Pi to thirty-nine decimal places can be used to calculate the volume of our observable universe, accurate to the size of one hydrogen atom.

π = 3.14159265358979323846264338327950288420

Ludolph van Ceulen spent the major part of his life in 16th century Leiden calculating the numerical value of the mathematical constant π to 32 decimal places, using a similar method as employed by Archimedes in Ancient Greece some seventeen hundred years earlier. By the 18th century, Abraham Sharp in Bradford, England, had calculated π correctly to 71 decimal places. π kept on growing through the centuries – being confirmed as both transcendental and irrational – when in 1949 DF Ferguson and John Wrench, using a desk calculator, reached 1,120 decimal places. From here on computers took over, with ENIAC the first electronic general-purpose computer, taking less than three days to produce 2,037 decimal places.

In the 208 days leading up to October 2014, a home computer in Japan, constructed of commercially available parts, calculated π to the largest ever expression at 13.3 trillion decimal places, filling 68.9 terabytes of digital space, which is about three times the space needed for an audio recording of all of the 97 million songs ever written. This vast number of digits fulfils a human desire to break records, and has the practical benefits of testing supercomputers, though testing numerical analysis algorithms including high-precision multiplication algorithms, and pure mathematics itself by providing data for evaluating randomness.

For most numerical calculations involving π, mainly in design and construction, a few decimal places provide sufficient precision. According to Jörg Arndt and Christoph Haenel, thirty-nine decimal places are sufficient to perform most cosmological calculations, because that is the accuracy necessary to calculate the volume of the known universe with the precision of one atom. An atom is the smallest unit of ordinary matter with the properties of a chemical element. Atoms are very small; typical sizes are around 100 picometres or a ten-billionth of a metre. However, atoms do not have well-defined boundaries, and there are different ways to define their size, which give different but close values.

The universal emergence of atomic hydrogen first occurred during the recombination epoch, when the universe was roughly 378,000 years old. Hydrogen, a colourless, odourless, tasteless, non-toxic, nonmetallic and highly combustible diatomic gas, was not discovered until centuries after π, in 1766. It is the smallest and lightest atom, and is the most abundant chemical substance in the universe, constituting roughly 75% of all baryonic mass. A hydrogen atom has a diameter of 50 picometres, or 0.000000000005 metres.

The best estimate of the age of the universe is 13.798 ± 0.037 billion years based on its observable expansion. It is estimated that the diameter of the observable universe is about 93 billion light-years, or 8.8 × 1026 metres, so its edge is about 46–47 billion light-years away, enough time for 2.8 billion human generations (at most there have been ten thousand so far). The volume of the observable universe is 4 x 1032 cubic light-years or 4 x 10116 cubic picometres.

If the universe’s volume consisted entirely of the most densely packed hydrogen atoms, using lattices of either face-centred cubic or hexagonal close-packed atoms, the number of atoms that would fit would be the number 6 followed by 116 other digits. This order of magnitude does not have a specific name, but it is greater than a septentrigintillion and less than a octotrigintillion. In this example, the empty gaps left between all the hydrogen atoms would account for a quarter of the total volume.

Thomas Harriot first studied the problem of the close packing of spheres around 1587, after a question regarding the most efficient method of piling and counting cannonballs aboard ships was posed to him by Walter Raleigh on their expedition to Roanoke Island, America. Cannonballs were usually piled in a rectangular or triangular wooden frame, forming a three-sided or four-sided pyramid. Both arrangements produce a face-centred cubic lattice but with different orientations to the ground. Carl Friedrich Gauss proved in 1831, with the help of π, the highest average density that can be achieved by a lattice packing.

The first camera in space was an American Ansco branded Minolta. Ansco was the corporate successor to the E&HT Anthony & Company, which provided photographic equipment to Mathew Brady, the American Civil War documenter and father of photojournalism, who was compelled to give Anthony & Company his life’s work of over 7000 glass negative plates in default of payment for large arrears. Brady was also the first person to use a corporate credit line, every image produced by his large studio was labelled “photo by Brady”. His efforts represent the first instance of the comprehensive photo-documentation of a war. Largely unappreciated in his lifetime, a full set of his war prints was purchased by the US Congress shortly before his death for a quarter of its production cost. The nature of photography at the time, requiring cumbersome equipment with long static exposures, limited his subjects to the objects and logistics required for war, the rests between battles and the aftermath of battles as animal and human corpses littered the fields. His photographs from the Civil War onwards were albumen prints made using unstable collodion-coated glass negatives. The prints were toned with selenium, a dark grey chemical element. Selenium is named after Selene, the Greek goddess of the moon, by Jöns Jacob Berzelius in 1817. Selenium was used in photographic prints to neutralise the colours against the paper and to stabilise the chemical in the prints. It is still used today for archival prints, and it is thanks to selenium that Brady’s work survives today.

Like her brother Helios, the Sun god, who drives his chariot across the sky each day, Selene is also said, according to the Homeric Hymn, to drive upon long-maned horses across the heavens in a great orbit. The earliest known depiction of Selene driving a chariot, comes from Ancient Greece not long before Archimedes, and is inside an early 5th century BCE red-figure cup attributed to the Brygos Painter, showing within a perfect circle, Selene plunging her chariot, drawn by two winged horses, into the sea.

Martin John Callanan

This text was printed and published September 2015