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17-592: Manhasset Bay , New York, is an embayment in western Long Island off Long Island Sound . Manhasset Bay forms the northeastern boundary of the Great Neck Peninsula and the southwestern boundary of the Cow Neck Peninsula ( Port Washington Peninsula or Manhasset Neck), in Nassau County , New York . On the north side of the bay, there are three points, Barkers Point at the entrance, Plum Point coming

34-459: 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

51-477: 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

68-402: 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

85-453: 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

102-589: 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. 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

119-411: Is considered to be one of the best harbors on Long Island Sound with little tidal current except at the entrance and average tidal displacement of only six feet. By the 1980s it was full of marinas and yacht clubs. The Sands Point Seaplane Base on Manhasset Bay was at one time the main airport for passenger service between New York and Europe. At the beginning of the 21st century, it had about 16% of all

136-423: 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

153-576: The Bay of Bengal and Hudson Bay, have varied marine geology . The land surrounding 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

170-616: The English settled around the bay in the 17th century because of the proximity of fish . The Bay was called Schout's Bay by the Dutch, and then Howe's Bay by the English. Subsequently, due to the presence of cattle raising, it came to be called Cow Bay, and the local neck, to the northeast, "Cow Neck". It finally became Manhasset Bay in 1907. In the 1920s, the bay began to switch from the cow-and-fish industry to support services for commercial boating, as it

187-529: 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 ),

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204-432: 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

221-521: 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

238-643: The furthest into the Bay, and Tom's Point in the back bay. On the other side, Hewlett Point forms the entrance nearly a mile from Barkers Point . Hart Island lies in the Sound just outside the mouth of Manhasset Bay. The Manhasset Bay area was likely first inhabited in the 17th century by the Matinecock tribe of Algonquin Indians . However, that view has been challenged. Then the Dutch and

255-414: The marinas and yacht clubs in the whole of Long Island Sound . Manhasset Bay's watershed consists of many smaller sub-water sheds. These sub-watersheds are: Bay 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

272-443: 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

289-401: 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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