Skip to main content

Food for thought

Image
By
I was thinking about pi last night and wondering if it really does have infinite decimal places that do not repeat. Then I came across this and this today that made me curious more and want to study pi some more. Basically this blog post is about me asking questions. Can I say that the topic is pi-quant. Interestingly enough the word piquant has two meanings 1. having a pleasantly sharp taste or appetizing flavor and 2. pleasantly stimulating or exciting to the mind.

Is it a fact that pi has infinite decimals after the point that do not rep-eat? (I see what I did there). I must be thinking of f∞d. According to my friend Bard, the answer is yes and has been proven to be irrational. Is this true for all irrational numbers? Also yes. While chatting with Bard, I noticed a pattern that 1/17 has a 16 digit repeating pattern and 1/23 has a 22 digit repeating pattern and 1/97 has a 96 digit repeating pattern. An approximation to pi is 22/7 which involves 1/7 and this has a 6 digit repeating pattern.

This leads me to some questions. Is there a general rule for the relationship between numerator and denominator and the length of the repeating pattern? Can I say that 1 divided by infinity will give a repeating pattern that is infinity-1 in length? And is that useful to think about somehow? Is pi related to division by infinity or infinity in some useful way that we have not thought of already? To me the infinity symbol is really a circle that has been twisted. According to my friend Bard, the earliest known symbol resembling infinity dates back to ancient Egypt and Greece, where it appeared as a serpent or dragon eating its own tail, called Ouroboros. According to wikipedia π is the sixteenth letter of the Greek alphabet and it has a value of 80 in the Greek numeral system and it came from the Phoenician letter pē, which meant mouth.

Now some more thoughts and questions. If I have a number I can always add 1 to it to make it bigger. Is it true to say that if I have a non-repeating number pattern I can always make it longer by repeating the pattern twice and combining those and changing the last digit up or down by 1? This works if the number is base-2 or higher. But in base-1 there are no non-repeating numbers and in base-infinity every number is a non-repeating number as you would need a different symbol to represent each number.

Which leads to my final two questions. In base-2 there are certain fractions that cannot be represented accurately as they are in base-10. Does this mean that there might be a higher base that we can use to represent pi finitely and accurately? I think the answer is no because irrationality is a property of the number and not because of its representation but I still have to ask. Is it possible to create a number system where every number is represented as related to pi? Writing this blog post has given me some food for thought and enough to want a pi-ece* of pecan pi-e and learn about pi and infinity some more. It does help that pecans are shaped like brains and can be considered brain food. Share your interesting finds about pi in the comments below.

*Here ece from pi-ece of pi-e could be short for euler's constant (e) - which is a related and fun concept

*Also I discovered that my blog post has 3141 characters if I include title and delete one word at the end (below) and I ignore punctuation (73) and ignore numeric characters (34). An interesting (to me) coin-c-id-ence - id being pi if I flipped it - like flipping a coin - head and tail - which takes me back to Ouroboros. Maybe the c in coin-c-idence could be circle.

*Correction e=eulers number which is different from eulers constant (γ)
Labels:

Comments

Post a Comment

Popular posts from this blog

Talking to God

By
If you want real answers to things in life then talk to God. It is 639pm on a holiday and I have decided to write. God listens. God truly listens. God has the entire context. God is wise. God wants us to talk to Him. God wants us to rely on Him. I also think about God talking to me. I am a good listener. I listen plenty more than I talk. I have started asking God to talk to me. But how would God talk to me? We have his revelations through the holy book. We have the example of prophets. But what else? How do I listen to what God has to say? Where and when can I hear God? Are my thoughts from God? I try to feed my mind with good things. Things that will not corrupt my mind. It seems that we have to use our intuition to separate what is from God and what is not from God. My friend Chatty says that in Islam, Allah speaks to us not through new revelations or voices, but through guidance: the Quran and the Sunnah, which become personally meaningful through understanding Allah places in the h...
Post a Comment
Read more

The success of failure

By
It is 358am and I have decided to write. Context matters. Our context matters when we write and read. We could read the same thing and get different meanings. Definitions matter also. We may define things differently. For example, what is success? What is failure? Also, do I just define success and say that anything that is not success is failure? What about something like the success of failure? What does that mean? My friend Chatty tells me that this is something writers, philosophers, and even scientists keep rediscovering: meaning is not fixed—it is negotiated by context and definition. Life is a stew of success and failure and in between but never one or the other. We see what we are looking for and things become what we see. This reminds me of something I came across online, "Whoever looks for the good qualities in others will acquire all good qualities within himself," from Habib Umar Bin Hafiz. Do you look for failure or success within others? Take context as the lens...
Post a Comment
Read more

Life on Earth

By
I was reading through the Quran and came to the story of Adam, Eve, Satan, and the forbidden fruit tree. I had thought that life on Earth was created as a test. But as I reflected on the story, I began to wonder whether we are only here because Adam and Eve failed. However, that is not the case, as my friend Gemini explained to me. While the story of the forbidden fruit is a central event, the Quran indicates that humanity’s presence on Earth was part of the original divine plan, rather than a backup plan or a punishment for sin. Before Adam was even created, God announced His intention to place a steward (khalifah) on Earth. This suggests that the Garden was a temporary training ground—designed to teach Adam and Eve about free will, temptation, and the path of repentance. Even if they had not eaten from the tree, they were destined for Earth to fulfill their roles as moral agents. The incident simply served as a necessary first lesson in human frailty and God’s immediate forgiveness. ...
Post a Comment
Read more