How to find pi using round objects

Video: Finding Pi Using Everyday Objects

Content

Steps
Method 1 of 4: Basic geometry of a circle on a plane
Method 2 of 4: Create a formula
Method 3 of 4: Finding the exact pi value
Method 4 of 4: Hints and Tips
Tips
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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 find out about the original source of the origin of this constant. Pi can be found by drawing any circle or sphere. We will tell you how to do this and what you need to draw. Read on to find out more.

Steps

Method 1 of 4: Basic geometry of a circle on a plane

1 Remember the basics of the geometry of a circle on a plane. You must know what point, 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 a distance at equal intervals.
- Circle - when all points of the shape are at the same distance from the center.
- The following things are related to the circle, but are not part of it:
  - Center - a point equidistant from any point on the surface of the circle.
  - Radius is a segment located between one of the edges of the circle and its center.
  - Diameter is a segment passing from one point of a circle to another through its center.
  - Segment, area, sector - are inside the circle, but are not its parts.
  - A circle is a closed line that defines the boundary of a circle.

Method 2 of 4: Create a formula

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

Method 3 of 4: Finding the exact pi value

1 You need 4 round containers or lids of different sizes. A sphere or ball is also suitable for this, but with them it will be a little more difficult.
2 Use a non-stretchable thread and a measuring tape or ruler.
3 Draw a table like the one shown in the picture: circumference / diameter / cut C / d.
1. __________|________|__________________
2. __________|________|__________________
3. __________|________|__________________
4. __________|________|__________________
4 Measure the circumference of each piece by wrapping the thread around them. Mark the distance on the thread and place the thread against the ruler. Write down the length of the circle, that is, its perimeter.
5 Line up the thread and measure the part you marked. Write down the value you find using the decimal system. The length of the circle must be measured very accurately by placing the thread close to the object being used.
6 Turn the used container, lid or sphere upside down, and locate the center of the lid or container on the bottom of the container. This is necessary for measuring the diameter.
7 Measure the length of the section from one end of the lid to the other through the center of the lid. Write down the value.
- By measuring the radius and multiplying it by 2, you will find the diameter. So 2R = D.
8 Divide each circle by its diameter. Write down 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 resulting value will be to Pi (3.14), that is, Pi is the ratio of the circle to the diameter.
9 Find the average by dividing the sum of your four results by 4. You will get a more accurate result. For example, 3.1 + 3.15 + 3.1 + 3.2 = 12.55 / 4 = 3.1375. Let's round up this value to 3.14. This is the pi value. The length of all diameters of the circle is the same, so pi is constant.
- The radius is placed 6 times on the circumference of a circle or sphere. This means that the diameter fits on it 3 times. We get the circle formula C = 2X3.14XR. Hence C = 3.14XD, since 2R = D.
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 object 3 times. This will be true for every round or rounded container. You can verify the correctness of this formula by performing an experiment like this.

Method 4 of 4: Hints and Tips

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 kids. Such an experiment will awaken their interest in the subject and make them forget about the fear they experience at the sight of mathematical formulas.
2 You can take this project home to students by asking them to draw a table and do it at home.
3 Give them some hints. they have to come to a conclusion on their own, don't 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.
- There is 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 you need to experience it yourself, and not hear about the way it is carried out and the result from the teacher. Ask students to give a presentation of this experiment, and hang their designs on the wall board at school.
4 You can do this project in a math or handicraft class, or in an art class. You can do this during class, or ask your students to do this project as a homework assignment.

Tips

By the way, an arc on a circle with a length of a radius is called a radical. It is a constant that is used in trigonometry.
The diameter of a circle, circle or sphere will fit more than 3 times along the length (perimeter) of this circle. It is placed along the circumference 3 and 1/7 times, that is, 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 this way:

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 see the different options for pi, which differ in their accuracy in the chronological order of their finding. ...
The meaning of 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 π 22/7. Archimedes knew that π was not equal to 22/7 and did not say that he had found the exact value of π. This is just an approximate value for the constant π. If we claim that π is an intermediate value between 223/71 and 22/7, we get 3.1418 with an error of 0.0002 (that is, with an error of less than 1%).
- 15 centuries before the birth of Archimedes, the Egyptian mathematician, whose works were written on papyrus, used the value of pi in ancient mathematical texts for the first time in history. He identified it as 256/81. This equals approximately (16/9) ^ 2, which is 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: (3 + 1/13 + 1/17 + 1/160) = 3.1415).