The Unicursal Pythagram

🜛 The Unicursal Pythagram
08 October 2025

The unicursal pythagram is a geometric figure drawn on a 6×6 grid.
It is made from sixteen points connected by thirty-two straight lines, and the whole pattern can be drawn without lifting the pen. That is what makes it unicursal — it is one continuous path that begins and ends at the same point.

The figure is related to the 3:4:5 right triangle, just like the standard pythagram.

But while the standard version is about static shapes, the unicursal version adds movement.
It shows how all the parts of the pattern connect together in a single, flowing line.

Points used (A–P)
A(2,2), B(3,4), C(4,2), D(2,3), E(4,4), F(3,2), G(2,4), H(4,3),
I(0,3), J(1,5), K(5,5), L(6,3), M(3,0), N(1,1), O(3,6), P(5,1)

Drawing order (32 lines)
A→B, B→C, C→D, D→E, E→F, F→G, G→H, H→A,
A→I, I→J, J→B, B→K, K→L, L→C, C→M, M→N,
N→D, D→J, J→O, O→E, E→L, L→P, P→F, F→N,
N→I, I→G, G→O, O→K, K→H, H→P, P→M, M→A

In simple terms
The unicursal pythagram shows how a complex pattern can be built from a few simple steps.
Every point is connected, every line leads to the next, and everything joins up in the end.
It is a clear example of unity through continuity — a single path holding the whole design together.