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93-638: The characteristic pyramid -shaped peak actually consists of two pinnacles, the Großglockner and the Kleinglockner (3,770 m or 12,370 ft, from German: groß 'big', klein 'small'), separated by the Glocknerscharte col . The name Glocknerer is first documented in a 1561 map designed by the Viennese cartographer Wolfgang Lazius . The denotation Glogger is mentioned in

186-404: A Platonic solid and deltahedra , and it has tetrahedral symmetry . A pyramid with the base as circle is known as cone . Pyramids have the property of self-dual , meaning their duals are the same as vertices corresponding to the edges and vice versa. Their skeleton may be represented as the wheel graph , that is they can be depicted as a polygon in which its vertices connect a vertex in

279-533: A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex . Each base edge and apex form a triangle , called a lateral face. A pyramid is a conic solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon (regular pyramids) or by cutting off the apex (truncated pyramid). It can be generalized into higher dimensions, known as hyperpyramid . All pyramids are self-dual . The word "pyramid" derives from

372-601: A tourist activity. There are different activities associated with the sport. Mountaineering lacks formal rules – though appropriately empowered bodies make many pertaining to specific use of mountains and practices on them. In theory, any person may climb a mountain and call themself a mountaineer. In practice, the sport is defined by the safe and necessary use of technical skills in mountainous terrain: in particular, roped climbing and snow travel abilities. A variety of techniques have been developed to help people climb mountains that are widely applied among practitioners of

465-409: A "base camp," which is an area used for staging attempts at nearby summits. Base camps are positioned to be relatively safe from harsh terrain and weather. Where the summit cannot be reached from base camp in a single day, a mountain will have additional camps above base camp. For popular mountains, base camps may be at a fixed location and become famous. The Everest base camps and Camp Muir are among

558-589: A 1583 description of the Tyrolean Kals legal district, then referring to the whole ridge south of the Alpine main chain. In the 1760s, the Atlas Tyrolensis listed a Glockner Berg , the prefix Gross- ("great") is not mentioned before the first expedition in 1799. According to the scholar Belsazar Hacquet (1735–1815), Glockner is possibly derived from German: Glocke (" bell "), referring to

651-679: A branch-off to the Franz-Josefs-Höhe viewpoint. It was built across the historic Hochtor Pass of the Alpine divide between 1930 and 1935 according to plans designed by engineer Franz Wallack . The pass road, Austria's highest, reaches 2,576 m (8,451 ft), and is one of the most popular tourist attractions in the country (second after Schönbrunn Palace ) with about 270,000 vehicles and 900,000 visitors every year, about 50 million since its opening. Also famous for its historic vehicle hill climb races . Computer-generated virtual panoramas Pyramid (geometry) In geometry ,

744-407: A climber who ascends the rock. The first climber, called the leader , will reach a point on the rock and then build an anchor , which will secure subsequent climbers. Anchors could be created by using slings around a tree or boulder, or by using protection devices like cams and nuts . Once anchored, the leader will then belay the climber coming up from below. Once the follower reaches the leader,

837-426: A few different forms of shelter depending on the situation and conditions; alpine shelters or arctic shelters. Shelter is a very important aspect of safety for the climber as weather in the mountains may be very unpredictable. Tall mountains may require many days of camping. Short trips lasting less than a day generally do not require shelter, although for safety, most mountaineers will carry an emergency shelter, such

930-559: A large body of professional guides, equipment, and methodologies. In the early years of the " golden age ", scientific pursuits were intermixed with the sport, such as by the physicist John Tyndall . In the later years, it shifted to a more competitive orientation as pure sportsmen came to dominate the London-based Alpine Club and alpine mountaineering overall. The first president of the Alpine Club, John Ball ,

1023-401: A light bivouac sack . Typical shelters used for camping include tents and bivouac sacks . The ability of these shelters to provide protection from the elements is dependent on their design. Mountaineers who climb in areas with cold weather or snow and ice will use more heavy-duty shelters than those who climb in more forgiving environments. In remote locations, mountaineers will set up

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1116-707: A means of payment. In the UK the term "hut" is used for any cottage or cabin used as a base for walkers or climbers. These are mostly owned by mountaineering clubs for use by members or visiting clubs and generally do not have wardens or permanent staff, but have cooking and washing facilities and heating. In the Scottish Highlands small simple unstaffed shelters without cooking facilities known as "bothies" are maintained to break up cross country long routes and act as base camps to certain mountains. Where conditions permit, snow caves are another way to shelter high on

