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Author: lievenlb

Designer Maths

Published May 22, 2021 by lievenlb

This fall, I’ll be teaching ‘Mathematics for Designers’ to first year students in Architecture.

The past few weeks I’ve been looking around for topics to be included in such as course, relevant to architects/artists (not necessarily to engineers/mathematicians).

One of the best texts I’ve found on this (perhaps in need of a slight update) is the 1986-paper by Jay Kappraff: A course in the mathematics of design. He suggests the following list of topics:

  • graph theory
  • polyhedra
  • tilings of the plane
  • three dimensional packings
  • proportion and the golden mean
  • transformations
  • symmetry
  • vectors

We all know that an awful lot of math and computation is needed to design a building, but today all of the hardcore use of vectors, equations and transformations is conveniently hidden from the architect’s view by digital design platforms and CAD-programs.

These computational tools offer new creative possibilities, as illustrated in the beautiful book The new mathematics of architecture by Jane Burry and Mark Burry, also available in Dutch with a cover picture of the Möbius bridge in Bristol



In this book, about 50 recent architectural projects are clustered around these topics:

  • mathematical surfaces and seriality
  • chaos, complexity, emergence
  • packings and tilings
  • optimization
  • topology
  • datascapes and multi-dimensionality

In the description of the projects, cool math-topics are (sadly only) touched, including

It will take me some time to find a balance between these two approaches. Common themes clearly are

  • Shapes : what is possible/impossible in 2D and 3D, and how can mathematics help us to find new exciting shapes (think minimal and Seifert surfaces, knot complements, etc.)
  • Symmetry : what is possible/impossible in 2D and 3D, and what can mathematics tell us about new symmetries (think emerging symmetries from aperiodic tilings and quasicrystals)

Over the coming months I’ll be writing the course notes and may post about it here. For this reason I’ve included a new category DesignerMaths.

If you have suggestions, please let me know.

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Lockdown reading : SNORT

Published May 2, 2021 by lievenlb

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk.



This must have been the third time I’ve read The genius in by basement – The biography of a happy man by Alexander masters.

I first read it when it came out in 2011.

Then, in conjunction with Genius at play – The Curious Mind of John Horton Conway Conway’s biography by Siobhan Roberts, in july 2017, which is probably the best way to read this book.

And, then again last week, as Simon Norton‘s work pops up wherever I look, as in the previous post.

It takes some time to get used to the rather chaotic style (probably used because that’s how Masters perceives Norton), and all attempts at explaining Simon’s mathematics can better be skipped.

The book tries to find an answer as to why a child prodigy and genius like Simon Norton failed to secure a safe place in academics.

Page 328:

Simon’s second explanation of his loss of mathematical direction is heartbreaking. Now that Conway has fled to America, there is no one in the mathematical world who will work with him.

They say he is too peculiar, too shabby, too old.

His interests are fixed in mathematics that has had its day. His brilliance is frigid. His talent, perfectly suited to an extraordinary moment in algebraic history (the symmetry work at Cambridge during the early 1970s and 1980s) is out of fashion.

This may give the impression that Norton stopped doing good math after Conway left for Princeton in 1985. This is far from true.

Norton’s Wikipedia page mentions only post 1995 publications, which in itself is deplorable, as it leaves out his contributions to the ATLAS and his seminal paper with Conway on Monstrous moonshine.

Here’s Alexander Masters talking about ‘Genius in my basement’

I’ll leave you with a nice quote, comparing Monstrous Moonshine to a Sainsbury’s bag on Jupiter.

Page 334:

This much I do know: Monstrous Moonshine links the Monster to distant mathematics and the structure of space in ways that are as awe-inspiring to a man like Simon as it would be to an astronaut to step out of his space machine on Jupiter, and find a Sainsbury’s bag floating past. That’s why it’s called ‘Moonshine’, because mathematicians can even now hardly believe it.

‘I think’, said Simon, standing up from his berth and shaking crumbs and clotted blobs of oil and fish off his T-shirt onto the covers, ‘I can explain to you what Moonshine is in one sentence.’

When he really tries, Simon can be a model of clarity.

‘It is,’ he said, ‘the voice of God.’

Ps, wrt. SNORT.

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