Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#3 Re: This is Cool » Miscellany » Today 01:33:19

1071) Atoll

Atoll, coral reef enclosing a lagoon. Atolls consist of ribbons of reef that may not always be circular but whose broad configuration is a closed shape up to dozens of kilometres across, enclosing a lagoon that may be approximately 50 metres (160 feet) deep or more.

Most of the reef itself is a submarine feature, rising from the abyssal floors of the ocean to just beneath high-tide level. Around the rim along the top of the reef there are usually low, flat islands or more continuous strips of low, flat land. Some of these islands have been settled by oceanic peoples like the Maldivians, Polynesians, and Micronesians for many centuries.

The origin of atolls has always fascinated sailors and naturalists, who early appreciated that, although reef-building organisms inhabit only the shallowest depths of the sea (about 100 metres [330 feet]), the reefs rose from much deeper. The modern explanation of atolls incorporates the theory of Charles Darwin, who suggested that atolls represented the final stage of a continuing upgrowth of reef around a sinking extinct volcanic island that had long since disappeared from view.

Reefs tend to grow outward from a fringing-reef stage toward the better conditions of open water and also grow upward if the foundations beneath are sinking. After thousands of years the actively growing reef structure becomes separated from the volcanic shoreline by an intervening stretch of lagoon water. This is the barrier-reef stage. The volcanic island eventually subsides from view, leaving a reef whose uppermost part is like a saucer whose rim reaches up to sea level and whose deeper central area is a lagoon.

Different kinds of reefs and volcanic islands are found together in the tropical oceans, related to each other in such a way that they can be interpreted as representing the progressive stages postulated by the subsidence theory. Stronger direct evidence for subsidence has come from geologic drilling of atolls (first at Enewetak atoll in 1952), which revealed the presence of volcanic rock about 1,400 metres (4,600 feet) below the modern reef top. Changes in sea level complicate the subsidence model. These have been relatively frequent during the last 2,000,000 years or more and mostly result from cycles of glaciation.

atoll.jpg

#5 Re: Maths Is Fun - Suggestions and Comments » From Member to Real Member » Today 01:06:09

Hi jabah013.307,

Its too early for becoming a real member for new members. You are in the early stages!

#8 Jokes » Miscellaneous Jokes - 5 » Today 00:25:50

ganesh
Replies: 1

Q: Where should you go in the room if you’re feeling cold?
A: The corner—they’re usually 90 degrees.
* * *
I can never take my dog to the park because the ducks keep trying to bite him.
I guess that’s what I get for buying a pure bread dog.
* * *
Q: What’s the difference between a poorly dressed man on a unicycle and a well-dressed man on a bicycle?
A: Attire.
* * *
Q: You know why you never see elephants hiding up in trees?
A: Because they’re really good at it.
* * *
A horse walks into a bar.
The bartender says, “Why the long face?”
* * *

#10 Re: Ganesh's Puzzles » General Quiz » Today 00:02:42

Hi,

#7951. What does the term in Chemistry 'Chemical process' mean?

#7952. What does the term in Chemistry 'Chemical reaction' mean?

#12 Re: This is Cool » Miscellany » Yesterday 00:44:26

1070) Tributary

A tributary is a freshwater stream that feeds into a larger stream, river or other body of water. The larger, or parent, river is called the mainstem.

A tributary is a freshwater stream that feeds into a larger stream or river. The larger, or parent, river is called the mainstem. The point where a tributary meets the mainstem is called the confluence. Tributaries, also called affluents, do not flow directly into the ocean.

Most large rivers are formed from many tributaries. Each tributary drains a different watershed, carrying runoff and snowmelt from that area. Each tributary's watershed makes up the larger watershed of the mainstem.

The Missouri River's massive watershed, for example, is created by the watersheds of dozens of tributaries extending from the provinces of Alberta and Saskatchewan, Canada, through seven states in the Upper Midwest of the U.S. The Missouri, in turn, is the largest tributary of the Mississippi River, which it meets at a confluence in St. Louis, Missouri. The Mississippi River watershed is the fourth-largest in the world.

A "left-bank tributary" or "right-bank tributary" indicates the side of the river a tributary enters. When identifying a left-bank or right-bank tributary, a geographer looks downstream (the direction the river is flowing).

