"Vaults” is a beautiful photo series of the intricate geometric patterns found on the ceilings of European cathedrals. The series, and companion book Heavenly Vaults, are by photographer David Stephenson.
via laughingsquid.com
Eclectic Perambulations in the Noosphere
Aerial view of suburban neighborhood urban sprawl in Las Vegas, Nevada
"Is living in the suburbs in one’s own home a dream come true or a living hell? Does homeownership, space and a certain amount of freedom within one’s own four walls outweigh the financial burden, traffic snarls and uniformity that suburban life represents? We’ve taken to the skies to take an aerial view of residential communities around the world and found 15 amazing examples of suburban beauty – a result of the patterns formed by buildings that from ground level would appear somewhat less enthralling."
"David Brewster, a nineteenth-century scientist… observed a related form of stereo illusion. Gazing at wallpaper with small repetitive motifs, he observed that sometimes, with the proper convergence or divergence of gaze, the patterns might quiver or shift and then jump into startling stereoscopic relief, seeming to float in front of or behind the wallpaper.
…it seems likely that such “autostereograms” have been experienced for millennia, with the repetitive patterns of Islamic art, Celtic art, and the art of many other cultures. Medieval manuscripts such as the Book of Kells or the Lindisfarne Gospels, for example, contain exquisitely intricate designs done so exactly that whole pages can be seen, with the unaided eye, in stereoscopic relief. (John Cisne, a paleobiologist at Cornell, has suggested that such stereograms may have been “something of a trade secret among the educated elite of the seventh- and eighth-century British Isles.”)
In the past decade or two, elaborate autostereograms have been widely popularized in Magic Eye books." - Oliver Sacks, The Mind’s Eye
Those unfamiliar with "Magic Eye" books can read about them at Wikipedia. The embedded image is "Geometric arabesque tiling on the underside of the dome of the Tomb of Hafez in Shiraz." For extensive research on Islamic design, visit the Catnaps.org website..
by Nick Sayers
"We looked at playing card constructions before in this column, but this one by Nick Sayers is impressively intricate. The 270 playing cards each have four slits, and lock together like the classic IQ Lamp. Each card is forced into a curved form because it locks with a neighboring card at two points which are closer together than a card’s width. Light from an internal lamp escapes dramatically from under these curves."
"Color remains a mystery to me. I can’t say that any specific color triggers any specific emotions. My interest in colors is based more in color interaction than specific colors. Yellow and black are especially important though.
Music is at the center of my artistic life. As a musician I have always been fascinated by the harmony and the physics of sound; in a sense defining music as waveforms, waveforms whose properties and proportions define our scales, from which we write our melodies, in which we weave our emotions and memories into songs.
I would have to say that the relationship between Science and Nature in my work is based in observation of both internal and external worlds. The process in which I work is based in observation, measurement and experimentation. In a sense it is very similar to the Scientific Method."
Credit & Copyright: Robert Arn (Colorado St. U.)
"If you travel several kilometers off a main highway through Wyoming, you may see an unusual sight. In particular, near Buford, Wyoming, USA, you could run across the geometric Ames Monument, visible on the right, built to commemorate the financiers of a historic transcontinental railroad across North America. The above spectacular wide field mosaic, however, has also captured other geometric designs, many of them far in the distance. On the far left, for example, is a lunar halo surrounding by a lunar corona surrounding the setting Moon. On the right, however, is the arch of the central band of our Milky Way Galaxy surrounding the pyramidal structure. Illuminating the horizon to the right of the monument are the city lights of Cheyenne. The menagerie of images used to create this 360-degree composite were all taken during a single night last month. Still, the digital stitching of images taken over such a long period of time has led to a few unnatural land and sky justapositions. Can you identify any?"
To cut an equilateral triangle into four pieces that can be rearranged to make a square. The Haberdasher's Puzzle, the greatest mathematical discovery of Henry Dudeney, was first published by him in the Weekly Dispatch in 1902 and then as problem no. 26 in The Canterbury Puzzles (1907).
The accompanying diagram shows the solution, which Dudeney describes as follows:
Bisect AB in D and BC in E; produce the line AE to F making EF equal
to EB; bisect AF in G and describe arc AHF; produce EB to H, and EH
is the length of the side of the required square; from E with distance EH,
describe the arc HJ, and make JK equal to BE; now from the points D and
K drop perpendiculars on EJ at L and M.
For a step by step construction, see Beyond Euclid
A remarkable feature of the solution is that the each of the pieces can be hinged at one vertex, forming a chain that can be folded into the square or the original triangle. Two of the hinges bisect sides of the triangle, while the third hinge and the corner of the large piece on the base cut the base in the approximate ratio 0.982: 2: 1.018. Dudeney showed just such a model of the solution, made of polished mahogany with brass hinges, at a meeting of the Royal Society on May 17, 1905.