1209-623: A popular ski mountaineering tour. The Grossglockner became Austria's highest mountain, when the South Tyrolean Ortler region had to be ceded to the Kingdom of Italy according to the 1919 Treaty of Saint-Germain , which promoted its reputation as a tourist attraction . Mass tourism was decisively promoted by the scenic High Alpine Road ( Großglockner-Hochalpenstraße ) running from Heiligenblut to Bruck in Salzburg with

1302-470: A popular venue for Alpinists like Hermann and Adolf Schlagintweit , who all followed the route of the first ascent. By the mid 19th century, the developing Alpine tourism began to alter the traditional agriculture economy in the Heiligenblut area. Therefore, the people of Kals tried to lay out a straight ascent from the western side, which however was not reached until Julius von Payer explored

1395-439: A pyramid as a solid figure, constructed from one plane to one point. The context of his definition was vague until Heron of Alexandria defined it as the figure by putting the point together with a polygonal base. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces as triangles, trapezoids , and parallelograms . Pyramids are classified as prismatoid. A right pyramid

1488-495: A pyramid is the one-third product of the base's area and the height. The pyramid height is defined as the length of the line segment between the apex and its orthogonal projection on the base. Given that B {\displaystyle B} is the base's area and h {\displaystyle h} is the height of a pyramid, the volume of a pyramid is: V = 1 3 B h . {\displaystyle V={\frac {1}{3}}Bh.} The volume of

1581-408: A pyramid was recorded back in ancient Egypt, where they calculated the volume of a square frustum , suggesting they acquainted the volume of a square pyramid. The formula of volume for a general pyramid was discovered by Indian mathematician Aryabhata , where he quoted in his Aryabhatiya that the volume of a pyramid is incorrectly the half product of area's base and the height. The hyperpyramid

1674-413: A rope team. For example, when traveling over glaciers , crevasses pose a grave danger to a climber who is not roped in. These giant cracks in the ice are not always visible as snow can be blown and freeze over the top to make a snowbridge . At times snowbridges can be as thin as a few inches and may collapse from people walking over them. Should a climber fall, being protected by a rope greatly reduces

1767-405: A roped team may choose not to use anchors; instead, all members of the team will prepare to use their ice axes to self-arrest in the event should a team member fall. It is not always wise for climbers to form a rope team, since one falling climber may pull the entire team off the mountain. However, the risks of individual, unprotected travel are often so great that groups have no choice but to form

1860-540: A southeasterly direction and forming the boundary between the East Tyrolean municipality of Kals am Großglockner, about 8 km (5.0 mi) in the southwest at 1,324 m (4,344 ft), and Carinthian Heiligenblut , about 12 km (7.5 mi) in the northeast at 1,291 m (4,236 ft). This boundary is also the watershed between the Kals Valley and its Teischnitz and Ködnitz side valleys on

1953-659: A track in the snow, had installed fixed ropes at some steeper sections up to the end of the Glocknerleitl, and even built a second refuge, called Hohenwarte Hut. The vanguard reached the Kleinglockner peak, however, according to the expedition records by the Dellach priest Franz Joseph Horasch (Orasch), only the four guides and Mathias Hautzendorfer, the local priest of the Rangersdorf parish, were able to cross

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2046-495: A variety of hazards . When climbing mountains, there are two types of hazards, objective (mountain-based) and subjective (human-based) . Objective hazards relate to the environment, and may include inclement weather conditions, dangerous terrain, duration of exposure , and other environmental conditions. Subjective hazards relate to a climber's poor judgement, poor planning, lack of skills, faulty analysis and conclusions, or inadequate conditioning. In terms of objective hazards,

2139-535: A voluntary basis by members of alpine clubs. The manager of the hut, termed a guardian or warden in Europe, will usually also sell refreshments and meals, both to those visiting only for the day and to those staying overnight. The offering is surprisingly wide, given that most supplies, often including fresh water, must be flown in by helicopter, and may include glucose-based snacks (such as candy bars) on which climbers and walkers wish to stock up, cakes and pastries made at

2232-537: A wide group of mountain sports . Unlike most sports, mountaineering lacks widely applied formal rules, regulations, and governance; mountaineers adhere to a large variety of techniques and philosophies (including grading and guidebooks ) when climbing mountains. Numerous local alpine clubs support mountaineers by hosting resources and social activities. A federation of alpine clubs, the International Climbing and Mountaineering Federation (UIAA),

2325-464: A young generation of Norwegian mountaineers such as George Paus , Eilert Sundt and Kristian Tandberg appeared, and later founded Norsk Tindeklub , the third oldest mountaineering association in the world. By the turn of the 20th century, mountaineering had acquired a more international flavour. In 1897 Mount Saint Elias (18,008 ft (5,489 m)) on the Alaska - Yukon border was summitted by

