Gresham GI Special Edition Stainless Steel Tonnaeu Case White and Blue Colourway Watch G1-0001-WHT

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There were two key questions people always had about curves, known as “quadrature” and “rectification”. Quadrature is finding the area under a curve. Galileo approximated the quadrature by making a cycloid out of metal and weighing it, but he didn’t know the exact formula. We don’t know for sure when he did this, but he wrote in 1640 that he’d been studying cycloids for 50 years. At any rate, it took until the 1630s for the correct solution to be found (probably first by Gilles de Roberval): if the rolling circle has area π r 2 , then the area under each cycloid arch is 3π r 2 . Very nice. But the cycloid had still not been “rectified”: this means finding its length. The first person to do this, of all the illustrious mathematicians who had studied it, was Christopher Wren. He showed that the length is another beautifully simple formula. If the rolling circle has diameter d , its circumference is πd , and each cycloid arch has length precisely 4d . (Actually, Roberval claimed to have done this first too, but he did that a lot. He only started making this claim after Wren told Pascal the result, and Wren’s proof was the first to be published, as far as I know. The general consensus at the time and since seems to be that Wren was indeed the first to rectify the cycloid.)

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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. All logarithmic spirals are self-similar, in that they retain precisely the same shape as they grow. In nature, if we think of how plants and animals grow, if they are growing out from a central point at a fixed rate, as happens with something like a Nautilus shell, then the outer parts continue to grow while they expand out from the centre. Logarithmic spirals allow for this to happen while keeping the same shape. The spiraling makes room for new growth. The three-dimensional version of a logarithmic spiral that Wren studied is just the right solution for shells, and is achieved in nature by one side of the structure growing at a faster rate than another. By varying the parameters in the general equation for a solid logarithmic spiral, many different shell-like shapes can be created. Wren’s ideas continue to inspire. In 2021, a team at Monash University came up with a “power cone” construction generalizing the cone-to-spiral idea (and Wren is referenced extensively in their article) that gives a mathematical basis for the formation of animal teeth, horns, claws, beaks and other sharp structures. The story of the y = x 3approximation to the perfect masonry dome, and a derivation of the correct equation, is given in Hooke's Cubico-Parabolical Conoid, by Jacques Heyman, in Notes and Records of the Royal Society of London, Vol. 52, No. 1 (Jan., 1998), pp. 39-50 https://www.jstor.org/stable/532075.

This lecture is part of the seriesThe Victorians: Culture and Experience in Britain, Europe and the World 1815-1914 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.

Allan H Brooks/ New Control Tower Newcastle Airport/Image use permitted under CC BY-SA 2.0 https://commons.wikimedia.org/wiki/File:Newcastle_International_Airport_Control_Tower.jpg 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 Within major cities, tram systems, and suburban and underground railways began to speed up traffic, just as the main roads were becoming clogged with horse-drawn cabs and carriages, automobiles and omnibuses. In 1863 the world's first underground railway, the Metropolitan, opened in London, and was soon extended, but steam locomotives posed many problems, and the cut-and-cover method of construction soon ran out of roads that could be dug up, and London turned to boring deeper lines for 'tube' trains powered by electricity, the first of which was opened in 1890. Above ground, the electric tramway system devised by Werner von Siemens began running in Berlin in 1879, and soon spread to many other countries. The following paper is a helpful summary of Wren’s mathematical work which gives detail of the original sources, for example the places in Wallis’s Tractatus de Cycloide where he explain’s Wren’s rectification of the cycloid and solution to Kepler’s problem. Wren the Mathematician, D.T. Whiteside, Notes & Records of the Royal Society, 15, pp107-111 (1960). 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.

John Wallis had shown in the 1650s how to “rectify” a logarithmic spiral, in other words how to find its length (or more properly the length of any part of it), by transforming, or “convoluting”, it into a straight line without changing the length. Wren managed to show that a version of this idea could work a dimension higher, and could be used in reverse to convolute or twist a cone into a kind of three-dimensional or solid logarithmic spiral. He suggested these spirals could be behind the growth of snail shells and seashells. And it’s since been found that this is absolutely right. How a watch keeps time is vital to how accurate its timekeeping is. Quartz movement watches are often prized for their accuracy, while a well-crafted automatic watch is a true investment piece. Prefer something vintage? Browse our collection of stunning manual watches. Ramsdens Watch Services Loft of Casa Batlló, designed by Antoni Gaudí, image by Francois Lagunas, CC BY-SA 3.0, via Wikimedia Commons https://en.wikipedia.org/wiki/Casa_Batll%C3%B3The 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.