A bay is a recessed, coastal body of water that directly connects to a larger main body of water, such as an ocean , a lake , or another bay. A large bay is usually called a gulf , sea , sound , or bight . A cove is a small, circular bay with a narrow entrance. A fjord is an elongated bay formed by glacial action. The term embayment is also used for related features , such as extinct bays or freshwater environments.
16-522: Massachusetts Bay is a bay on the Gulf of Maine that forms part of the central coastline of the Commonwealth of Massachusetts . The bay extends from Cape Ann on the north to Plymouth Harbor on the south, a distance of about 42 miles (68 km). Its northern and southern shores incline toward each other through the entrance to Boston Harbor , where they are about five miles apart. The depth from
32-465: A and b , and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter. The length of the resulting segment is the geometric mean. This can be proven by applying the Pythagorean theorem to three similar right triangles, each having as vertices the point where the perpendicular touches the semicircle and two of the three endpoints of the segments of lengths
48-477: A and b . The construction of the geometric mean can be used to transform any rectangle into a square of the same area, a problem called the quadrature of a rectangle. The side length of the square is the geometric mean of the side lengths of the rectangle. More generally, it is used as a lemma in a general method for transforming any polygonal shape into a similar copy of itself with the area of any other given polygonal shape. The Farey sequence of order n
64-402: A semicircle is a one-dimensional locus of points that forms half of a circle . It is a circular arc that measures 180° (equivalently, π radians , or a half-turn ). It only has one line of symmetry ( reflection symmetry ). In non-technical usage, the term "semicircle" is sometimes used to refer to either a closed curve that also includes the diameter segment from one end of the arc to
80-441: A bay often reduces the strength of winds and blocks waves . Bays may have as wide a variety of shoreline characteristics as other shorelines. In some cases, bays have beaches , which "are usually characterized by a steep upper foreshore with a broad, flat fronting terrace". Bays were significant in the history of human settlement because they provided easy access to marine resources like fisheries . Later they were important in
96-453: A bay unless its area is as large as (or larger than) that of the semi-circle whose diameter is a line drawn across the mouth of that indentation — otherwise it would be referred to as a bight . There are various ways in which bays can form. The largest bays have developed through plate tectonics . As the super-continent Pangaea broke up along curved and indented fault lines, the continents moved apart and left large bays; these include
112-644: A torpedo into Provincetown , a depth charge into Gloucester , and mustard munitions into New Bedford . Bay A bay can be the estuary of a river, such as the Chesapeake Bay , an estuary of the Susquehanna River . Bays may also be nested within each other; for example, James Bay is an arm of Hudson Bay in northeastern Canada . Some large bays, such as the Bay of Bengal and Hudson Bay, have varied marine geology . The land surrounding
128-690: Is sometimes considered to be part of Massachusetts Bay. Under this interpretation, the name "Massachusetts Bay" denotes the entire rectangular area of ocean between Cape Ann and Cape Cod . The Massachusetts Bay Disposal Site in deep water off the coast has been used for ocean dumping , to dispose of munitions, dredged material, rock and construction debris and sunken vessels. Chemical warfare munitions were dumped between 1919 and 1970, and hundreds of thousands of tons of surplus artillery and munitions were dumped after World War II. The majority later washed up on shore. Most of them are inert unexploded ordnance , but occasionally they are live. Fishermen have brought
144-423: Is the sequence of completely reduced fractions which when in lowest terms have denominators less than or equal to n , arranged in order of increasing size. With a restricted definition, each Farey sequence starts with the value 0, denoted by the fraction 0 / 1 , and ends with the fraction 1 / 1 . Ford circles can be constructed tangent to their neighbours, and to
160-483: The Gulf of Guinea , the Gulf of Mexico , and the Bay of Bengal , which is the world's largest bay. Bays also form through coastal erosion by rivers and glaciers . A bay formed by a glacier is a fjord . Rias are created by rivers and are characterised by more gradual slopes. Deposits of softer rocks erode more rapidly, forming bays, while harder rocks erode less quickly, leaving headlands . Semi-circle In mathematics (and more specifically geometry ),
176-420: The base of the triangle to Boston Harbor is about 21 miles (34 km). The westmost point of the bay is at the city of Boston . The northern shore of Massachusetts Bay is rocky and irregular, but the southern shore is low, marshy, and sandy. Along the shores are a number of capes and headlands, and off the coast a number of small islands, especially in the entrance to Boston Harbor. The principal inlets are: on
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#1732772352444192-432: The center of the circle containing the given semicircle. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass. For a semicircle with a diameter of a + b , the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths
208-527: The development of sea trade as the safe anchorage they provide encouraged their selection as ports . The United Nations Convention on the Law of the Sea defines a bay as a well-marked indentation in the coastline, whose penetration is in such proportion to the width of its mouth as to contain land-locked waters and constitute more than a mere curvature of the coast. An indentation, however, shall not be regarded as
224-470: The north coast, Gloucester Harbor, Nahant Bay, Salem Harbor , Marblehead Harbor , and Lynn Harbor, and on the west, Boston Harbor , Dorchester Bay , and Quincy Bay (the two latter being part of the Outer Boston Harbor), and on the south coast, Hingham Bay . Massachusetts Bay is itself part of the Gulf of Maine , which extends from Nova Scotia south to Cape Cod Bay . Cape Cod Bay
240-443: The other or to the half- disk , which is a two-dimensional geometric region that further includes all the interior points. By Thales' theorem , any triangle inscribed in a semicircle with a vertex at each of the endpoints of the semicircle and the third vertex elsewhere on the semicircle is a right triangle , with a right angle at the third vertex. All lines intersecting the semicircle perpendicularly are concurrent at
256-401: The x-axis at these points. Semicircles joining adjacent points on the x-axis pass through the points of contact at right angles. The equation of a semicircle with midpoint ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} on the diameter between its endpoints and which is entirely concave from below is If it is entirely concave from above,
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