2418-453: Is C n v , a symmetry of order 2 n : the pyramids are symmetrical as they rotated around their axis of symmetry (a line passing through the apex and the base centroid), and they are mirror symmetric relative to any perpendicular plane passing through a bisector of the base. Examples are square pyramid and pentagonal pyramid , a four- and five-triangular faces pyramid with a square and pentagon base, respectively; they are classified as

2511-485: Is a pyramid whose base is circumscribed about a circle and the altitude of the pyramid meets the base at the circle's center; otherwise, it is oblique. This pyramid may be classified based on the regularity of its bases. A pyramid with a regular polygon as the base is called a regular pyramid. For the pyramid with an n - sided regular base, it has n + 1 vertices, n + 1 faces, and 2 n edges. Such pyramid has isosceles triangles as its faces, with its symmetry

2604-435: Is also a prerequisite of success in all aspects of mountaineering. Alpine rock climbing involves technical skills including the ability to place anchors into the rock to safely ascend a mountain. In some cases, climbers may have to climb multiple pitches of rock to reach the top. Typically, for any one pitch, there is a belayer who is stationary and creates tension on the rope to catch a climber should he or she fall, and

2697-441: Is at least four feet of snow. The addition of a good quality bivouac bag and closed cell foam sleeping mat will also increase the warmth of the snow cave. Another shelter that works well is a quinzee , which is excavated from a pile of snow that has been work hardened or sintered (typically by stomping). Igloos are used by some climbers, but are deceptively difficult to build and require specific snow conditions. Mountaineers face

2790-510: Is considered to be the discoverer of the Dolomites , which for decades were the focus of climbers like Paul Grohmann and Angelo Dibona . At that time, the edelweiss also established itself as a symbol of alpinists and mountaineers. In the 19th century, the focus of mountaineering turned towards mountains beyond the Alps. One of the earliest mountain areas to be explored beyond the Alps in

2883-618: Is counted as an independent peak in mountaineering literature. The Obere Glocknerscharte between the two peaks, at 3,766 m (12,356 ft), is the highest col in Austria, from which a couloir up to 55° in gradient and 600 m (2,000 ft) in altitude descends down to the Glocknerkees glacier, called Pallavicinirinne after the Austrian mountaineer Alfred von Pallavicini (1848–1886). It runs northeastwards and borders on

Grossglockner - Misplaced Pages Continue

2976-442: Is deemed obligatory, and in many cases is essential as some popular huts, even with more than 100 bed spaces, may be full during good weather and at weekends. Once made, the cancellation of a reservation is advised as a matter of courtesy – and, indeed, potentially of safety, as many huts keep a record of where climbers and walkers state they plan to walk to next. Most huts may be contacted by telephone and most take credit cards as

3069-764: Is the International Olympic Committee -recognized world organization for mountaineering and climbing. The consequences of mountaineering on the natural environment can be seen in terms of individual components of the environment (land relief, soil, vegetation, fauna, and landscape) and the location/zone of mountaineering activity (hiking, trekking, or climbing zone). Mountaineering impacts communities on economic, political, social and cultural levels, often leading to changes in people's worldviews influenced by globalization, specifically foreign cultures and lifestyles. Humans have been present in mountains since prehistory. The remains of Ötzi , who lived in

3162-508: Is the 1100 AD ascent of the Untersberg . The famous poet Petrarch describes his 26 April 1336 ascent of Mount Ventoux (1,912 m (6,273 ft)) in one of his epistolae familiares , claiming to be inspired by Philip V of Macedon 's ascent of Mount Haemo . For most of antiquity, climbing mountains was a practical or symbolic activity, usually undertaken for economic, political, or religious purposes. A commonly cited example

3255-456: Is the 1492 ascent of Mont Aiguille (2,085 m (6,841 ft)) by Antoine de Ville, a French military officer and lord of Domjulien and Beaupré. Because ropes, ladders and iron hooks were used, and because it was the first climb of any technical difficulty to be officially verified, this ascent is widely recognized as being the birth of mountaineering. Conrad Gessner , A mid-16th Century physician, botanist and naturalist from Switzerland,

3348-422: Is the generalization of a pyramid in n - dimensional space. In the case of the pyramid, one connects all vertices of the base, a polygon in a plane, to a point outside the plane, which is the peak . The pyramid's height is the distance of the peak from the plane. This construction gets generalized to n dimensions. The base becomes a ( n − 1) - polytope in a ( n − 1) - dimensional hyperplane. A point called

