Scratch

Project Notes

this is a project that simply calculates the value of pi (approximately)

the value of pi it shows offline is off after it gets to 2653 because it shows the next digit as 7. it might work on the java player online, but if it doesn't, it isn't my fault. there must be some sort of bug at the very low decimal places.

btw press 0 to reset pi min and set n to 1000000. you can stop, press 0, and then start to reset the whole thing with pi min at 0 and n at 2.

ANYWAYS this is HOW IT WORKS:

using a very early form of what later became calculus (developed by Isaac Newton later), the ancient greeks calculated the value of pi by using their knowledge of finding the lengths of sides of triangles.

Given a value of n (a whole number 2 or greater) you can construct an n-sided polygon (or n-gon) inscribed in a circle with radius 1. if you draw a line from two consecutive points of the n-gon to the center of the circle, you have an isosceles triangle. if you call the two outer points A and B and the center point C, you know that sides AC and BC are equal to the radius, 1. the angle value of ACB is able to be determined based on dividing the 360 degrees of the circle into the n number of segmented sides (and therefore isosceles triangles) of the inscribed n-gon. since it is an isosceles triangle, you know that the total number of angles equals 180 and that ABC and CAB are equal, so you can figure out their angle values. knowing this information, you can do a little mathematics (trigonometry) to find the length of segment AB. then you multiply this by n for the n segments to find the perimeter of the n-gon. pi is the perimeter of an infinite-gon (if that is a word and it probably isn't) inscribed (and circumscribed, but I haven't made that yet, that's the maximum limiter) in a circle (an infinite-gon is the same as a circle) with radius 1 divided by 2 (since pi is the ratio of the DIAMETER to the circumfrence, so you have to divide it by two so that the diameter equals 1) so there you can find your calculus expression for pi, which is, of course, irrational.

thank you, if you would like me to attempt the calculation of the maximum of pi based on a circumscribed n-gon, then comment.

I would also like to later attempt something harder, the calculation of the area of a section bordered by a parabola.

IF YOU HAVE READ TO HERE THEN CONGRATULATIONS YOU EITHER HAVE LEARNED A NEW THING ABOUT MATH TODAY OR YOU ARE COMPLETELY AND TOTALLY CONFUSED