Peaking into the Why of Pi: A Further Look
Hello again math-curious minds on yet another pi day! Following our previous ponderings on π, today we take a further look and continue piecing together the π puzzle. If your journey here with π is just beginning, I warmly encourage you to explore my earlier posts as well as Episode #017 of Mister Marx Math Adventures on YouTube; they serve as the foundation to today’s exploration.
Catch those previous blog posts here: 🔗 https://www.mistermarx.com/blog/mister-marx-math-adventures-017-what-does-pi-equal-how-pi-value-is-derived-pi-demonstrate-pi-value-derived 🔗 https://www.mistermarx.com/blog/peaking-into-the-why-of-pi 🔗
Or watch the full episode over on YouTube: 🔗 https://www.youtube.com/watch?v=ghSAORlyewE 🔗
In our prior exploration, pi revealed itself to be more than just the never-ending 3.141592653… number, but to be the storyteller of the relationship of a circle and its circumference. Take another look at the animated GIF we’re now all-too familiar with, but with a fresh coat of paint.
Let’s explore the questions posed previously one by one:
How is π represented in the gif? How is it measured?
In our animated GIF, there is a circle with exactly diameter 1. This circle then proceeds to roll along a straight path. As it rolls, it traces a line in red. This traced line only happens for exactly one roll of the circle. Upon conclusion of that single roll, the line left behind by the unrolling of the circle’s circumference measures π exactly.
How does the gif demonstrate the relationship between a circle's circumference and its diameter? What is that relationship?
This animated GIF reveals one of math’s fundamental truths - the circumference of a circle is always π multiplied by its diameter. No matter the size of your circle, this ratio remains constant - a universal truth for all circles. (Don’t believe me? Try it yourself! Try recreating the animated GIF with a circle of diameter=1, diameter=2, or even diameter=10! If you do, share your recreations and findings in the comments)
How does the gif relate to real-world applications of pi, such as in geometry or engineering? Do you know anyone who uses π in their personal work?
Now let’s peak your interest into how π and its story-telling abilities appear in the real-world. In the fields of geometry and engineering, π is the key to exploring circles and spheres - each essential for designing wheels, 3D Models, architecture, & more. Calculating planetary trajectories? Assessing structural integrity? π is at the heart of so many of these vital endeavors. π demonstrates to us that mathematics is not merely about numbers and equations, but about wrapping our minds around as well as shaping the world around us.
Keep thinking about it, and you may begin to realize the ubiquity of π - it’s everywhere! So many disciplines rely upon the universal language of mathematics, and π is a core vocabulary word crossing and connecting those disciplines.
How did you do? Were your answers similar or different from mine? Share your thoughts and reactions in the comments! When it comes to universal constants the likes of π, there seems to never be an end to the amount of layers which can be peeled back to reveal new insights.
Before we part ways on this π day, let's pause for a moment to think about one of π's most mesmerizing qualities—its existence as an irrational number.
Unlike the whole numbers like 1, 5, 314, and -23, or simple fractions like 1/4 and -7/3, π cannot be precisely pinned down. Its digits stretch infinitely without repetition or pattern.
This characteristic of π is a gateway to curiosity and wonder. It reminds us that even in our age of immense knowledge and technology, there remain mysteries reluctant to being pinned down. The infinite nature of π challenges us to embrace the unknown, to find comfort in questions, and to never stop exploring.
So, please let your thoughts today be your invitation to ponder the infinite. What does it mean for a number to go on forever? How do we grapple with concepts that deny our want for neatness and order? These are the questions that not only advance our understanding but also enrich our sense of knowing about the world.
Happy π Day!
Mister Marx