3441-462: Is the side of Grossglockner with the least ice (people feared glaciers in these times). These valiant men, called "Glockners" in the records, did more than they were ordered to do—and probably reached the Kleinglockner summit on 23 July 1799. One month later the bishop's expedition started: a mountain hut (the first Salm Hut) had been built and the path in the Leitertal valley was prepared so that

3534-402: Is used to describe terrain in which no technical equipment is needed. To traverse this terrain, mountaineers hike long distances to a base camp or the beginning of rough terrain, either following trails or using navigation techniques to travel cross-country. Hiking may be a strenuous activity, and adequate physical fitness and familiarity with the wilderness is necessary to complete a hike; it

3627-650: Is widely recognized as being the first person to hike and climb for sheer pleasure. In the Andes , around the late 1400s and early 1500s many ascents were made of extremely high peaks by the Incas and their subjects. The highest they are known for certain to have climbed is 6739 m at the summit of Volcan Llullaillaco . The Age of Enlightenment and the Romantic era marked a change of attitudes towards high mountains. In 1757 Swiss scientist Horace-Bénédict de Saussure made

3720-709: The n - dimensional volume of the hyperpyramid. A denotes the ( n  − 1) - dimensional volume of the base and h the height, that is the distance between the apex and the ( n  − 1) - dimensional hyperplane containing the base A . Mountaineering Mountaineering , mountain climbing , or alpinism is a set of outdoor activities that involves ascending mountains . Mountaineering-related activities include traditional outdoor climbing , skiing , and traversing via ferratas that have become sports in their own right. Indoor climbing , sport climbing , and bouldering are also considered variants of mountaineering by some, but are part of

3813-470: The 4th millennium BC , were found in a glacier in the Ötztal Alps . However, the highest mountains were rarely visited early on, and were often associated with supernatural or religious concepts. Nonetheless, there are many documented examples of people climbing mountains prior to the formal development of the sport in the 19th century, although many of these stories are sometimes considered fictional or legendary. A rare medieval example of mountaineering

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3906-584: The Academy of Ljubljana . He travelled the Eastern Alps from 1779 to 1781 and published an itinerary in 1783, describing the Glokner mountain and stating that it had not been climbed yet. He estimated the mountain's height with converted 3,793 m (12,444 ft) and left an engraving illustrating Grossglockner and Pasterze, the first known depiction of the mountain. Inspired by Hacquet's book and

3999-770: The Duke of the Abruzzi and party. In 1879–1880 the exploration of the highest Andes in South America began when English mountaineer Edward Whymper climbed Chimborazo (20,549 ft (6,263 m)) and explored the mountains of Ecuador. It took until the late 19th century for European explorers to penetrate Africa. Mount Kilimanjaro in Africa was climbed in 1889 by Austrian mountaineer Ludwig Purtscheller and German geologist Hans Meyer , Mount Kenya in 1899 by Halford Mackinder . The greatest mountain range to be conquered

4092-794: The French Federation of Mountaineering and Climbing , remain independent. The premier award in mountaineering is the privately granted Piolet d'Or , which has expanded from a single recognition to multiple. While there are many competitions, particularly in toproped climbing wall disciplines, there are no "official" world championships or other similar competitions for mountaineering broadly. Mountaineering techniques vary greatly depending on location, season, terrain, and route. Both techniques and hazards vary by terrain, spanning trails, rock, snow, and ice. Mountaineers must possess adequate food, water, information, equipment, stamina, and skill to complete their tasks. The term "walk-up" or "trek"

4185-579: The Golden Age of Alpinism , with the first mountaineering club – the Alpine Club – being founded in 1857. One of the most dramatic events was the spectacular first ascent of the Matterhorn in 1865 by a party led by English illustrator Edward Whymper , in which four of the party members fell to their deaths. By this point the sport of mountaineering had largely reached its modern form, with

4278-895: The Grossglockner in 1800, the Ortler in 1804, the Jungfrau in 1811, the Finsteraarhorn in 1812, and the Breithorn in 1813. In 1808, Marie Paradis became the first woman to climb Mont Blanc, followed in 1838 by Henriette d'Angeville . The beginning of mountaineering as a sport in the UK is generally dated to the ascent of the Wetterhorn in 1854 by English mountaineer Sir Alfred Wills , who made mountaineering fashionable in Britain. This inaugurated what became known as

