ARCHITECTURE EHLINGER & ASSOCIATES SECOND QUARTER 2014 Structures, First Into the Crowns of the Palm Trees on of Cast and Display

ARCHITECTURE EHLINGER & ASSOCIATES SECOND QUARTER 2014 structures, first into the crowns of the palm trees on of cast and display. The arches were held together at wrought iron, their base and at right angles by cables then of steel as within tubes to tension the building the technology together, and support the glass panes that advanced were originally hand blown and tinted green learning how to with copper oxide to reduce the solar heat make the iron gain. less brittle and - Kew Gardens originated in the exotic more ductile, garden at Kew Park formed by Lord Capel eventually John of Tewkesbury. It was enlarged and leading to the extended by Augusta, Dowager Princess development of of Wales, the widow of Frederick, Prince steel (iron with of Wales, for whom Sir William Chambers carbon and built several garden structures. One of other metals in---these, the lofty Chinese pagoda built in alloy). This age 1761 still remains. George III enriched the also developed gardens, aided by William Aiton and Sir PALM HOUSE, Kew Botanical Gardens, London the mathematics Joseph Banks. and knowledge The Crystal Palace designed by The Palm House in Kew Botanical of the engineering mechanics of what Joseph Paxton was built in 1850-51 for the Gardens, London, is this edition’s limited made buildings stand up (and fall down): for the Great Exhibition (World’s Fair) of edition print of a sketch by Ladd P. Ehlinger. forces, stresses, strains, how to calculate 1851 in Hyde Park, London. It was This building is an archetype of the them, and the engineering properties of subsequently disassembled and re- skeleton frame of metal (cast and wrought materials that enabled rational erected after being revised, in Sydenham, iron) with glass infill that was beginning to manipulation of this environment. London. It was destroyed by fire in 1936. be experimented with at the dawn of the Consequently, there was a paring The Crystal Palace was much larger Industrial Revolution. Palm House was built down of superfluous elements in buildings than the Palm House, had the “ridge & in 1844-48, and was a collaboration between that had little, if anything to do with the furrow” method of glazing developed by Decimus Burton, Architect and Richard work of enveloping the space, and a more Paxton at Chatsworth, and garnered a great Turner, an iron founder and Engineer. It is spare use of ornament, which now was deal more publicity because of the based upon the glass house design begun to be thought of as a means to importance of the Great Exhibition of 1851, principles developed contemporaneously express these aspects of how the building though the Palm House is probably the by John Claudius Loudon and Joseph stood up. better of the three seminal buildings Paxton, and as such is a seminal work of Palm House is a space frame barrel architecturally. Architecture. This was the first large scale vault of structure to use wrought iron. It is wrought considered the world’s most important iron surviving Victorian age glass and iron arches, structure. two story The only predecessor to Palm House tall in the was the Conservatory at Chatsworth (1836- central 40) which was done by Joseph Paxton. Its nave 19 M appearance was of a “ridge & furrow” on high, with the skin, a sort of “Vee” shaped surface, a viewing whereas the Palm House has a remarkably gallery at smooth contiguous surface finish. The the “ridge & furrow” system in essence is a second series of valley gutters formed by the glass level 9 M running in the direction of the roof slope - high, so very prone to severe leakage. viewers This was the age of experimental metal could see

2200 Houma Blvd., Metairie, LA 70001-1399 (504) 455-8911 . 3109 Ivy Ave. SW, Huntsville, AL 35805-4698 (256) 534-1900 © 2014 Ehlinger & Associates, P.C. Architects, A Professional Corporation Gr The Plastic Number who called it the Radiant Number. Cordonnier spent a great deal of the rest of by R. Perrin Ehlinger his life writing a book about it, which he never finished. If he had, he might be bet- E&A has occasionally written about ter known as the discoverer of the Plastic the Golden Ratio, Phi. While I was re- Number, and we might call it the Radiant searching another article to discuss Phi, I Number. stumbled across something interesting to Instead, Cordonnier corresponded share, but it requires a quick re-introduc- with a Dutch Benedictine monk and archi- tion to Phi to explain: tect named dom Hans van der Laan. Even outside of the fields of architec- Cordonnier