This is a chapter from my eight book called Learn to live
If you are observant, you may have noticed that all my chapters so far end in -y (I wonder why?). This has happened by chance but I like that it has and I will continue the trend. Keep asking questions. Keep asking why. Keep learning. Stay curious. Today I learnt that, "The idea of factorial is how many times you can arrange data in different orders, being unable to arrange them counts as ONE possible outcome." Hence 0! = 1. Then I came across an article that somehow computes ∞! = √(2π)
Intuitively I think that infinity is not a number therefore infinity factorial cannot be computed. Maybe we can talk about limits and my limited math has me thinking that n! factorial approaches infinity as n approaches infinity. This has me thinking what is the relationship between infinity and pi? And about circles and pi?
My friend Chatty tells me that many series converge to pi as n approaches infinity. For example, the Leibniz formula for pi. A circle can be viewed as a limit of a regular polygon as the number of sides approaches infinity. Thinking about infinity and circles led me to watching this youtube video. Is a dot or point a circle? Which leads me to learn about point circles, real circles and imaginary circles. Also some thoughts I had on the fourth of February. It seems that it is impossible to draw the smallest circle. For every small circle we draw, we can draw a smaller one. The following are a set of questions I had then:
What can fit in the smallest circle?
Can we draw a square inside every circle?
Can we draw a circle inside every square?
Can these both be true?
Can we draw a square in the smallest circle?
Can we draw a circle in the smallest square?
When are a circle and square the same?
Maybe related but I read that "squaring the circle" is a geometric problem from Greek mathematics that involves constructing a square with the same area as a given circle using only a compass and straightedge. In 1882, it was proven impossible due to the Lindemann–Weierstrass theorem, which shows that pi is a transcendental number. The phrase is also used metaphorically to describe attempting the impossible.
Infinity has me thinking of zero. Let us say zero represents nothing. Infinity represents everything. The set of everything cannot contain nothing. Nothing is when you take away everything. If you take away nothing then how can you still be left with nothing. I am thinking that if infinity as a number does not exist then zero as a number does not exist. Zero is not a number. Zero really represents the middle. Numbers are really points on a circle. You start with a dot. Then you create a line (two dots). Then you create a triangle (three dots). The more dots you add the more well defined the circle becomes. Numbers are just ways to label points and counting is just a way to get from one point to the other.
How can I now come back to where I started? Let us take a look at ∞! = √(2π) again. A square inscribed in a circle of r=1 has a side of √2. The √π is related to the ratio of the areas of a square inscribed in a circle. I imagine that somehow we are looking at a square becoming a circle or when a square is a circle and this all makes sense. One day I will know and understand more to make a better conclusion and point of all that I have come across in this chapter but here is a joke nonetheless. What did the square say to the circle? You are pointless! Maybe the point is that there is no beginning and no end just like a big old circle.
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