a tour of mathematics

The first settlements in Petra were simple structures of rough stones and clay, which may have been built so travellers could store items until they returned to the city Even after settlement began, “their domestic architecture remained simple, and stone built single story houses covered the undulating slopes of Petra”.

To access the city one must travel through a rather narrow entrance walkway known as the siq with steep mountain walls that soar 100 metres high. Inscriptions and carvings line the walls as well as rock-cut chambers and a water channel that threads its way along the winding siq for nearly one mile.

The columns and walls of this temple were plastered and painted in various reds, yellows, and white, similar to the temples of ancient Greece. On each side of the Lower Temenos visitors would pass a large staircase and exedra, each with two entrance columns on their way up towards the main temple. The Great Temple measures 35.5 meters by 42.5 meters, making it square meters, the largest freestanding building yet excavated in Petra.

The actual temple was a minimum of 19 to 20 meters in height, its porch is tetra style in antis with widely spaced central columns and a pair of interior columns 5 meters beyond those of the porch. An engaged column supports each corner of the cella and four smaller columns span the rear while eight columns flank the cella walls. More about interior

To the east of the Great Temple was a lower terrace long thought to be Petra’s Agora but recent excavations have revealed that it was a large pool and garden complex. To create this enormous garden complex a “large shelf (65 x 32m) was carved into the rocky slope east of the Great Temple, leaving vertical escarpments 16m high on the south and east, requiring the removal of up to 33,280 cubic meters of stone”.

Excavating the residential sites means gaining information about the Nabataeans themselves. Among the artefacts discovered are a relief carving of a standing eagle, an elaborately carved marble Roman vase with handles in the shape of panthers, a selection of gold and silver jewellery, decorative friezes and stuccowork from temples and private homes, and an extensive collection of finely painted ceramic ware.

That story begins with water, one of the desert's most precious commodities. In an area that averages six inches of rainfall per year the Nabataeans were able to harness the rainfall and the desert springs to the extent that Petra had a daily supply of fresh water for 100,000 people. Archaeologists estimate that the system carried about 12 million gallons of fresh spring water a day! Among the items on display as part of Petra: Lost City of Stone are two watertight ceramics pipes that were part of the system. Each 16-inch segment measures seven inches in diameter and the pipes were all connected via a watertight system of bell and spigot joints, a technique that still exists today. WATER'S VITAL ROLE

Over the last kilometer the road has dropped dramatically, but the clever Nabataeans kept the water pipes dropping slowly so as to provide water pressure within the city center. Throughout the city of Petra are hundreds of underground water cisterns. Every possible drop of rainwater, as well as the water piped into the city was stored and used later.

For an upper estimate of the volumetric flow rate that the Jebel el Khubtha pipeline system could sustain, it is the angle of about shown by the elevated channel supporting the pipeline corresponds to the critical flow angle. The maximum flow height within the piping is at critical depth equal to perhaps 50 per cent or more of the pipe diameter. This condition means that water flows in open channel mode through the piping, with an airspace above the water surface, and that the flow rate is maximum for given diameter and slope. This type of hydrostatically unpressurized flow reduces leakage between socketed pipeline.

There are approximately 800 structures in Petra. The most famous is Pharoah's Treasure, a mausoleum. The city’s red sandstone cliffs can provide more scholarly research than just the architectural structure itself. Only 15% of Petra has been explored by archeologists. The rest remains to be discovered.

1 Vivek kr. Mishra Manan thareja Harshika choudhary Devyani EFFORTS BY TTHANK YOU