Pyramids have often been attributed with mystical properties, from resurrecting pharaohs to re-sharpening blunt razor blades, but last week those clever architects Herzog and de Meuron unveiled a new piece of pyramid-powered prestidigitation with their new Triangle project in Paris: the building will cast no shadows.  It all sounds a bit David Copperfield, but it's not done with mirrors. Instead, the Tate Modern designers have crafted an ingenious computer-aided skinny pyramid design for the 50-storey building – more like a shark's fin - which, thanks to its shape and orientation, will not block out sunlight from its neighbours, they say. The shape will also allow for "optimum solar and wind power generation", apparently.  The context for this architectural conjuring feat is that the Triangle is the first building in Paris to break through the city's long-standing height limit of 37 metres, which was recently scrapped for certain locations by outgoing socialist mayor Bertrand Delanoë. The Triangle, situated close to Porte de Versaille in the south-west of the city, is one of six new skyscrapers proposed for the city, and is due to open in 2012. There are still a great many Parisians, however, who would prefer to keep their beloved city low-rise, all the better to set off the Eiffel Tower. So playing up its magical shadowlessness is probably a smarter move than labelling it, say, the fin of a gigantic shark circling the city centre.  Like many new skyscrapers in crowded old cities, the Triangle has conquered the height barrier only to be confronted with the light barrier. Paris, London and other cities have learned to love, or at least tolerate, tall buildings within their historic fabric, which has only exacerbated issues of overshadowing or blocking out neighbours' sunlight. In fact, "right to light" regulations are some of the oldest (and most confusing) planning regulations in the book. In Britain, the rather romantically named "Ancient Lights" ruling – from 1832 - stipulates that a window that has had access to sunlight for 20 years is entitled to go on receiving it – or at least some of it. At one stage, signs reading "Ancient Lights" were fixed below windows in vulnerable areas of London, such as back alleys of Chinatown or Clerkenwell, to deter potentially light-blocking developments close by (is that what they mean by daylight robbery?). Some of the signs are still there. The history goes back even further, to 6th-century Rome, where the Justinian code established that every individual had "sun rights".  On a domestic scale these disputes come up a great deal – with the neighbour's new shed/extension/Leylandii, but they apply equally to large public and private projects. Hence the current demand for "shadow studies", in which new designs are computer tested in a virtual landscape to see where shadows will fall at different times of the day and year. Such studies are useful to architects and campaigners alike, especially in countries like the US where there are no "right to light" laws.  In a recent case, architects Kohn Pedersen Fox had to use a shadow study to prove that their odd design for an office block near the World Trade Centre site in New York wouldn't block out any more sunlight than a conventional shape. The 42-storey building is a regular, rectangular office block, except for seven storeys halfway up that jut out, potentially overshadowing the church and park below – hence its nickname, the "tower of darkness".  New York, of course, found the solution to building high without casting the streets into darkness nearly a century ago. Unlike Paris, the local authorities chose not to limit the height of new buildings; instead they regulated their shape. As early as 1916, the city passed laws that allowed buildings to reach a certain height, after which they had to be stepped back to ensure light and air reached the street. It seems to have worked. In fact, counter to instinct, a tall, skinny building can create fewer overshadowing problems than a low, wide building. A tall building's shadow will move like a sundial across the ground, travelling relatively rapidly as the sun rises and sets, so that no area is in its shadow for very long. With a low, squat building, though, its shadow can simply creep out, growing longer and longer as the day progresses.  Which suggests that New York has been doing it right, and Paris has been doing it wrong all these years. Will Herzog and de Meuron usher in a new era of sensitive high-rises for the French capital, or is it all a clever feat of misdirection? It's all very well conquering the shadow problem, but their Triangle building will still have an almighty silhouette on the skyline – unless they've found a way around that too. The world's first invisible building, anyone?
Many Parisians would like to see the city's skyscraper ban reinstated, but can Herzog and de Meuron's shade-less ziggurat appease the naysayers, asks Steve Rose