The Euphrates River, the longest river in southwestern Asia, stretches 2,700 kilometers (1,678 miles). The tiny streams that feed the Euphrates originate in the mountains of eastern Turkey. These streams become the Balikh and the Sajur Rivers, which join the Euphrates at different confluences in Syria. The Balikh is a left-bank tributary of the Euphrates, while the Sajur is a right-bank tributary.

Sometimes, tributaries have the same name as the river into which they drain. These tributaries are called forks. Different forks are usually identified by the direction in which they flow into the mainstem.

The Shenandoah River, for example, flows through the U.S. states of West Virginia and Virginia. It has two long tributaries, the North Fork and South Fork, which meet at a confluence in Harpers Ferry, West Virginia.

The opposite of a tributary is a distributary. A distributary is a stream that branches off and flows apart from the mainstem of a stream or river. The process is called river bifurcation.

At the Continental Divide in the U.S. state of Wyoming, the small North Two Ocean Creek bifurcates into Pacific Creek and Atlantic Creek. The water from each of these distributaries flows into the ocean for which it is named.

Classifying Tributaries

There are two leading methods geographers and potamologists (people who study rivers) use to classify tributaries.

The first method lists a river's tributaries starting with those closest to the source, or headwaters, of the river. The earliest tributaries of the Rhine River, for example, include the Thur River of Switzerland and the Ill River of Austria. The Rhine, one of the longest rivers in Europe, has its source in the Alps and its mouth in the North Sea.

The second method lists a river's tributaries by their flow. Small streams are identified with low numbers, while larger tributaries have higher numbers. The Tshuapa and Kasai Rivers are both left-bank tributaries of the Congo River, the deepest river in the world. The Tshuapa is a smaller river, and has a lower tributary ranking, than the Kasai.

People and Tributaries

Human activity in tributaries is often responsible for polluting the mainstem. The river carries all the runoff and pollution from all its tributaries.

Rivers with tributaries that drain land that is not used for agriculture or development are usually less polluted than rivers with tributaries in agricultural or urban areas.

Development, not size, determines the pollution of rivers. The Amazon River, with the largest drainage basin in the world, is much cleaner than the Hudson River, for instance. Tributaries to the Amazon flow through undeveloped regions of the Andes Mountains and rain forests in Brazil, Venezuela, Colombia, Peru, and Bolivia. The Hudson River flows through one of the largest urban areas on Earth, New York City.

confluence-missouri-mississippi.jpg

#13 Re: Dark Discussions at Cafe Infinity » crème de la crème » Yesterday 00:28:54

910) Pär Lagerkvist

Pär Lagerkvist, in full Pär Fabian Lagerkvist, (born May 23, 1891, Växjö, Sweden—died July 11, 1974, Stockholm), novelist, poet, dramatist, and one of the major Swedish literary figures of the first half of the 20th century. He was awarded the Nobel Prize for Literature in 1951.

Lagerkvist was reared in a traditional religious manner in a small town. The influence of his early years remained strong despite his introduction to modern scientific ideas and his eventual break with the religion of his forefathers. He became involved with socialism and soon began to support artistic and literary radicalism, as demonstrated in his manifesto entitled ‘Ordkonst och bildkonst’ (1913; “Literary and Pictorial Art”). In ‘Teater’ (1918; “Theatre”), the three one-act plays ‘Den Svåre Stunden’ (“The Difficult Hour”) illustrate a similar modernist viewpoint.

The extreme pessimism that pervaded Lagerkvist’s works during World War I, such as ‘Ångest’ (1916; “Anguish”), slowly subsided, starting with ‘Det eviga leendet’ (1920; ‘The Eternal Smile’) and his autobiographical novel ‘Gäst hos verkligheten’ (1925; ‘Guest of Reality’), until finally he declared his faith in man in the great prose monologue ‘Det besegrade livet’ (1927; “The Triumph over Life”), which became a positive point of departure for much of his later work.

When the new creeds of violence were being proclaimed in the early 1930s, he quickly recognized their danger. His prose work ‘Bödeln’ (1933; ‘The Hangman’), later dramatized, is a protest against the everlasting brutality in the world. The play ‘Mannen utan själ’ (1936; ‘The Man Without a Soul’) is also an expression of Lagerkvist’s indignation with Fascism. During the 1940s he wrote his most unusual play, sometimes called a “stage oratorio,” ‘Låt människan leva’ (1949; ‘Let Man Live’), which deals with man’s readiness throughout history to judge his fellows and condemn them even to death.

