Don’t worry about finding the perfect watch for your budget, because our collection of luxury watches also boasts new and pre-owned watchitems with a price-match promise, meaning if you find it cheaper elsewhere, we could match it (T&Cs apply). Wren’s solution of Kepler’s problem manages to relate the areas into which the semicircle must be divided to lengths of specific circle arcs. These are then equated to carefully positioned “stretched” or “prolate” cycloids – which of course Wren already knew how to find the length of, from his own earlier work. And so he was able to solve Kepler’s problem. His solution was published by John Wallis in a 1659 treatise on the cycloid (which also included Wren’s rectification of the cycloid). If your Latin is tip-top, you can give it a read: John Wallis: Tractatus duo, prior de cycloide et corporibus inde genetis: posterior, epistolaris in qua agitur de cissoide. In a 1668 letter, the English mathematician John Wallis said that although the challenge of Kepler’s problem had been issued to the French mathematicians almost a decade previously, “there is none of them have yet (that I hear of) returned any solution”. Take that, Jean de Montfort! When buying a luxury watch, the brand is a key factor. Whether you're a loyal collector or looking for fashion-forward, we have a wide range of designer watches from leading brands such as Rolex, Tag Heuer, Omega and Breitling. All of our watches are individually assessed and valued by our expert buyers to ensure pristine quality. Shop by Watch Movement

You can play with the effects of different shaped lenses – spherical, parabolic, and hyperbolic – using Lenore Horner’s Geogebra simulation at https://www.geogebra.org/m/Ddbpxd5X We’ve got a huge range of 100% genuine luxury watches from leading brands such as Rolex, Tag Heuer, Omega and Breitling, all individually assessed and valued by our expert buyers. So, Wren and Hooke’s best guess for the ideal shape of a masonry dome is a cubic curve in cross-section. They took the part of the curve y= x 3 for positive x , and rotated it around a vertical axis to create what Hooke called a “cubico-parabolical conoid”. And it’s this shape that Wren used for the middle dome, which supports the hemispherical outer dome and its central lantern. By the way, if you stand inside the cathedral and look up, you think you can see through the dome to the lantern, but in fact what you are seeing is a painting of the lantern on the base of the middle dome! In summary, the dome of St Paul’s is in fact a triple dome: a catenary inside a cubic curve inside a hemisphere. Pretty amazing, and a tour de force of Wren’s mathematical and architectural skill. In February 1658, mathematicians in England received a challenge from France. It read “Jean de Montfort [possibly a pseudonym for Pascal] greatly desires that those distinguished gentlemen, the Professors of Mathematics, and others in England renowned for mathematical skill, may condescend to resolve this problem”. The problem was, given an ellipse of known dimensions, and a chord of the ellipse crossing the major axis at a known point and angle, to find the lengths of the segments of that chord. Wren solved the problem, and then in return challenged the mathematicians of France to solve another problem about ellipses, which I’ll tell you about now.Neither of these demonstrations have been preserved, and it’s not clear if they were mathematical proofs or the outcomes of physical experiments. However, some years later Hooke did write down in anagram form a phrase which indicates that he had determined the solution to the problem (even if he had not necessarily found a mathematical proof): it’s a catenary. A catenary is the curve made by a chain or rope allowed to hang freely between two points. Galileo had talked about this problem; he thought that to a good approximation the solution was a parabola, but it was discovered later to be a subtly different curve. Hooke found that the equations describing the forces acting on a hanging chain are equivalent to those describing the forces acting on an arch (this time not tension and gravity but compression and gravity). That would imply that the most stable, strongest shape for an arch is a catenary, but upside-down. You can make the actual curve of the arch a slightly different shape but the line of thrust is still a catenary curve, so that needs to be part of the structure of the arch. This means the shape that requires the least amount of material, the most efficient shape, is indeed a catenary. So, we now have an outer hemispherical dome with a gigantic lantern, that can’t support itself and needs some kind of internal structure. To hide that internal structure, Wren built an inner dome whose cross section is a catenary, fitting in very nicely with other elements of the internal design. At the beginning of the nineteenth century, communication was slow, even relatively short journeys were uncertain and time-consuming, and people were dependant on the forces of nature for energy; this lecture charts the development of new modes of communication, from the railway to the radio, the telegraph to the telephone, the steamship to the motor-car and examines their efforts on perceptions of time and space. In the course of my exploration I will not simply confine myself to English or even British history, for Britain was connected to Europe and the wider world in multifarious ways during the nineteenth and early twentieth centuries. Anyone seeking an illustration of this could do worse than to cast an eye over the Table of Contents of A. N. Wilson'sThe Victorians, with its chapters on France, Germany and Italy, India, Jamaica and Africa, and its coverage of Wagner, Dostoevsky and Tolstoy. Many of the ideas, beliefs and experiences of the Victorians were shared by people in a variety of different countries, from Russia to America, Spain to Scandinavia, and were reflected in the literature and culture of the nineteenth century, up to the outbreak of the First World War. Beyond this, overseas Empire loomed ever larger in the consciousness of the Victorians, until it came to express itself in an ideology, the ideology of imperialism.