4371-631: The Obere Glocknerscharte and climb the Grossglockner summit. Hautzendorfer had to be persuaded to venture the step and administered the last rites in advance. The two "Glockners" are usually identified as the brothers Joseph ( Sepp ) and Martin Klotz , however, this surname is not listed in the Heiligenblut parish register. A local peasant named Sepp Hoysen is documented as a member of the second Grossglockner expedition in 1802, and

4464-512: The ancient Greek term "πυραμίς" (pyramis), which referred to a pyramid-shaped structure and a type of wheat cake. The term is rooted in the Greek "πυρ" (pyr, 'fire') and "άμις" (amis, 'vessel'), highlighting the shape's pointed, flame-like appearance. In Byzantine Greek , the term evolved to "πυραμίδα" (pyramída), continuing to denote pyramid structures. The Greek term "πυραμίς" was borrowed into Latin as "pyramis." The term "πυραμίδα" influenced

4557-530: The first ascent of the Mont Blanc in 1786, the Gurk prince-bishop Count Franz Xaver of Salm (1749–1822) together with his vicar general Sigismund Ernst Hohenwart (1745–1825) and Baron Franz Xaver von Wulfen (1728–1805) started efforts for a Grossglockner expedition. They engaged two peasants from Heiligenblut as mountain guides to do the first explorations for an ascent through the Leitertal valley, which

4650-407: The star pyramid in which its base is the regular star polygon . The truncated pyramid is a pyramid cut off by a plane; if the truncation plane is parallel to the base of a pyramid, it is called a frustum . The surface area is the total area of each polyhedra's faces. In the case of a pyramid, its surface area is the sum of the area of triangles and the area of the polygonal base. The volume of

4743-521: The vasodilator padutin , and a stimulant tea made from coca leaves. K2 (8,611m), the second-highest peak in the world, was first scaled in 1954 by Lino Lacedelli and Achille Compagnoni . In 1964, the final eight-thousander to be climbed was Shishapangma (8,013m), the lowest of all the 8,000-metre peaks. Reinhold Messner from the Dolomites mountain range (Italy) was then the first to climb all eight-thousanders up to 1986, in addition to being

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4836-525: The 19th century were the mountains of Norway —particularly Jotunheimen —where British mountaineers such as William Cecil Slingsby , Harold Raeburn and Howard Priestman were early pioneers. Slingsby's book Norway, the Northern Playground contributed greatly to the popularization of mountaineering in Norway among the international mountaineering community. Around the turn of the century,

4929-854: The 3,721 m (12,208 ft) high Glocknerwand . A prominent ridge, the Stüdlgrat , named after the Prague Alpinist Johann Stüdl (1839–1925), runs from the Grossglockner away to the southwest. Together with its extension, the Luisengrat , it separates the West Face and the Teischnitzkees glacier at its foot from the South Face and its Ködnitzkees glacier. A couloir known as the Pillwaxrinne crosses

5022-598: The Alps. Even its topographic prominence , at 2,424 m (7,953 ft), is the second highest after Mont Blanc in the entire Alps (see the list of Alpine peaks by prominence ). That makes it one of the most independent peaks in the Alps. The view from the Grossglockner summit is one of the farthest of all mountains in the Eastern Alps. It ranges out to 220 km (140 mi) or, taking account of atmospheric refraction , almost 240 km (150 mi). Its view over more than 150,000 km (58,000 sq mi) of

5115-800: The Earth's surface reaches as far as the Upper Swabian Plateau in the northwest, to Regensburg and the peaks of the Bohemian Forest in the north, to Ortler in the west, to the Padan Plain in the south, and to Triglav and the Totes Gebirge range in the east. The Grossglockner rock summit, due to its high Alpine, heavily glaciated appearance, is often compared to the mountains of the Western Alps . Together with

5208-421: The Kleinglockner to the southeast it forms a distinctive double peak . There are differing views in the literature as to whether the Kleinglockner is a subpeak or a separate main summit. Due to its low topographic prominence and isolation as well as its close links in climbing history, it is counted as part of that of the Grossglockner in historic publications; however, in view of its separate climbing routes it

5301-726: The Northeast and North Faces of the Grossglockner. The latter faces are bounded by the Northwest Ridge, part of the main Glockner crest, which runs over the Grögerschneid , 3,660 m (12,010 ft), and the ridge elevations of Glocknerhorn , 3,680 m (12,070 ft), and Teufelshorn , 3,677 m (12,064 ft), to the Untere Glocknerscharte , 3,598 m (11,804 ft), which connects to