It was not until his novel ‘Dvärgen’ (1944; ‘The Dwarf’ ) appeared that he had unqualified success with Swedish critics; it became his first best-seller. With ‘Barabbas’ (1950) he achieved world recognition.

‘Evening Land’= ‘Aftonland’ (1975) is a literal translation into English by Leif Sjöberg and verse rendering by W.H. Auden of 66 of Lagerkvist’s poems. ‘The Marriage Feast’ (1973) contains English translations of 19 Lagerkvist short stories.

em11pCB18lQPCq6MKTa1d2ZC7Cn-175x250.jpg

#14 Re: Dark Discussions at Cafe Infinity » Mathematical thinking » Yesterday 00:22:58

Mathematical thinking is a lot more than just being able to do arithmetic or solve algebra problems. It is a whole way of looking at things, stripping them down to their essentials, whether it’s numerical, structural or logical and then analyzing the underlying patterns. Math is about patterns. When we are teaching a mathematical method, we are showing something that happens all the time, something that happens in general. Getting students to see these underlying structures, whether it’s in a math problem, in society, or in nature, is one of the reasons that studying mathematics is so worthwhile. It transforms math from drudgery to artistry.

As Steven Strogatz says, ‘Math is not just what we heard about in high school, the known and straightforward part of the subject. There are all sorts of interesting theoretical and applied problems out there.’ Helping students to see the beauty and wonder in math will go a long way in getting them to think more mathematically. Let them know that what makes mathematicians is the quality of their creativity and the quality of their technique. Combining these two is what leads to great mathematical thinking.

The problem lies in the fact that students usually have no idea about their strengths and weaknesses in these two areas. Schools emphasize the procedural side of math. There is the misconception that it only involves mechanical, robotic thinking. What pervades is a ‘we didn’t cover that’ mentality when they encounter a novel problem.

Once you have identified a task or situation to explore, mathematical thinking involves these steps that are often done together and simultaneously:

1) break task down into components
2) identify similar tasks that may help
3) identify appropriate knowledge and skills
4) identify assumptions
5) select appropriate strategy
6) consider alternative approaches
7) look for a pattern or connection
8) generate examples

This all leads to formulating a conjecture (solution, generalization or relationship) that can then be tested for counter examples or special cases. Similar to the design process, if it doesn’t work, it’s time to iterate and try again. Proving the solution, making connections, considering limitations, and extending it further to ‘what if’ questions are additional aspects of mathematical thinking. Spending the time to think of and ask really good questions is at the heart of math.

John Mason’s questions and prompts provide a nice framework for ensuring and promoting students’ mathematical thinking.

#16 Re: Ganesh's Puzzles » Doc, Doc! » Yesterday 00:12:12

Hi,

#1681. In which part of the human body is 'Glenoid cavity' situated?

#17 Re: Ganesh's Puzzles » English language puzzles » Yesterday 00:04:11

Hi,

#4009. What does the noun flume mean?

#4010. What does the verb (used with object) flung mean?

#19 Jokes » Miscellaneous Jokes - 4 » 2021-07-25 00:25:48

ganesh
Replies: 0

Q: How many tickles does it take to get an octopus to laugh?
A: Ten tickles.
* * *
Q: Why doesn’t Dracula have any friends?
A: Well, honestly, he’s a real pain in the neck.
* * *
My teachers told me I’d never amount to much since I procrastinate so much.
I told them, “Just you wait!”
* * *
Q: Why were they called the “dark ages?”
A: Because there were a lot of knights.
* * *
Q: What gets wetter the more it dries?
A: A towel.
* * *
Q: Why aren’t koalas considered bears?
A: They don’t have the right koala-fications.
* * *

#20 Re: This is Cool » Miscellany » 2021-07-25 00:15:25

1069) Lagoon

Lagoon, area of relatively shallow, quiet water situated in a coastal environment and having access to the sea but separated from the open marine conditions by a barrier. The barrier may be either a sandy or shingly wave-built feature (such as a sandbar or a barrier island), or it may be a coral reef. Thus, there are two main types of lagoons: (1) elongated or irregular stretches of water that lie between coastal barrier islands and the shoreline and (2) circular or irregular stretches of water surrounded by coral atoll reefs or protected by barrier coral reefs from direct wave action. Lagoon depths are maintained at a moderate level by sedimentation, and this compensates for the subsidence that commonly attends reef formation. Because the reef is an organic structure, the lagoonal sediments contain much calcareous material. The sheltered waters support highly productive ecosystems made up of a distinctive flora and fauna.

