(April 28, 2013 at 9:27 pm)Venom7513 Wrote: This is technically not true because there are no perfect circles!
To see why, first note that Pi is irrational. That is, Pi can not be expressed as a ratio of integers. Now note that all lengths exist as a multiple of the smallest length, planck length (~1.61619926 × 10^-35 m). The circumference and diameter of a given circle are lengths and, therefore, exist as integral multiples of plank length. In other words the ratio of a given circles circumference to its diameter is a rational number!
The larger the circle, the closer the ratio gets to Pi, but in a universe with finite resources, no such object can ever exist.
Wow.. you've just mathematically and physically proven circles can't exist and are therefore only a concept. The only way I knew how to do that was by rigorously trying to point out how a circle in real life doesn't fit the description of the concept of a circle...
"It is the mark of an educated mind to be able to entertain a thought without accepting it" ~ Aristotle
