Architecture and Math

Posted on 1 January 2022 by John

I recently received a review copy of Andrew Witt’s new book Formulations: Architecture, Mathematics, and Culture.

The Hankel function on the cover is the first clue that this book contains some advanced mathematics. Or rather, it references some advanced mathematics. I’ve only skimmed the book so far, but I didn’t see any equations.

Hankel functions are defined in terms of Bessel functions:

$H^{(1)}_\nu(z) = J_\nu(z) + i Y_\nu(z)$

where J is the Bessel function of the first kind, Y is the Bessel function of the second kind, and ν is the order. I’ve only ever seen one subscript on Hankel functions, but my suspicion is that the two subscripts allow for different orders on J and Y. That is, my guess is that

$H^{(1)}_{(m,n)}(z) = J_m(z) + i Y_n(z)$

Here’s my quick attempt to reproduce the cover art in Mathematica:

    H[m_, n_, z_] := BesselJ[m, z] + I BesselY[n, z]
    ComplexPlot3D[H[3, 5, z], {z, -4 - 4 I, 5 + 5 I}]

This produces the following plot.

I’m amazed that people ever had the patience and skill to manually make plots like the one on the cover of Witt’s book.

While thumbing through the book I noticed some curves that I recognized as Lissajous curves. Turns out these were curves made by Lissajous himself. The plots were accompanied by the mechanical devices Lissajous used to draw them.

Houston Public Library, 1976

Posted on 17 December 2011 by John

Behold the architectural splendor of the Houston Public Library building that opened in 1976:

Contrast with the Houston Public Library building that opened in 1926:

Maybe this isn’t a fair comparison. There are slightly more interesting views of the new library. However, both photos represent what comes to mind when I think of each building.

Houston Public Library, 1926

Posted on 16 December 2011 by John

In 1926, Houston completed construction of a new public library. This building has been restored and reopened to the public this month. My wife and I visited the library yesterday and I took a few photos.

When you visit the library, now known as the Julia Ideson building, the staff recommend you begin your tour on the third floor to see the ceiling.

Then on the second floor you’ll see something like this.

The reading room opens next week and so I could only photograph it from outside.

The children’s library also opens next week and so I could only photograph it through the door.

Finally, here is a meeting room.

My photos of the building’s murals and tapestries turned out poorly and so I’ll spare you from seeing those. (I’ve hardly ever used a camera. Someday I’d like to learn how to take decent photos.) You can find more photos of the library, current and historical, on the website for The Julia Ideson Library Preservation Partners.

In 1976 a new library opened next to the 1926 building. The contrast between the buildings is stark. No historical society will ever lobby to preserve or restore the new Houston library building. It’s just a typical, bland, modern box. The old library feels like a library. The new library feels like an office building. The old library makes you want to stay and lose yourself in a good book. The new library makes you complete your transaction and leave.

How to design a quiet room

Posted on 11 July 2011 by John

How would you design a quiet study room? If you know a little about acoustics you might think to avoid hard floors, hard surfaces, parallel walls, and large open spaces. The reading room of the Life Science Library at the University of Texas does the opposite. And yet it is wonderfully quiet.

The room is basically a big box, maybe 100 ft long. The slightest noise reverberates throughout the room. But because the room is so live, the people inside are very quiet.

Houston Deco

Posted on 13 April 2008 by John

This weekend I stumbled across the book Houston Deco at the library. The book is filled with photos of Art Deco and Art Moderne architecture in Houston and the surrounding area. I had no idea how much Art Deco architecture there was in Houston until I read the book. Some of the photos were of buildings I’ve seen or even been inside without paying much attention to the architecture. More photos are available at the Houston Deco website.

Architecture