Pi (π) is one of the most important and interesting numbers in mathematics. Around 3.14, pi is a constant used to calculate the circumference of a circle from the radius or diameter of the circle. Pi is also an irrational number, which means that pi can be counted to infinity of decimal places without repeating the pattern. This makes it difficult to calculate pi, but that doesn't mean it's impossible to calculate it correctly
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Method 1 of 5: Calculating Pi Using Circle Size
Step 1. Make sure you use a perfect circle
This method cannot be used on ellipses, ovals, or other planes, except perfect circles. A circle is defined as all points on a plane that are equidistant from a central point. The jar lid is a suitable household item for this experiment. You should be able to calculate the approximate value of pi because to get an exact result, you need to have a very thin plate (or other object). Even the sharpest graphite pencil is a great object for getting precise results.
Step 2. Measure the circumference of the circle as accurately as you can
The circumference is the length that goes around all the sides of the circle. Because of its curved shape, the circumference of a circle is difficult to calculate (this is why pi is important).
Wrap the yarn around the loop as tightly as you can. Mark the thread at the end of the circumference of the circle, and then measure the length of the thread with a ruler
Step 3. Measure the diameter of the circle
The diameter is calculated starting from one side of the circle to the other side of the circle through the center of the circle.
Step 4. Use the formula
The circumference of a circle is found using the formula C= *d = 2*π*r. Thus, pi is equal to the circumference of a circle divided by its diameter. Enter your numbers into the calculator: it should be around 3, 14.
Step 5. For more accurate results, repeat this process with several different circles, and then average the results
Your measurements may not be perfect on any circle, but over time, averaging the results should give you a fairly accurate calculation of pi.
Method 2 of 5: Calculating Pi Using Infinite Series
Step 1. Use the Gregory-Leibniz series
Mathematicians have discovered several different mathematical sequences that, if written down to infinity, can calculate pi so accurately to obtain many decimal places. Some of these sequences are so complex that they require a supercomputer to process them. One of the easiest, however, is the Gregory-Leibniz series. While not very efficient, with each iteration it gets closer and closer to the value of pi, accurately producing pi to five decimal places with 500,000 repetitions. Here is the formula to apply.
- = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) …
- Take 4, and subtract 4 by 3. Then add 4 by 5. Then, subtract 4 by 7. Continue in turn adding and subtracting fractions with the numerator of 4 and the denominator of consecutive odd numbers. The more often you do this, the closer you are to getting to the value of pi.
Step 2. Try the Nilakantha series
This series is another infinite series for calculating pi that is quite easy to understand. Although this series is somewhat more complicated, it can find pi much faster than Leibniz's formula.
- = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10) + 4/(10*11 *12) - 4/(12*13*14) …
- For this formula, take three and start taking turns adding and subtracting fractions with a numerator of 4 and a denominator consisting of the multiplication of three consecutive integers that increase with each new iteration. Each successive fraction starts its whole number series from the largest number used in the previous fraction. Do this calculation several times and the result will be quite close to the value of pi.
Method 3 of 5: Calculating Pi Using Buffon's Needle Experiment
Step 1. Try this experiment to calculate pi by throwing a hotdog
Pi can also be found from an interesting experiment called the Buffon's Needle Experiment, which tries to determine the probability that randomly thrown long objects of the same type will fall between or across a series of parallel lines on the floor. It turns out that if the distance between the lines is the same length as the object thrown, the number of objects that fall across the line compared to the number of throws can be used to calculate pi. Read the Buffon needle experiment article for a full explanation of this fun experiment.
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Scientists and mathematicians do not yet know how to calculate the exact value of pi, because they cannot find material so thin that it can be used to find precise calculations.
Calculate Pi Step 8
Method 4 of 5: Calculating Pi Using Limit
Step 1. First of all, choose a large value number
The larger the number you choose, the more accurate the pi calculation will be.
Step 2. Then, plug the number, hereinafter referred to as x, into the following formula to calculate pi: x * sin(180 / x). To perform this calculation, make sure your calculator is set in Degrees mode. This calculation is called Limit because the result is a limit close to pi. The larger the number x, the calculation results will be closer to the value of pi.
Method 5 of 5: Arc Sine/Inverse Sine Function
Step 1. Choose any number between -1 and 1
This is because the Arc sine function is undefined for numbers greater than 1 or less than -1.
Step 2. Plug your number into the following formula, and the approximate result will be equal to pi
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pi = 2 * (Arc sine(akr(1 - x^2))) + abs(Arc sine(x)).
- The sine arc represents the inverse of the sine in radians
- Akr is an abbreviation for square root
- Abs shows absolute value
- x^2 represents the exponent, in this case, x squared.
