We are faced with the question: "How to calculate the circumference?"
One ruler is not enough, you need to know the special formulas. The only thing that is required of us is to determine the diameter or radius of the circle. In some problems, these quantities are indicated. But what if we have nothing but a picture? No problem. Diameter and radius can be calculated using a standard ruler. Now let's get down to the most basic.
Formulas Everyone Should Know
Even in Ancient Babylon, almost 4,000 years ago, scientists discovered an amazing relationship: if you divide the circumference of a circle by its diameter, you get the same number, which is approximately 3.14. This value was called the number "Pi", it is with this letter in the ancient Greek language that the word "perimeter" and "circle" began. Based on the discovery made by ancient scientists, you can calculate the length of any circle:
P = d P
Where P is the circumference (perimeter),
d is the diameter, P is the number "Pi".
The circumference of a circle can also be calculated through its radius (r), which is equal to half the length of the diameter. Here is the second formula to remember:
P = 2r P
How to find out the diameter of a circle?
The diameter of the circle is a chord that passes through the center of the figure. At the same time, it connects the two most distant points in the circle. Based on this, you can independently draw a diameter (radius) and measure its length using a ruler.
Method 1: fit a right triangle into a circle
It will not be difficult to calculate the circumference if we find its diameter. It is necessary to draw a right triangle in the circle , where the hypotenuse will be equal to the diameter of the circle. To do this, you must have at hand a ruler and a square, otherwise nothing will work.
Method 2: enter any triangle
On the side of the circle, mark any three points, connect them - we get a triangle. It is important that the center of the circle lies in the triangle, this can be done by eye. Draw the medians to each side of the triangle, the point of their intersection coincides with the center of the circle. And when we know the center, we can easily draw the diameter with a ruler.
Method 3: how to calculate the circumference with available tools
This method is very similar to the first, but can be used in the absence of a square or in cases where it is not possible to draw on a figure, for example on a plate. You need to take a sheet of paper with right angles. We attach the sheet to the circle so that one vertex of its corner is in contact with the edge of the circle. Next, mark the points where the sides of the paper intersect with the circle line. Connect these points with a pencil and a ruler. If nothing is at hand, just bend the paper. This line will be equal to the length of the diameter.
Task example
We have a task: how to calculate the circumference if no numerical values are given except for the circle itself. Remember the algorithm:
- We are looking for the diameter using a square, a ruler and a pencil according to method No. 1. Suppose we get 5 cm.
- Knowing the diameter, we can easily insert it into our formula: P = d P = 5 * 3.14 = 15.7 In our case, it turned out about 15.7. Now you can easily explain how to calculate the circumference.