What exactly is Pi?
Pi (π) is the number you get when you divide a circle’s circumference by its diameter. Sounds simple, but this one ratio hides an entire universe of ideas behind it.
Every circle, no matter the size, gives you the same number. That alone makes π feel a bit magical.
Why Pi matters more than we realise
Most students only meet π when they need to find the area or circumference of a circle. But π shows up in far more places:
waves and oscillations
electromagnetism
probability
quantum mechanics
geometry and trigonometry
It’s everywhere.
And it never ends, literally.
π is irrational, so its decimal expansion goes on forever with no repeating pattern. Yet humans have pushed its digits to over 31 trillion places (for no real practical reason other than “because we can”).
A quick tour through history
Different ancient civilisations tried estimating π long before calculators existed:
Babylonians used 3.125
Egyptians used a value close to 3.1605
Archimedes (Greek mathematician) used polygons to trap the value between 3.1408 and 3.1429 — a huge breakthrough for his time
The symbol π didn’t appear until 1706, introduced by William Jones, and was later popularised by Euler.
Since then, mathematicians, scientists, and now computers have spent centuries uncovering its behaviour, and we still don’t fully understand the patterns hiding inside its digits.
Some cool things about Pi
Here are a few reasons π keeps mathematicians hooked:
1. Its digits look totally random
Even though π is generated by a very clean formula, its digits behave like chaos. No repeating pattern. No predictable sequence. Just endless digits that look random.
2. It’s transcendental
This means π isn’t the solution to any algebraic equation with rational coefficients.
You can’t “solve for π”. It sits outside those rules entirely.
3. It appears in unexpected places
Even things that have nothing to do with circles, like probability distributions, quietly use π behind the scenes.
It’s almost like the universe can’t resist sneaking π into its equations.
So why should students care?
Because once you see π as more than “just another number”, concepts like area, circumference, angles, waves, and even problem-solving strategies start to feel connected instead of random.
When students stop memorising and start understanding, maths becomes lighter, not heavier.
What’s coming next!
There’s a lot more I want to unpack:
how to use π smartly in calculations
common mistakes students make
little shortcuts that help them think instead of memorise
If you’re curious, keep a lookout for the next post.
See you in the next one.
~MathSifu