Numerous technical obstacles had to be overcome in creating a universal system of standard time. In 1872, when the first transatlantic cable, the transmission of messages revealed that Paris was half a second further away from London than had previously been thought. Trying to fix a precise difference in longitude between Paris and Berlin, engineers noted that signals were slowed by mechanical and other factors such as the 'non-instantaneity of the transmission of the electric flux'. Despite such technical problems, and overcoming a bitterly fought rearguard action by the French, who eventually abstained on the decisive motions, in 1884, delegates from 25 states met in Washington to agree on the standardization of world time. Sailors had already synchronized time using chronometers set by longitudinal measurements based on the Greenwich Meridian, reflecting British dominance of seaborne mercantile traffic, and this was the standard adopted at the Washington conference, which divided the world into 24 time-zones by longitude, treating the meridian as the zero line, dividing the Eastern from the western hemisphere. Robert Hooke, oil painting on board by Rita Greer, history painter, 2009, who has made the digitized version available under the Free Art Licence http://artlibre.org/licence/lal/en/. It’s available from Wikimedia https://commons.wikimedia.org/wiki/File:17_Robert_Hooke_Engineer.JPG Keen to recapture the initiative from the British, the French government organized an International Conference on Time in 1912, which established a generally accepted system of establishing the time and signaling it round the globe. The Eiffel Tower was already transmitting Paris time by radio signals, receiving calculations of astronomical time from the Paris Observatory. At 10 a.m. on 1 July 1913, it sent the first global time-signal, directed at eight different receiving stations dotted around the world. Thus, as one French commentator boasted, Paris, 'supplanted by Greenwich as the origin of the meridians, was proclaimed the initial time centre, the watch of the universe'. The coming of wireless telegraphy had indeed signaled the death-knell for the remaining local times. So the focus of these lectures will be on identifying and analyzing six key areas of the Victorian experience, looking at them in international and global perspective: time and space, art and culture, life and death, gender and sexuality, religion and science, and empire and race. I'll try to tease out some common factors amongst all the contradictions and paradoxes, and trace their change over time. And in no area was change more startling to contemporaries than in the topic I want to deal with this evening, namely the experience of time and space. As the century progressed, people felt increasingly that they were living, as the English essayist William Rathbone Greg put it in 1875, 'without leisure and without pause - a life ofhaste'. Comparing life in the 1880s with the days of his youth half a century before, the English lawyer and historian Frederic Harrison remembered that while people seldom hurried when he was young, now 'we are whirled about, and hooted around' without cessation. 'The most salient characteristic of life in this latter portion of the 19thcentury', Greg concluded, 'is its SPEED.' Time was becoming ever more pressing.Christopher Wren, who died 300 years ago this year, is famed as the architect of St Paul’s Cathedral. But he was also Gresham Professor of Astronomy, and one of the founders of a society “for the promotion of Physico-Mathematicall Experimental Learning” which became the Royal Society. Markhor Screw-horned Goat, by Rufus46, Boreray Ram, by Gibbja, Giant Eland by Greg Hume, all CC BY-SA 3.0, via Wikimedia Commons The Genesis GI Features a hybrid Steel and Aluminium Exo frame chassis which embodies the exposed skeleton custom automatic movement with self-winding mechanism. The case is seamlessly integrated on a custom designed high density rubber strap. Gresham College, Wellcome Collection, https://www.lookandlearn.com/history-images/YW011977M Attribution (CC BY 4.0) Have a designer watch you want to sell? Or, have your eyes on a particular brand and want to part exchange? Ramsdens is happy to help. Learn More About Watches