Lagoon Types

Barrier island lagoons

Barrier island, or coastal, lagoons are characterized by quiet water conditions, fine-grained sedimentation, and, in many cases, brackish marshes. Water movements are related to discharge of river flow through the lagoon and to the regular influx and egress of tidal waters through the inlets that normally separate the barrier islands. Coastal lagoons are generally characteristic of coasts of low or moderate energy, occurring especially on the east coasts of continents where the swells are less violent and in high latitudes where offshore ice provides some protection. They also are associated with low coasts and rarely occur where high cliffs form the coast. They can form only where there is abundant sediment for construction of the protective barrier islands. Too much sediment from the mainland, however, can lead to delta formation rather than lagoons, although lagoons frequently occur along the outer delta margin and between delta distributaries

Coastal lagoons are widely distributed throughout the world and have been estimated to constitute about 13 percent of the total world coastline. Lagoons are more common on coasts with moderate to low tidal ranges; for example, they occur widely on low coasts of the southern Baltic, the southeast North Sea, the Black Sea, the Caspian Sea, and the Mediterranean Sea, as well as on low coasts of the southeastern United States and the Gulf of Mexico. Lagoon coasts also occur along southern Brazil, the east coast of Madagascar, northeastern Russia, Japan, and isolated parts of Africa, India, Australia, and New Zealand.

Coral lagoons

Coral lagoons are restricted to tropical open seas that provide the conditions necessary for coral growth. They are best exemplified by the roughly circular quiet waters that are surrounded by warm-water coral atoll reefs. Coral lagoons occur widely in the western Pacific, in parts of the Indian Ocean, and in isolated places in the Caribbean, mainly within 25° latitude of the Equator. Coral lagoons are of great importance to many island communities in the Pacific, particularly where they provide the only quiet water for use as harbours, although the passage through the reef into the lagoon is often perilous.

Coral-reef lagoons also occur on marginal reefs such as the Great Barrier Reef of Australia, but the most spectacular examples are the atolls of the Pacific Ocean, some of which are more than 50 km (30 miles) across. Some atolls consist only of a lagoon, often with a fairly uniform depth, surrounded by a low-lying coral reef; some include one or more high, rocky volcanic islands, and others are complex, with small reefs surrounded by lagoons within a larger reef. All are thought to have been built by the upward growth of coral during a relative rise in sea level due to subsidence and eustatic (global) change.

Nature Of The Lagoon Environment

Dimensions

Coral lagoon dimensions range from small atolls to those so wide that the coral reefs on the far side cannot be seen across the lagoon. Atoll widths range from about 2.5 to nearly 100 km (1.5 to nearly 62 miles), but the mean value is about 20 km (about 12 miles). Depths rarely exceed 60 metres (about 200 feet) and many are shallower, usually less than 20 metres (about 65 feet) deep. The lagoon of Mayotte island in the Comoro archipelago in the Indian Ocean attains a maximum depth of about 92 metres (about 300 feet), but it is generally shallower. That lagoon is about 16 km (about 10 miles) in width at its widest point and lies behind a barrier reef that encircles the island, forming an atoll about 55 km (about 34 miles) in diameter.

Barrier island lagoons are usually elongated, though irregular ones may occur where river estuaries flood behind barriers. This occurs on the east coast of the United States, where lagoons extend intermittently for nearly 1,500 km (about 900 miles) along the coast. The Gippsland Lakes in Victoria, Australia, exemplify a complex lagoon system formed behind a 149-km (93-mile) beach. Elongated lagoons up to 64 km (about 40 miles) in length lie behind the beach barrier, and larger lagoons, such as Lake Wellington, lie behind the southwestern end. Postglacial subsidence has flooded the lowland in this area. The lagoons are shallow: Lake Wellington is less than 3.5 metres (11.5 feet) in depth, and much of Lake King is less than 6 metres (about 20 feet) deep. Scour holes as deep as 16.5 metres (about 54 feet) do occur, however. The elongated lagoon behind the barrier is only 1 to 1.5 metres (3 to 5 feet) deep, typical of barrier island lagoons.

