[Verse 1]
Start with one lonely number at the peak
One sits alone, mysterious and sleek
Drop down a row, now one becomes two
Mirror images, perfectly true
Add the neighbors from the row above
Watch the pattern that mathematicians love
[Chorus]
Pascal's pyramid, climbing every tier
Add the two above, the answer will appear
One plus one makes two, two plus one makes three
Combinations hiding in this mystery
Row five sums to thirty-two, that's two to the fifth degree
Pascal's triangle holds the binomial key
[Verse 2]
Count the ways to choose from a set
Coefficients that you'll never forget
Row four gives you one, four, six, four, one
Expanding polynomials, the work is done
Each diagonal tells a secret tale
Fibonacci emerges without fail
[Chorus]
Pascal's pyramid, climbing every tier
Add the two above, the answer will appear
One plus one makes two, two plus one makes three
Combinations hiding in this mystery
Row five sums to thirty-two, that's two to the fifth degree
Pascal's triangle holds the binomial key
[Bridge]
Color every even number white, odds in black
Sierpinski's fractal gazes right back
Alternating sums cancel to zero's dance
Except row zero gives one a chance
Ten choose three or three from ten
Pascal shows they're equal again
[Verse 3]
Probability problems find their solution here
Lottery tickets make the pattern clear
How many paths through a lattice grid
Pascal's entries keep the answer unhid
From Chinese roots to European fame
Different cultures, but the math's the same
[Outro]
Every entry knows its place
Two guardians from the upper space
Infinite rows stretch toward the sky
Pascal's legacy will never die