Hans Walser, [20260624]

Rational Leg Ratio

Idea and inspiration: Hanna Roeckle, A Silver Lining, 2025, Wall Installation | Wall Installation, Kunstmuseum Liechtenstein

1 What it's about

Examples of a tessellation with congruent right triangles with a rational leg ratio.

2 The simplest example

The simplest non-trivial example is the right triangle with a leg ratio of 2:1 (Fig. 1).

Fig. 1: Base triangle

Figure 2 shows a rather irregular tessellation.

Fig. 2: Tessellation

The example can be assembled into a larger tessellation (Fig. 3).

Fig. 3: Composition

We can proceed analogously with any right triangle whose leg ratio is rational.

In the example shown in Figures 4 and 5, we have a leg ratio of 3:2.

Fig. 4: Rational leg ratio 3:2

Fig. 5: Tessellation

A checkerboard-like shape is likely to be found in a right-angled isosceles triangle (Fig. 6).

Fig. 6: Right-angled isosceles triangle

Weblinks

Hans Walser: Das einfachste nichttriviale Beispiel (Vortrag)