6 Oct 2023 1:20 pm
seems to me that set of figures just proves a measurement was off or you were just measuring the leg of a right angle to a hard sided object.Skans » 04 Oct 2023, 6:02 pm » wrote: ↑ Actually, Pi does change with the roundness of the circle. If you construct a near circle with a thousand tiny lines linked together around a centerpoint, Pi (not true Pi, because its not a true circle) will be a rational number. Lets take this to the extreme and perhaps you can follow me:
C = 2 π R
π = C/2R
Where the Circumference of the near-circle is actually 10 equal-length lines around a centerpoint, a Decagon, Pi will be a rational number:
Assume each line of the Decagon is exactly 10 centimeters long. The Circumference of this near-circle would be 100 centemeters. The radius is 16.18034. So, let's calculate π.
π = C/2R.
π = 100/2*16.18034
π = 100/32.36068
π (near pi) = 3.0901699222685 The digits to the right of the decimal will eventually repeat or stop.
As the circle approaches being perfectly round,π will approach the 3.1415....irrational number. With each iteration of smaller and smaller lines making up the near-circle, π needs to "shift" and morph to accommodate the new near-circle structure.
This should be able to be expressed as a calculus limit. But, its not that easy:
lim π→irrational number−C→more perfect roundness.
It's not easy because I don't know how to express something becoming "more round" to a point of perfect roundness. But, this guy, Yasuhiro Takashimizu, has some additional thoughts on this. https://progearthplanetsci.springeropen ... 015-0078-x
100/Pi=31.8309886............
strike a arc!