Water circulation

The degree of water circulation depends on the width of the tidal inlets, the tidal range, and the amount of runoff from adjacent land areas. Maximum velocities are attained at the points where the water passes through the barriers. In the entrance to the Gippsland lagoons, for example, tidal currents reach 5.6 km (3.5 miles) per hour, but river floods that escape to the ocean can raise the velocity to 13 km (8 miles) per hour. Water may be blown into the lagoon by strong winds; the increased level results in an outflowing current when the wind drops. Seiches—that is, rhythmic oscillations of water in enclosed or partially enclosed water bodies—can be created in this way. Small waves can be generated within lagoons when the wind blows along their maximum dimension. These may reach 1.25 metres (about 4 feet) in height and 1.5 to 9 metres (about 5 to 30 feet) in length in the Gippsland lagoons. In coral atoll lagoons there is little or no runoff, and seawater moves in and out through the passes, where tidal currents reach their maxima. Velocities of 19 to 22 km (12 to 14 miles) per hour have been recorded in the Hao Channel of the Tuamotu Archipelago in French Polynesia.

A lagoon into which a major river flows is known as an estuarine lagoon and may be regarded as a special kind of estuary.

Water temperature and salinity

In the Mayotte lagoon the water has the same properties as the upper layers of the open ocean. The salinity is close to 35 parts per thousand (ppt), and the temperature varies between 27 and 24 °C (81 and 75 °F). This is typical of coral lagoons, but the temperature and salinity of barrier island lagoons are more variable because of their wider climatic range. Because they are shallow, lagoon waters approximate the air temperature: colder than the open ocean in winter, warmer in summer.

Salinities decrease as a function of the amount of runoff entering the lagoon in relation to the tidal influx. Lagoons may be considered brackish, marine, or hypersaline. Brackish lagoons receive much runoff, and salinity increases toward the tidal inlets. The Gippsland lagoons exemplify this type. The salinity at the inner end varies from 0.5 to 5 ppt according to season, and central values vary between 5 and 20 ppt.

In hot arid regions lagoons lose more water by evaporation than they receive from land drainage. This causes surface waters to become more dense than seawater and to sink to the bottom. Seawater flows in at the surface to replace that lost by evaporation, creating a circulation the reverse of that found in estuaries. If exchange with the open sea is limited, the lagoon may become much more saline than the open sea. Consequently, various species of plants and animals become adapted to life in high salinities. Laguna Madre in Texas and Syvash Sound in the Black Sea are examples of hypersaline lagoons. (They have salinities of 65 and 132 ppt, respectively.) Salt deposits may form in these conditions. The denser saline water tends to lie beneath the fresher water, where mixing is not severe.

Equilibrium bottom profiles

Lagoons behind coastal barriers normally are zones of fine sedimentation. Their bottom profiles, therefore, build up gradually with time. Typical depths of the Texas lagoons vary between 1.25 and 3.5 metres (4 and 11 feet), and their floors are flat. Early theories that attempted to relate the form of the offshore and lagoon profile are no longer held; and, because the lagoon profile changes with continued deposition, it cannot be used to establish the process of lagoon formation. The profile is usually gently undulating, but it may contain deeper channels, especially near the tidal inlets. Profiles across coral lagoons either are smooth and flat from calcareous sedimentation or contain knolls of growing or dead coral. There are 2,300 such knobs in the Enewetak Lagoon in the Marshall Islands.

Factors Involved In Lagoon Formation

The essential feature that causes the lagoon to exist is the barrier that separates it from the ocean. In the coral lagoon the formation of the reef depends on the existence of suitable conditions for reef growth.

Barrier bars and sediment sources

The barrier island lagoons, on the other hand, depend not on organic processes but on waves, which act in a suitable environment on an adequate supply of bottom material, most commonly sand. Barrier islands are formed in those areas where the coastal slope is flatter than the equilibrium slope required by the long constructive swells—i.e., the waves that build up the foreshore in front of their breakpoint. They are, therefore, found on low coasts. They may occur in areas of subsidence, stability, or emergence, wherever sufficient sand exists.

