Diffy Squares | Interactive Geometry Lab

SUBTRACT · CONNECT · REPEAT

How many squares until zero?

Put a number at each corner. Find the absolute difference along each edge, then connect the midpoints to make the next square.

How it works

01 / SET YOUR CORNERS

Start with four numbers

Your last 10 starting sets

Saved on this browser. Each entry lists A, B, C, D clockwise and the total squares, including the starting square.

THE DIFFY RULE

A small rule. A surprising ending.

Subtract neighbors. Go clockwise around the square, including the last corner back to the first.
Take absolute values. Put each nonnegative difference at that edge’s midpoint.
Connect and repeat. Those four midpoints become the corners of a new square.

(a, b, c, d) →
(|b − a|, |c − b|, |d − c|, |a − d|)

For four integer or finite-decimal starting values, the process eventually reaches four zeros. The squares shrink by geometry, independently of their numbers.

02 / EXPLORE THE PATTERN

One square becomes the next

Starting square

Choose how to exploreOption 1 · ManualWork out the four differences yourself.Option 2 · AutomaticStep through or play the calculated sequence.

Earlier squares Current square Next midpoints

Show next midpoints Focus current square

Explore steps0 / 0

Playback speed

FOLLOW THE MATH

The next four midpoints

Clockwise ↻

03 / TRACE THE NUMBERS

Your square-by-square journey

Select a row to revisit a square. Values follow the corners clockwise.

All computed squares in clockwise order. Use the row buttons to display a square.
Square	Corner 1	Corner 2	Corner 3	Corner 4	Largest value

NEED A STARTING POINT?

Try these starting numbers

Browse a few starting sets, then use one in either mode. Values go clockwise: A (top left), B (top right), C (bottom right), D (bottom left).

How many squares until zero?

One square becomes the next

Your next four differences

The next four midpoints

Your square-by-square journey

Try these starting numbers