiplying it by 2, you will find the diameter. So 2R = D.
  8. 8 Divide each circle by its diameter. Record the 4 results obtained in the third column of the table. You should get a value of 3 or 3.1. The more accurate your measurements, the closer the result will be to the Pi number (3.14), that is, Pi is the ratio of the circle to the diameter.
  9. 9 Find the average by dividing the sum of the four results obtained by 4. You will get a more accurate result. For example, 3.1 + 3.15 + 3.1 + 3.2 = 12.55 / 4 = 3.1375. Round this value to 3.14. This is the meaning of pi. The length of all circle diameters is the same, so pi is a constant.
    • The radius is placed 6 times on the circumference of a circle or sphere. So the diameter is placed on it 3 times. We get the circle formula C = 2X3.14XR. Hence C = 3.14XD, since 2R = D.
  10. 10 Take the thread and cut it at the mark that you set when measuring the diameter of the circle. The thread will wrap around the circumference of your cap or other item 3 times. This will be true for every round or round container. You can verify the correctness of this formula by conducting such an experiment.

Method 4 Tips and Tricks

  1. 1 If you want to show this experiment to your children or students, we will give you some tips. This is one of the best ways to explain math to children. Such an experiment will arouse their interest in the subject and make them forget about the fear that they experience when they see mathematical formulas.
  2. 2 You can ask students to go home by asking them to draw a table and complete it at home.
  3. 3 Give them some clues. they must come to a conclusion on their own, do not tell them what to do. Just point them in the right direction. If you explain everything to them yourself, they will not be so interested. Give them the opportunity to come to their own conclusions.
    • No need to make a lecture out of this and explain the essence of the experiment in the lesson. An experiment is called an experiment precisely because it needs to be experienced independently, and not heard about the method of its conduct and the result from the teacher. Ask students to make a presentation of this experiment, hang their projects on a wall board at school.
  4. 4 This project can be completed in a math or craft lesson, or in a visual arts lesson. You can do this during the lesson or ask students to complete this project as homework.
  • By the way, an arc on a circle with a length of a radius is called a radical. This is a constant that is used in trigonometry.
  • The diameter of a circle, circle, or sphere will be placed more than 3 times along the length (perimeter) of this circle. It is placed along the circumference 3 and 1/7 times, i.e. 3.14 times. the larger the circle, the less accurate the formula will be (0.14 * 7 = 0.98, that is, the error is 0.02 = 2/100 = 2%.)
  • Circle formula = Pi x diameter.
    • Find pi like this:

C = pi x DC / D = (pi x D) / DC / D = pi x D / DC / D = pi x 1, since D / D = 1, therefore C / D = pi C / D is defined as a constant pi, regardless of the size of the circle. Pi is used not only in mathematics, but also in geometric equations.

  • You can look at various options for the value of pi, differing in their accuracy in the chronological order of their location. .
  • The meaning pi is denoted by the Greek letter "π". The Greek philosopher Archimedes first mentioned the approximate value of this constant. He calculated it this way: 223/71
    • Fifteen centuries before the birth of Archimedes, the Egyptian mathematician, whose work was recorded on papyrus, used the value pi for the first time in history in ancient mathematical texts. He defined it as 256/81. This equates to approximately (16/9) ^ 2, i.e. 3.16.
    • Archimedes, who lived in 250 BC, also defined the value of π as 256/81 = 3 + 1/9 + 1/27 + 1/81. The Egyptians defined this value as follows: (3 + 1/13 + 1/17 + 1/160) = 3.1415).

The number π and the circumference

Before you figure out how the circumference is counted, you need to find out what is the number π (read as "Pi"), which is so often mentioned in the classroom.

In ancient times, mathematicians in ancient Greece carefully studied the circle and came to the conclusion that the length of the circle and its diameter are interconnected.

The ratio of the circumference of a circle to its diameter is the same for all circles and is denoted by the Greek letter π ("Pi").
π ≈ 3,14…

The number "Pi" refers to numbers whose exact value cannot be written using ordinary fractions or decimal fractions. For our calculations, it suffices to use the value of π,
rounded to the discharge of hundredths π ≈ 3.14 ...

Now, knowing what π is, we can write the formula for the circumference.

Circumference Is the product of the number π and the diameter of the circle. The circumference is indicated by the letter "C" (read as "Tse").
C = π D
C = 2 π R, since D = 2R

Chord and arc of a circle

In the figure below, we mark on the circle two points “A” and “B”. These points divide the circle into two parts, each of which is called an arc. This is the blue arc “AB” and the black arc “AB”. Points "A" and "B" are called ends of arcs.

Connect the points "A" and "B" by a line. The resulting segment is called chord.

Points “A” and “B” divide the circle into two arcs. Therefore, it is important to understand which arc you mean when writing the arc “AB”.

In order to avoid confusion, they often introduce an additional point on the desired arc and refer to it at three points.

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