5394-692: The South Face below the Obere Glocknerscharte; most of the South Face lies east of this gully below the Kleinglockner. The east side of the Kleinglockner, the Glocknerleitl , is glaciated to just below the summit and is continued by the Kleinglocknerkees and Hofmannskees before reaching the Pasterze. The history of the climbs started with French-born natural scientist Belsazar Hacquet , from 1773 professor of anatomy at

5487-780: The Tyrolean side and the Möll Valley with the Pasterze glacier on the Carinthian side. The region around the mountain has formed part of the Grossglockner-Pasterze special protected area within the High Tauern National Park since 1986. The Glockner is the highest mountain in the Alps east of the Ortler range, about 175 km (109 mi) away, and, after Mont Blanc , has the second greatest topographic isolation of all mountains in

5580-423: The apex is located outside the hyperplane and gets connected to all the vertices of the polytope and the distance of the apex from the hyperplane is called height. The n - dimensional volume of a n - dimensional hyperpyramid can be computed as follows: V n = A ⋅ h n . {\displaystyle V_{n}={\frac {A\cdot h}{n}}.} Here V n denotes

5673-478: The bishop could use a horse to reach it. 30 people, among them Salm, Hohenwart and Wulfen, were part of the expedition. They suffered with bad weather and a first effort failed, but on 25 August 1799 Hohenwart and at least four other people, including the two "Glockners", reached—again—the Kleinglockner, where they installed one of the first summit crosses (one of the main goals of the church expedition). Hohenwart's reports did not tell clearly that they had not touched

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5766-464: The bottom of a mountaineer's boots and provide additional traction on hard snow and ice. For loose snow, crampons are less suitable, and snowshoes or skis may be preferred. Using various techniques from alpine skiing to ascend/descend a mountain is a form of the sport by itself, called ski mountaineering . Ascending and descending a steep snow slope safely requires the use of an ice axe and different footwork techniques that have been developed over

5859-401: The center called the universal vertex . A right pyramid may also have a base with an irregular polygon. Examples are the pyramids with rectangle and rhombus as their bases. These two pyramids have the symmetry of C 2v of order 4. The type of pyramids can be derived in many ways. The base regularity of a pyramid's base may be classified based on the type of polygon: one example is

5952-556: The dangers mountaineers face include loose or falling rocks, falling ice, snow- avalanches , the climber falling, falls from ice slopes, falls down snow slopes, falls into crevasses, and the dangers from altitude and weather. From 1947 to 2018 in the United States "2,799 people were reported to be involved in mountaineering accidents and 43% of these accidents resulted in death." Climbers themselves are responsible for nearly all climbing accidents. When planning and preparing for

6045-549: The evolution of the word into "pyramid" in English and other languages. A pyramid is a polyhedron that may be formed by connecting a polygonal base and a point, called the apex . Each base edge and apex form an isosceles triangle called a lateral face. The edges connected from the polygonal base's vertices to the apex are called lateral edges. Historically, the definition of a pyramid has been described by many mathematicians in ancient times. Euclides in his Elements defined

6138-403: The first and second Johnson solid if their regular faces and edges that are equal in length, and their symmetries are C 4v of order 8 and C 5v of order 10, respectively. A tetrahedron or triangular pyramid is an example that has four equilateral triangles, with all edges equal in length, and one of them is considered as the base. Because the faces are regular, it is an example of

6231-509: The first expedition up the steep glaciated Northeast Face, chopping 2,500 steps into the Pallavicinirinne in an ice climbing master stroke not repeated for 23 years. In 1879 Count Pallavicini dedicated a new iron summit cross on the occasion of the silver wedding of Emperor Franz Joseph of Austria and Empress Elisabeth ; both had visited Heiligenblut and walked to the present-day Franz-Josefs-Höhe viewpoint in 1865. The cross

6324-471: The first of several unsuccessful attempts on Mont Blanc in France. He then offered a reward to anyone who could climb the mountain, which was claimed in 1786 by Jacques Balmat and Michel-Gabriel Paccard . The climb is usually considered an epochal event in the history of mountaineering, a symbolic mark of the birth of the sport. By the early 19th century, many of the alpine peaks were reached, including

6417-610: The first professional female mountaineers) made ascents in the Himalayas, including one of the Nun Kun peaks (23,300 ft (7,100 m)). A number of Gurkha sepoys were trained as expert mountaineers by Charles Granville Bruce , and a good deal of exploration was accomplished by them. In 1902 the Eckenstein–Crowley Expedition, led by English mountaineer Oscar Eckenstein and English occultist Aleister Crowley

