1:7 and a series of 8

I 1:7

Through its presence, architecture communicates. Its massive walls are intensely connected to the space they enclose.

In order to achieve this, Van der Laan asks himself a second question: what is the maximum difference between two sizes so that we can still relate them?

The answer is 1:7.

The thickness of the wall is 1:7 to the space it encloses.

This is called NEARNESS.

II Order of size: a series of 8 measures

With the ratios 3:4 and 1:7, Van der Laan makes a series of eight measures that he calls the order of size or measure-system.
All the measures are related by ca. 3:4.
The smallest and the largest measure relate as 1:7.

Van der Laan’s proportional series is unique, as it combines whole numbers into a hierarchical series.

The key is in the rounding off. In order to give these measures countable values, Dom van der Laan translates them arithmetically into the whole numbers 3, 4 and 7. So the relationship defining the series 1, 4/3, 7/4, … is a practical approximation of 1,324718…

Like the keys of a piano, you can use the 8 measures to make compositions.

Thus, the Plastic Number reconciles counting and measuring.


Dom Van der Laan names the 8 measures as major and minor  elements, pieces, parts and wholes.

III Authentic and derived order of size

In order to refine the possibilities when designing, Van der Laan interwove a second series with the first. As such, there is an authentic and a derived measure-system. Each authentic measure is coupled with a smaller derived measure that is referred to as its derivate.

Every derived measure is 6/7 of its authentic measure.

A derived measure is the double of an authentic measure.

An authentic measure exceeds its derivative with the same authentic measure of the underlying order of size. In a system of 8 measures the difference between the largest and its derivative is thus equal to the smallest.

IV Make your own Abacus

Dom Hans van der Laan considered the act of making essential for gaining an understanding about how to create equilibrium through the placement of various parts. Studying the plastic number and the design method therefore went hand in hand with the making of an abacus and a morphotheque or form-bank. They made it possible to practice with and perfect different proportions. These concrete tools were used during the design process to test various options.

The first abacus dates from 1952.

© drawing by HvdL, 26 November 1984 © drawing by HvdL, 26 November 1984

The abacus consists of 38 bars 12 mm wide and 7 mm high. Two orders of size are represented: the order from 3.5 mm up to 24.5 mm and the order from 24.5 mm up to 175.5 mm. To make it all fit, 2.5 mm from the lower order is also added, as well as the derived measure of 4 mm.

All measures in a building are linked to each other based on measure-systems. Synchronising all the sizes of the parts of a building is what Van der Laan called symmetry. The term is therefore not used here in the modern sense of reflection symmetry, which refers to the opposite identity of two halves. He meant symmetry in the sense of the study of proportions, the ratios between similar measurements in the same direction, such as two lengths or two heights.

V Make your own Form-Bank

Eurhythmy is the study of the form, of the proportions between the three dimensions, in which the length is compared to the breadth, the breadth with height, and the height with length, within a single form.

 © drawing by HvdL, November 1977  © drawing by HvdL, November 1977

The bars in the 1977 form-bank are 16 mm high. The smallest block is 16 mm x 16 mm x 16 mm, while the largest slab is 114 mm x 114 mm x 16 mm.

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