introducing Hans van der Laan ture, arts, and mathematics, many people to the Plastic Number, hoping to inspire him are familiar with the constant Phi, also to use the number as a proportion architec- known as the Golden Ratio. Phi is an irra- turally, since it was so closely related to tional number, which is derived from solv- the Golden Number, mathematically. Be- ing the equation: x²=x+1. This equation is Hans Van der Laan, Abbey in Vaals cause the Plastic Number is the solution of photo by Frans de la Cuisine. derived from the well known Fibonacci Se- a cubic formula, they supposed that the quence: Van der Laan foundation Plastic Number is thus intended for pro- http://www.vanderlaanstichting.nl/en/ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ,55, etc.. portioning three-dimensional grouping of Which is created by each number be- elements. tions, though clearly consistent, seem... not ing the sum of the previous two numbers, necessarily forced, but perhaps unfamiliar. Hans van der Laan took the idea and starting with 0 and 1. When you take the Good or not, I do not necessarily be- limit of the ratio of the Fibonacci Sequence, ran with it, developing a system of pro- lieve that just because the Plastic Number you get the irrational number 1.618..., which portions and sizes for architecture and is derived from a cubic formula that this is the solution of x²=x+1. It's also the solu- design based on the Plastic Number, and means the number is intrinsically related to tion of x1=x-1, which is to say, 1/Phi = Phi-1. then published a book about it: Architec- three dimensions, or endowed with any par- 1/1.618... = 0.618... = 1-1.618... tonic Space. ticular special purpose. Supposedly both The Golden Ratio is well known to ap- van der Laan and Cordonnier found ex- pear frequently in nature, because Phi is amples of this ratio in nature, but in my also the most efficient ratio in which to pack research, the only relations (outside of growth of subsequent elements. Example: Cordonnier and van der Laan’s claims) that the seeds on a sunflower. So the Golden I could find regarding the Plastic Number Ratio has been studied and used intention- to anything else is that it's the smallest Pisot ally in the arts and architecture as a method number (a very esoteric mathematical sub- of bringing natural harmony into man made set of numbers), and that it's integral to the works, for a long, long time. It is a useful radii formula of a Snub Icosi- tool for rationally proportioning elements dodecadodecahe-dron. Not exactly a wide- that people will find pleasing, because it Hans van der Laan's System of scaling. spread, intrensic connection to natural conforms to the proportions we are used (Richard Padovan, "Dom Hans Van Der forms. to seeing in nature. Laan and the Plastic Number") Still, it is a very interesting way to de- For a comprehensive, if perhaps fanati- rive a consistent set of proportions for de- cal, examination of phi, visit: As the innovative implementer of the sign, and in design, consistency is a criti- www.goldennumber.net Plastic Number into the creative design cal element. It’s also a method that has What most people don't know is that world, Hans van der Laan is often mistak- gained its own subset of followers among Phi has a brother number. This companion enly credited with the discovery of the Plas- European designers. wasn't discovered until 1924, and it wasn't tic Number, but really it's just the name that until 2002 that it was proven that Phi only bears his mark. Hans van der Laan termed had one brother, and no more. What am I it "Plastic" because of its applicability and talking about? Well, mathematically, there versatility to be used in three dimensional is only one other real number that solves a ratios (using his system, of course). Per- similar set of equations simultaneously, as sonally, I prefer Cordonnier's term Radiant, Phi does. If we look for any numbers that but it seems Plastic has taken root (bad math solve both xn = x+1 that simultaneously pun intended). solves x-m = x-1, we find that only one other Does the Plastic Number make for bet- number will, and it solves x3 = x+1, and x-4 = ter, more natural or perfect art and architec- x-1. This number, 1.3247..., is called the Plas- ture? I don't know - some find his few works tic Number. a little eerie and rarefied, but they do have It was discovered and studied by a simple, formulaic beauty that can easily French mathematician, Gerard Cordonnier, be appreciated and enjoyed. The propor- Snub Icosidodecadodecahedron R. Per- © 2014 Ehlinger & Associates, P.C. Architects, A Professional Corporation rin