6510-429: The first without supplemental oxygen. In 1978 he climbed Mount Everest with Peter Habeler without supplemental oxygen, the first men to do so. Long the domain of the wealthy elite and their agents, the emergence of the middle-class in the 19th and 20th centuries resulted in mass interest in mountaineering. It became a popular pastime and hobby of many people. Some have come to criticize the sport as becoming too much of

6603-534: The high mountains themselves – in extremely remote areas, more rudimentary shelters may exist. The mountain huts are of varying size and quality, but each is typically centred on a communal dining room and have dormitories equipped with mattresses, blankets or duvets, and pillows; guests are expected to bring and use their own sleeping bag liners . The facilities are usually rudimentary, but, given their locations, huts offer vital shelter, make routes more widely accessible (by allowing journeys to be broken and reducing

6696-498: The highest point but Bishop Salm (who had reached the Adlersruhe rock at 3,454 m (11,332 ft)) was informed. Dissatisfied, he invited another, even bigger expedition the next year. On 28 July 1800, 62 people, among them the pedagogue Franz Michael Vierthaler and the botanist David Heinrich Hoppe , started again into the Leitertal valley. Four peasants and carpenters (the "Glockners" and two others who are not known) did

6789-418: The hut, a variety of hot and cold drinks (including beer and wine), and high carbohydrate dinners in the evenings. Not all huts offer a catered service, though, and visitors may need to provide for themselves. Some huts offer facilities for both, enabling visitors wishing to keep costs down to bring their own food and cooking equipment and to cater using the facilities provided. Booking for overnight stays at huts

6882-401: The ice, as well as traditional rock climbing equipment for anchoring in mixed terrain. Often, mountaineers climbing steep snow or mixed snowy rock terrain will not use a fixed belay. Instead, each climber on the team will climb at the same time while attached to anchors, in groups of two. This allows for safety should the entire team be taken off their feet which also allows for greater speed than

6975-404: The leader will often transfer all necessary protection devices (known as a rack) to the follower. The follower then becomes the leader and will ascend the next pitch. This process will continue until the climbers either reach the top, or run into different terrain. For extremely vertical rocks, or to overcome certain logistical challenges, climbers may use aid climbing techniques. This involves

7068-448: The most famous base camps. Camping is not always an option, or may not be suitable if a mountain is close to civilization. Some regions may legally prohibit primitive camping due to concern for the environment, or due to issues with crowds. In lieu of camping, mountaineers may choose to stay in mountain huts . The European alpine regions, in particular, have a large network of huts. Such huts exist at many different heights, including in

7161-665: The mountain's characteristic shape. It may also be a Germanised version of the Alpine Slavic word Klek ("mountain"), as maintained in the Slovene name Veliki Klek . The Grossglockner lies on the border between the Austrian states of Carinthia and Tyrol ( East Tyrol ). The peak is part of the Glocknerkamm ridge in the Glockner Group that branches off the main chain of the Alps at Eiskögele , heading in

7254-424: The mountain. Some climbers do not use tents at high altitudes unless the snow conditions do not allow for snow caving, since snow caves are silent and much warmer than tents. They can be built relatively easily, given sufficient time, using a snow shovel. The temperature of a correctly made snow cave will hover around freezing, which relative to outside temperatures can be very warm. They can be dug anywhere where there

7347-542: The past century, such as the French technique and German technique . Teams of climbers may choose to attach everyone together with a rope, to form a rope team. The team may then secure themselves by attaching the rope to anchors. These anchors are sometimes unreliable and include snow stakes or pickets, deadman devices called flukes , or buried equipment or rocks. Bollards , which are simply carved out of consolidated snow or ice, also sometimes serve as anchors. Alternatively,

7440-573: The ridge between Glöcknerleitl and Ködnitzkees in 1863. Johann Stüdl had a via ferrata erected along the southwestern ridge the next year and the Stüdlhütte erected at its foot in 1868. Already in 1869, most expeditions to the summit started in Kals. The first winter ascent of the Grossglockner was made on January 2, 1875 by William Adolf Baillie Grohman , a member of the Alpine Club . In 1876 Count Pallavicini and his guide Hans Tribusser undertook

7533-403: The risk of injury or death. The other members of the rope team may proceed with a crevasse rescue to pull the fallen climber from the crevasse. For extremely slippery or steep snow, ice, and mixed rock and ice terrain climbers must use more advanced techniques, called ice climbing or mixed climbing. Specialized tools such as ice screws and ice picks help climbers build anchors and move up

