Walking in Hyde Park recently, I spied what appeared to be a huge red pyramid in the middle of the Serpentine. On closer approach, and with a changing angle of view, it became clear that it was prismatic in shape, composed of numerous barrels in red, blue and purple.
Changing perspective on approach to the Mastaba
An isoceles trapezoidal prism
A prism is a polyhedron with a polygonal base. It has an axis, with all cross-sections perpendicular to this axis being identical. The structure on the lake has a horizontal axis, with trapezoidal cross-section and rectangular sides. More specifically, the cross-section is an isosceles trapezoid having angles equal in pairs: since it was constructed from cylindrical barrels of equal size, the ends have a honeycomb pattern and the sides slope upwards at an angle of 60 degrees to the horizontal.
The Mastaba [image from De Zeen].
What I saw on the lake was The Mastaba, a temporary floating installation, unveiled in June 2018 and due to be deconstructed next week. It is made using 7,506 plastic barrels, and is in the form of a mastaba, an ancient Egyptian tomb with a flat roof and inward sloping sides. It sits on a floating platform anchored to the lake-bed, is 20 metres high and weighs 600 tonnes. The trapezoidal vertical ends are coloured in a mosaic of red, blue and mauve, whilst the sloping rectangular sides are red with bands of white. It is on free view to all, consistent with the artist’s dream to make art free to everyone.
The Mastaba [image from De Zeen].
The volume of the structure is easily estimated: if the widths of the end faces at top and bottom are a and b and the height is h then the area of the ends are A = h ( a + b ) / 2. Then if the length of the sides is L, the volume is V = L A. Knowing how many barrels are along the top and bottom edges of the ends, and the diameter of a barrel, one could easily estimate a and b. Likewise, from the barrel length, the overall length follows. I leave it to you to have fun with these calculations.
Christo
Christo Vladimirov Javacheff was born in Gabrovo, Bulgaria in 1935, and his wife Jeanne-Claude in Casablanca, Morocco in the same year (indeed, on the same day). Jeanne-Claude died in 2009. Christo and Jeanne-Claude have created many “environmental” works of art, including wrapping the Reichstag in Berlin using fireproof polypropylene fabric covered by a layer of aluminum.
If you miss the installation on the Serpentine (deconstruction starts on 23 September), there is still some hope: Christo and his wife had plans to build a much larger installation, The Mastaba at Al Gharbia, 100 miles from Abu Dhabi. It is unclear whether this will ever be realised but, if it is, it will also be a trapezoidal prism, much larger that that on the Serpentine, made of about 410,000 oil barrels, and it will be the only permanent large-scale Christo/Jeanne-Claude artwork.
Sources
ThatsMaths 