PASCAL’S TRIANGLE

the first thirteen rows, the sum of each row and the pattern of the odd numbers

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: maths · school · reference · classroom

Rows are numbered from zero, and row n holds n + 1 numbers. To learn in how many ways k things can be chosen out of n, take row n and count k places along it, again from zero. The number of each row stands to its left, and the sum of all its numbers to its right.

THE ODD NUMBERS MAKE UP THE SIERPIŃSKI TRIANGLE

Shade the odd numbers and stop reading the numbers themselves: what is left is the Sierpiński triangle — a triangle with a triangular hole in the middle, and the same hole again, smaller, in each of its thirds.

This is a count, not an impression. The first 128 rows hold 8 256 cells, of which 2 187 are odd — exactly three to the power of 7. Double the height and the shaded part grows threefold, not fourfold; that shortfall is what eats the holes.

On the sheet

Rows are numbered from zero, and row n holds n + 1 numbers. To learn in how many ways k things can be chosen out of n, take row n and count k places along it, again from zero. The number of each row stands to its left, and the sum of all its numbers to its right.
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 9 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

PASCAL’S TRIANGLE

THE ODD NUMBERS MAKE UP THE SIERPIŃSKI TRIANGLE

On the sheet

Printing

More like this

BARBELL MATHS

BENFORD’S LAW

THE BIRTHDAY PARADOX

THE CLOCK FACE