BENFORD’S LAW

the first digit of a number: why a one turns up more than six times as often as a nine, and in which sets that is true

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 · everyone · reference · study

Every percentage here is computed at build time: each run is generated in full and the first digit is taken as the first character of the decimal form, not from a logarithm. “Miss” is the largest gap between a run and the law on a single digit, in percentage points.

THE ONLY DISTRIBUTION THAT DOES NOT CARE ABOUT UNITS

This distribution is the only one that does not care what you measure in. Convert the whole set from metres to feet, from hryvnias to dollars, from grams to ounces — that is, multiply every number by a constant — and the first digits stay put. Measured: multiplying a run spread over a thousand orders of magnitude by 2, 3, 7 and 137 moves the largest share by 0.08 of a percentage point.

For an even run this is false, and grossly so: the same multipliers throw the run from 100 to 999 by 44.4 points. That is where the law comes from: if a general rule for the first digit exists at all, it must not depend on the units — and only one rule can do that.

On the sheet

Every percentage here is computed at build time: each run is generated in full and the first digit is taken as the first character of the decimal form, not from a logarithm. “Miss” is the largest gap between a run and the law on a single digit, in percentage points.
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 10 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.

BENFORD’S LAW

THE ONLY DISTRIBUTION THAT DOES NOT CARE ABOUT UNITS

On the sheet

Printing

More like this

BARBELL MATHS

THE BIRTHDAY PARADOX

THE CLOCK FACE

THE COLLATZ CONJECTURE