Tag: Spherical Trigonometry

Grid Corrections

[Image: From “Grid Corrections” by Gerco de Ruijter, courtesy of the Ulrich Museum of Art].

In case this is of interest, I’ve got a new article up over at Travel + Leisure about photographer Gerco de Ruijter. De Ruijter recently undertook an exploration of sites in the North American landscape where the Jeffersonian road grid is forced to go askew in order to account for the curvature of the Earth.

[Image: From “Grid Corrections” by Gerco de Ruijter, courtesy of the Ulrich Museum of Art].

De Ruijter is already widely known for his work documenting grids and other signs of human-induced geometry in the landscape, from Dutch tree farms to pivot irrigation systems, which gives this new focus an interestingly ironic air.

[Image: From “Grid Corrections” by Gerco de Ruijter, courtesy of the Ulrich Museum of Art].

In other words, these are places where a vision of geometric perfection—a seemingly infinite grid, dividing equal plots of land for everyone, extending sea to shining sea—collides with the reality of a spherical planet and must undergo internal deviations.

Those are the “grid corrections” of de Ruijter’s title, and they take the form of otherwise inexplicable T-intersections and zigzag turns in the middle of nowhere.

[Image: From “Grid Corrections” by Gerco de Ruijter, courtesy of the Ulrich Museum of Art].

The project includes a series of spherical panoramas de Ruijter made using kite photography at specific corrective intersections outside Wichita, in effect distorting the distortions, a kind of topographical reverb.

[Images: From “Grid Corrections” by Gerco de Ruijter, courtesy of the Ulrich Museum of Art].

And there is also a further sub-series of satellite images—all taken from Google Earth—stitched together to show intersections where grid corrections occur.

[Image: “Canada/USA 2015 Grid Correction Leota Minnesota,” from “Grid Corrections” by Gerco de Ruijter, courtesy of the Ulrich Museum of Art].

The actual article explains in more detail what these grid corrections are, why they exist in the first place, and how often they appear, including references to James Corner’s Taking Measures Across the American Landscape and to a 2007 post on Alexander Trevi’s blog, Pruned.

[Image: From “Grid Corrections” by Gerco de Ruijter, courtesy of the Ulrich Museum of Art].

For more, then, not only check out the Travel + Leisure piece, but click around on de Ruijter’s own website—and, if you’re in The Netherlands, stop by the Van Kranendonk Gallery in The Hague tomorrow, Saturday, December 12th, to see a few examples from “Grid Corrections” on display.

The light/surface fold: advertisements, Steven Holl, et cetera

I noticed several years ago that the pine forests outside Chapel Hill, NC, fill with a strange white light in winter, and not for the obvious reasons that, yes, it’s winter, so the leaves are all gone: ergo more light.
Nope: it’s because the angle that the earth takes in relation to the sun has changed, as it does every winter, and so the forests have literally begun to glow: the sun has begun hitting them at a different angle.
Winter, in this regard, is really a question of spherical geometry, angles, and trigonometric effects at long distances: sun–>earth/angle of incidence (or whatever). One of winter’s more interesting side effects, then, is the way that it transforms shadows – making them longer and thinner – while simultaneously illuminating objects from the side. This brings out details that go unremarked – and unlit – in other seasons.
All of these written reflections having been inspired by this photograph:


What’s interesting here is how the billboard enlists sun/earth trigonometry in the selling of suntan lotion. Who’da guessed?
But so I got to thinking about what would happen if you did more of that with architecture, if you learned a spatio-architectural lesson from however brief a glance at that billboard.
The deliberate shadow-machining effects of different times of day, say, in the vein of Steven Holl: entire hallways and galleries and courtyards and milled surface details could become visible only at specific hours, perhaps in pre-patterned ways.
Like an inhabitable sundial, you would always know it was 3 o’clock in the afternoon because the little grilled incisions in the plaster of the upstairs walls just appeared. They were invisible before that, and will be invisible again: but now is their moment in the light…
Or you know it’s noon because there are suddenly no shadows of any kind in your courtyard: you’ve angled everything perfectly for that moment. The space folds in on itself, reboots back to undisturbed white, and at 12:01pm the shadows reappear.
I just mean to point out the connection, here, between architecture and astronomy – via spherical, planetary trigonometrics – not because I’m the first to do so or even because it’s ultimately all that interesting, but because every little mundane trace – mere shadows – can be seen as an indication of literally superior, astro-stellar relationships.
Every shadow, if you do the math right, if you know the angles and the trig and the spherical velocity of objects in space, is actually an indication of the time of day – in a calendar that precedes Swatch and Swiss Army and electricity and even biological organisms as such.
And every kid with a flashlight – every person with a match or candle – every architect, even – can participate. Everything you build can be – and is automatically – an astronomical event.