Next, we straightened the yarn out and measured it with a ruler. Then, we took a piece of yarn and laid it across the top of the tuna can. That gave us its diameter. Then we did some division. If you try this at home and are still working on your long division, you can use a calculator.
We took the circumference and divided it by the diameter. We tried our yarn measurements again with a plate and a clock. We had to be very precise, but every time we divided the numbers, we got the same answer: about 3. Get our History Newsletter. Put today's news in context and see highlights from the archives.
Please enter a valid email address. Please attempt to sign up again. Sign Up Now. An unexpected error has occurred with your sign up. Please try again later. If you have a circle, you can measure two things: the distance around the perimeter of the circle circumference and the distance across the widest part of the circle diameter. No matter how big your circle, the ratio of circumference to diameter is the value of Pi.
Pi is an irrational numberyou can't write it down as a non-infinite decimal. This means you need an approximate value for Pi. The simplest approximation for Pi is just 3.
Yes, we all know that's incorrect, but it can at least get you started if you want to do something with circles. The early history of mathematics covers many approximations of the value of Pi. The most common method would be to construct a many-sided polygon and use this to calculate the perimeter and diameter as an estimate for Pi. Other cultures found ways to write Pi as an infinite seriesbut without a computer, this can be sort of difficult to calculate out very far.
There are many methods to calculate Pi but I will go over the simplest to understand. It starts with the inverse tangent function. No, you can't just plug it into your calculator and get Pithat assumes you already know Pi.
Instead, we need to do a Taylor Series expansion of the inverse tangent. The basic idea behind the Taylor Series is that any function sort of looks like a power series if you just focus on one part of that function. Using this, I can represent the inverse tangent of some value x as an infinite series:. That's it. Now you can just plug away at this formula for as long as you likeor you could have a computer do it. Here is a program that calculates the first 10, terms in the series just press play to run it :.
View Iframe URL. See, that's not so difficult for a computer. Between 3, and 4, years ago, people used trial-and-error approximations of pi, without doing any math or considering potential errors. The earliest written approximations of pi are 3. Both approximations start with 3. The first rigorous approach to finding the true value of pi was based on geometrical approximations. Around BC, the Greek mathematician Archimedes drew polygons both around the outside and within the interior of circles.
Measuring the perimeters of those gave upper and lower bounds of the range containing pi. He started with hexagons; by using polygons with more and more sides, he ultimately calculated three accurate digits of pi: 3. Independently, around AD , Chinese mathematician Liu Hui created another simple polygon-based iterative algorithm. He proposed a very fast and efficient approximation method, which gave four accurate digits. This record held for another years.
In , Austrian astronomer Christoph Grienberger arrived at 38 digits, which is the most accurate approximation manually achieved using polygonal algorithms.
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