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20-512: 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

40-523: A code point in Unicode at U+2300 ⌀ DIAMETER SIGN , in the Miscellaneous Technical set. It should not be confused with several other characters (such as U+00D8 Ø LATIN CAPITAL LETTER O WITH STROKE or U+2205 ∅ EMPTY SET ) that resemble it but have unrelated meanings. It has the compose sequence Compose d i . The diameter of

60-418: A diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere . In more modern usage, the length d {\displaystyle d} of a diameter is also called the diameter. In this sense one speaks of

80-669: A hypercube or a set of scattered points. The diameter or metric diameter of a subset of a metric space is the least upper bound of the set of all distances between pairs of points in the subset. Explicitly, if S {\displaystyle S} is the subset and if ρ {\displaystyle \rho } is the metric , the diameter is diam ⁡ ( S ) = sup x , y ∈ S ρ ( x , y ) . {\displaystyle \operatorname {diam} (S)=\sup _{x,y\in S}\rho (x,y).} If

100-441: 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

120-453: 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

140-626: 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

160-461: Is any chord passing through the centre of the ellipse. For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate diameter. The longest diameter is called the major axis . The word "diameter" is derived from Ancient Greek : διάμετρος ( diametros ), "diameter of a circle", from διά ( dia ), "across, through" and μέτρον ( metron ), "measure". It

180-477: Is often abbreviated DIA , dia , d , {\displaystyle {\text{DIA}},{\text{dia}},d,} or ∅ . {\displaystyle \varnothing .} The definitions given above are only valid for circles, spheres and convex shapes. However, they are special cases of a more general definition that is valid for any kind of n {\displaystyle n} -dimensional (convex or non-convex) object, such as

200-690: 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

220-446: Is the same as the diameter of its convex hull . In medical terminology concerning a lesion or in geology concerning a rock, the diameter of an object is the least upper bound of the set of all distances between pairs of points in the object. In differential geometry , the diameter is an important global Riemannian invariant . In planar geometry , a diameter of a conic section is typically defined as any chord which passes through

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240-449: The width is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers . For a curve of constant width such as the Reuleaux triangle , the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. For an ellipse , the standard terminology is different. A diameter of an ellipse

260-445: 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 . Diameter In geometry ,

280-478: The conic's centre ; such diameters are not necessarily of uniform length, except in the case of the circle, which has eccentricity e = 0. {\displaystyle e=0.} The symbol or variable for diameter, ⌀ , is sometimes used in technical drawings or specifications as a prefix or suffix for a number (e.g. "⌀ 55 mm"), indicating that it represents diameter. Photographic filter thread sizes are often denoted in this way. The symbol has

300-409: The diameter rather than a diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r . {\displaystyle r.} For a convex shape in the plane , the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and

320-420: 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

340-521: 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

360-414: The empty set as a special case, assigning it a diameter of 0 , {\displaystyle 0,} which corresponds to taking the codomain of ρ {\displaystyle \rho } to be the set of nonnegative reals. For any solid object or set of scattered points in n {\displaystyle n} -dimensional Euclidean space , the diameter of the object or set

380-469: The metric ρ {\displaystyle \rho } is viewed here as having codomain R {\displaystyle \mathbb {R} } (the set of all real numbers ), this implies that the diameter of the empty set (the case S = ∅ {\displaystyle S=\varnothing } ) equals − ∞ {\displaystyle -\infty } ( negative infinity ). Some authors prefer to treat

400-461: 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

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