Pascal's triangle · Mathematics

PASCAL'S TRIANGLE SIMULATION

▸ Placing the apex C(0,0) = 1…

▸ Building each row by Pascal's addition rule

▸ Attaching the combinatorial meaning C(n,k) to each cell

▸ Calibrating paths · binomial expansion

▸ Starting Sierpinski & Fibonacci modes…

▸ Ready — Online. ✅

Selected cell & figures

🔺 Pascal's triangle

C(n,k) = C(n−1,k−1) + C(n−1,k)

Rows shown—

Selected cell (n, k)—

C(n, k)—

Row sum = 2ⁿ—

Odd cells (shown)—

Tip

Each cell = the sum of the two above. The cell at row n, column k is C(n,k) — the number of ways to choose k items from n. Hover to see the two parents; click a cell to select it. Switch the Scenario to see paths, fractals, Fibonacci…

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Click a cell to select · drag Rows to build higher · switch the Scenario (paths · Sierpinski · mod 3 · expansion · hockey stick · Fibonacci)

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C(n,k) of selected cell · row sum (log) · odd-cell count — as it builds C(n,k) (log)sum 2ⁿ (log)odd cells