7626-536: The sport. Despite its lack of defined rules and non-competitive nature, certain aspects of mountaineering have much of the trappings of an organized sport, with recognition of specific climbing activities – including climbing wall -based competition – by the International Olympic Committee ; on a club level, the prominent international sport federation the UIAA counts numerous national alpine clubs as its members, while others, such as The Mountaineers and

7719-478: The summit) and in 1806, however, he himself never climbed beyond the Adlersruhe rock. The climbing of the Grossglockner was also described by the botanist Josef August Schultes , who explored the massif together with Count Apponyi in 1802. No further ascents were made during the Napoleonic Wars , the huts decayed and were plundered by locals. In the following Vormärz era, however, the mountain became

7812-565: The surveyor Ulrich Schiegg mentioned one Martin Reicher as "Glockner" guide. The peasants and several other members of the expedition (among them Schiegg and his young apprentice Valentin Stanič , who climbed Mt. Watzmann for the first time some weeks later) did the ascent again the next day and finally installed the summit cross and a barometer on the Grossglockner summit. Bishop Salm undertook two more ascents in 1802 (with Hohenwart reaching

7905-418: The traditional technique of belaying one climber at a time. This technique is known as simul-climbing or a running belay and is sometimes also used on ice, however, the risk of dropping frequently displaced ice on the lower team member(s) limits its usefulness on ice. Traditional belays are also used; in this case, this is sometimes necessary due to ice fall hazard, steepness, or other factors. Climbers use

7998-503: The use of equipment, such as ladders, fixed lines , and ascenders to help the climber push themself up the rock. In alpine climbing, it is common for climbers to see routes of mixed terrain. This means climbers may need to move efficiently from climbing glacier, to rock, to ice, back and forth in a number of variations. Compacted snow conditions allow mountaineers to progress on foot. Frequently crampons are required to travel efficiently and safely over snow and ice. Crampons attach to

8091-439: The weight of equipment needing to be carried), and offer good value. In Europe, all huts are staffed during the summer (mid-June to mid-September) and some are staffed in the spring (mid-March to mid-May). Elsewhere, huts may also be open in the fall. Huts also may have a part that is always open, but unstaffed, a so-called winter hut. When open and staffed, the huts are generally run by full-time employees, but some are staffed on

8184-463: Was also a pioneer in developing new equipment and climbing methods. He started using shorter ice axes that could be used single-handedly, designed the modern crampons , and improved on the nail patterns used for the climbing boots. By the 1950s, all the eight-thousanders but two had been climbed starting with Annapurna in 1950 by Maurice Herzog and Louis Lachenal on the 1950 French Annapurna expedition . The highest of these peaks Mount Everest

8277-481: Was climbed in 1953 after the British had made several attempts in the 1920s; the 1922 expedition reached 8,320 metres (27,300 ft) before being aborted on the third summit attempt after an avalanche killed seven porters. The 1924 expedition saw another height record achieved but still failed to reach the summit with confirmation when George Mallory and Andrew Irvine disappeared on the final attempt. The summit

8370-477: Was finally reached on 29 May 1953 by Sir Edmund Hillary and Tenzing Norgay from the south side in Nepal . Just a few months later, Hermann Buhl made the first ascent of Nanga Parbat (8,125 m), on the 1953 German–Austrian Nanga Parbat expedition , completing the last 1,300 meters walking alone, self-medicating with pervitin (based on the stimulant methamphetamine used by soldiers during World War II),

8463-540: Was installed on 2 October 1880. Pallavicini also had the Archduke John Hut erected at the former Adlersruhe resting place of Bishop Salm, today the highest situated mountain hut in Austria. The Austrian Alpine Club built the new Salmhütte and the Glocknerhaus along the alpine route from Heiligenblut. A first ascent by skiing was made in 1909 and the circumnavigation of the massif soon became

8556-793: Was the Himalayas in South Asia. They had initially been surveyed by the British Empire for military and strategic reasons. In 1892 Sir William Martin Conway explored the Karakoram Himalayas, and climbed a peak of 23,000 ft (7,000 m). In 1895 Albert F. Mummery died while attempting Nanga Parbat , while in 1899 Douglas Freshfield took an expedition to the snowy regions of Sikkim . In 1899, 1903, 1906, and 1908 American mountaineer Fanny Bullock Workman (one of

8649-413: Was the first to attempt to scale K2 . They reached 22,000 feet (6,700 m) before turning back due to weather and other mishaps. Undaunted, in 1905 Crowley led the first expedition to Kangchenjunga , the third highest mountain in the world, in an attempt which Isserman, Angas Weaver and Molenaar describe as "misguided" and "lamentable" due to Crowley's many failings as an expedition leader. Eckenstein

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