Not a mathematician here at all so perhaps my question is phrased incorrectly.
Let’s say through thorough testing in reality, we can prove with certainty Pi is correct up until 5 decimal places,
3.14159
The computers that are calculating Pi to an endless degree, how do they validate new values that are calculated as correct and cannot be otherwise?
In: 434
It’s been 30 years since I took calculus, but this is what I recall:
When people wanted to find the area of a circle, they could draw and measure a square with its four points touching the circumference of the circle and another square on the outside that contains the circle. The area of the circle is somewhere in between the area of those squares. This allowed a rough approximation.
The next step in the logic is that if I use increasingly smaller squares on the inside my measurement will be more accurate.
One of the basic elements of Calculus is the “limit” – it allows a calculation of how a number behaves as it gets closer and closer to a given number (usually 1 or zero). This principle allows you to calculate the area of all the squares above as the length of their sides gets closer and closer to 0.
Archimedes calculated pi (250BC) with a similiar approach by using polygons with ever increasing numbers of sides.
Latest Answers