A crinkle crankle wall, also known as a crinkum crankum, sinusoidal, serpentine, ribbon or wavy wall, is an unusual type of structural or garden wall built in a serpentine shape with alternating curves, originally used in Ancient Egypt, but also typically found in Suffolk in England. [1]
The sinusoidal curves in the wall provide stability and help it to resist lateral forces, [2] leading to greater strength than a straight wall of the same thickness of bricks without the need for buttresses.
The phrase "crinkle crankle" is an ablaut reduplication, defined as something with bends and turns, first attested in 1598 [3] (though "crinkle" and "crankle" have somewhat longer histories). [4] [5]
Sinusoidal walls featured extensively in the architecture of Egyptian city of Aten, thought to date from the period of Amenhotep III, some 3,400 years ago (1386–1353 BCE). [6] Other examples exist at Tel el-Retaba [7] and Thebes. [8]
As a minor part of a larger system of fortification, such a wall may have been used to force oncoming troops to break ranks from closed to open ranks, and further expose them to defensive assault.[ citation needed ]
Many crinkle crankle walls are found in East Anglia, England, where the marshes of The Fens were drained by Dutch engineers starting in the mid-1600s. The construction of these walls has been attributed to these engineers, who called them slangenmuur (nl), meaning snake wall. [9] The county of Suffolk claims at least 100 examples, [10] twice as many as in the whole of the rest of the country.[ citation needed ] The crinkle crankle wall running from the former manor house to All Saints' Church in the estate village of Easton is believed to be the longest existing example in England. [1] [11]
The term "crinkle crankle" began to be applied to wavy walls in the 18th century, and is said to derive from a Suffolk dialect.[ citation needed ] At that time these garden walls were usually aligned east-west, so that one side faced south to catch the warming sun. They were used for growing fruit. [2] [12]
In Lymington, Hampshire, there are at least two examples of crinkle crankle walls. The older of the two is thought to have been constructed at the time of the Napoleonic Wars (1803–1815) by exiled Hanoverian soldiers living in the adjacent house. [13]
Thomas Jefferson (1743–1826) incorporated serpentine walls into the architecture of the University of Virginia, which he founded in 1819. Flanking both sides of its landmark rotunda and extending down the length of the lawn are ten pavilions, each with its own walled garden separated by crinkle crankle walls. Although some authorities claim that Jefferson invented this design, he was merely adapting a well-established English style of construction. A university document in his own hand shows how he calculated the savings and combined aesthetics with utility. [14]
A crinkle crankle wall offers material-saving advantages when compared to a straight wall. This is primarily due to its ability to maintain structural integrity while being thinner, especially against horizontal forces like wind. [15]
The mathematical basis for this material efficiency involves the calculation of the wall's arc length. Modeled after a sine wave, the length of a crinkle crankle wall is given by the integral , where is the amplitude of the sine wave. For , this integral results in approximately 7.6404, indicating that the crinkle crankle wall is about 22% longer than a straight wall covering the same linear distance but can be thinner. [15]
Usually snake-shaped walls were built in orchards from east to west to retain heat from the sun, creating a suitable climate for fruit trees. A 120 m long snake wall can be found at Zuylen Castle in Maarsen, the Netherlands, which was built during the transformation of the formal garden by Jan David Zocher in 1841. [16] The church of San Carlo alle Quattro Fontane, Rome, Italy, designed by Francesco Borromini and built towards the end of his life in 1588–1593, has a sinuous façade. [17] At the Massachusetts Institute of Technology, the Baker House dormitory (1949) has a snake-like shape. [18]
Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together.
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In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
In mechanics and physics, simple harmonic motion is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an oscillation that is described by a sinusoid which continues indefinitely.
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.
In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of root mean square (RMS) current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average product of the two. A negative power factor occurs when the device generates real power, which then flows back towards the source.
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Bramfield is a village and civil parish in the east of the English county of Suffolk, and in the East Suffolk district. It is 5 miles (8.0 km) south of the market town of Halesworth on the A144 road between Halesworth and the A12 road, one of the main arterial routes through the county. The village is 24 miles (39 km) north-east of the county town of Ipswich and 15 miles (24 km) south-west of the port of Lowestoft. The East Suffolk railway line between Lowestoft and Ipswich passes close to the west of the village with Halesworth railway station being the nearest station.
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In mathematics, the values of the trigonometric functions can be expressed approximately, as in , or exactly, as in . While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots. The angles with trigonometric values that are expressible in this way are exactly those that can be constructed with a compass and straight edge, and the values are called constructible numbers.
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is widely used as a name for this function in software libraries.
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