The barrier islands that form the lagoons are made of sand, but the sediments of the lagoon are usually finer, as conditions are quieter. The lagoonal muds differ from shelf muds. Glauconite is rare in lagoon muds, but oyster reefs may occur as along the Texas coast. The muds are found away from the channels, in which only coarse sediment can rest, owing to strong currents. Flocculation in the saline lagoon water expedites clay deposition. The source of the fine sediment is from inland areas, and transport is by rivers. The details of lagoon sedimentation vary with the nature of the river load. Sedimentation rates are much greater in the lagoon than the adjacent open ocean, because deposition is continuous over much of the lagoon and is often aided by flocculation and vegetation. In the Texas lagoons from 1875 to 1936, 20 cm (about 8 inches) of deposition occurred in spite of 30 cm (about 12 inches) of subsidence; the sedimentation rate, therefore, was about one metre in 100 years.

Waves, tides, and surf

The barrier islands are formed by the waves, which build up their equilibrium profile by deposition on a gradient that is too flat. The level of the growing accumulation may be raised by the wind, forming dunes. Where the land behind the growing barrier is low, it will become flooded to form a lagoon if sea level rises slowly. Such a rise of sea level has occurred during the past 20,000 years. As long as the barrier island can maintain its level above the sea, as sea level rises, the lagoon will exist until it is filled with sediment. Not all lagoons and barrier island complexes have formed during rising sea-level conditions, but, where there is evidence that no open-sea foreshore sediments lie on the land side of the barrier, this hypothesis seems likely. In some barriers, however, outbuilding of material by glacial outwash streams or rivers may provide a suitably low gradient and enough sediment to form a barrier, as along the south coast of Iceland. In other areas material carried alongshore to form a spit may develop into a bay-mouth barrier, enclosing a lagoon. Such features can be of sand or shingle (pebbles). The Fleet, a brackish body of water behind Chesil Beach in southern England, is an example of the latter type.

Waves within the lagoon may develop cuspate (pointed) spits along the land side of the barrier and the inner edge of the lagoon. These features may eventually break the lagoon into almost circular or oval water bodies. Examples occur in the Chukchi Sea lagoons in northeastern Russia and elsewhere where vegetation does not form marshland.

Storms and catastrophic events

Storms and tsunamis exert an effect on lagoons when they breach or overtop the barriers around a lagoon by raising the water level temporarily. Major changes in configuration can occur in a short time. Hurricanes, for instance, can cause serious effects on the coast of Texas, along which lagoons are common. Padre Island was lowered to below mean low tide at its southern end by one storm in 1919, and several washover channels were cut. (Washover channels are inlets of water excavated by the wave action produced by a severe storm.) The mainland shore also suffered erosion.

Deposition may also occur; saline marls have been laid down on freshwater marsh, and small beach ridges may be built inside the lagoon where the high water level drives sand inland over mud. Coral reefs are more resistant to storms than are mobile sandy barriers.

The effect of time

Lagoons of both types change with time. In both, a relative rise of sea level with time is important in the development of the lagoon. In coral atolls there is evidence from deep boring that English naturalist Charles Darwin’s original subsidence hypothesis of atoll formation, via barrier reefs from fringing reefs around a subsiding volcanic peak, is substantially correct in many cases. As long as the coral can maintain its growth at a suitable level as its foundation subsides, the atoll will continue to enclose a lagoon, which is floored by coral or calcareous sediment derived from the reef and which maintains its depth by growth or deposition.

The postglacial rise of sea level also has influenced barrier island formation in many instances. When sea level rises too fast, a barrier may be drowned, and its lagoon will cease to exist.

rsz_kivalina.jpg

#22 Re: Ganesh's Puzzles » General Quiz » 2021-07-25 00:07:12

Hi,

#7949. What does the term in Chemistry 'Chemical law' mean?

#7950. What does the term in Chemistry 'Chemical nomenclature' mean?

#23 Re: Help Me ! » Reflex angles » 2021-07-24 12:36:55

Hi Milenne and jabah013.307,

Please see the link below.

Reflex angles.

#24 Re: Ganesh's Puzzles » Doc, Doc! » 2021-07-24 00:52:46

Hi,

#1680. What does the medical term 'Rongeur' (instrument) mean?

Board footer

Powered by FluxBB