The Importance of a Single Point

My central argument is simple yet profound: the diameter of a circle is not exactly equal to twice the radius. This claim is based on an observation about the parity of points: a diameter, including the central point, consists of an odd number of points, whereas two radii, added together, always result in an even number of points. Although the difference is minimal – just one point – this small discrepancy prevents the equality from being absolute.

This observation leads us to wonder: is it possible to form a circle from a segment that has an odd number of points? While the answer might be affirmative, the absence of a defined central point introduces an undefined aspect into our geometric construction. Delving deeper into this reflection, we might suggest that this duality of odd and even diameters introduces an indefiniteness at the central point, which could offer an explanation for why the number Pi is irrational. Pi represents the relationship between the circumference and its diameter in a perfectly closed circle, though conceptually the diameter might present these peculiarities.

I use this analysis to emphasize the importance of the "central point" in my Point Theory, which I explore on my blog. This concept is not only crucial in personal life but also has significant implications in mathematical calculation, such as in determining square roots, where the intersection point of two segments is counted twice.

Furthermore, I propose a corollary related to the theoretical versus practical nature of mathematics. Although mathematically we can calculate the decimals of Pi ad infinitum, physically it makes no sense to do so beyond the smallest possible physical distance. This is because a circle must close perfectly for any defined diameter with an integer number of points. Therefore, the decimals of Pi could theoretically be limited to those corresponding to the smallest possible distance and the nearest odd diameter as a conceptual limit.

This approach invites us to reconsider not only the foundations of geometry and calculation but also how we interpret and apply mathematical principles in the physical world. I am very interested in discussing these ideas further and receiving feedback that could enrich or challenge this perspective.