36-454: The trapezius is a large paired trapezoid -shaped surface muscle that extends longitudinally from the occipital bone to the lower thoracic vertebrae of the spine and laterally to the spine of the scapula . It moves the scapula and supports the arm . The trapezius has three functional parts: The trapezius muscle resembles a trapezium , also known as a trapezoid, or diamond-shaped quadrilateral . The word "spinotrapezius" refers to
72-406: A = 0 {\displaystyle d-c=b-a=0} , but it is an ex-tangential quadrilateral (which is not a trapezoid) when | d − c | = | b − a | ≠ 0 {\displaystyle |d-c|=|b-a|\neq 0} . Given a convex quadrilateral, the following properties are equivalent, and each implies that the quadrilateral
108-418: A special case the well-known formula for the area of a triangle , by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point. The 7th-century Indian mathematician Bhāskara I derived the following formula for the area of a trapezoid with consecutive sides a , c , b , d : where a and b are parallel and b > a . This formula can be factored into
144-540: A trapezoid ( / ˈ t r æ p ə z ɔɪ d / ) in North American English , or trapezium ( / t r ə ˈ p iː z i ə m / ) in British English , is a quadrilateral that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides ) if they are not parallel; otherwise, the trapezoid
180-419: A drooping shoulder, and shoulder and neck pain . Intractable trapezius palsy can be surgically managed with an Eden–Lange procedure . The trapezius muscle is one of the commonly affected muscles in facioscapulohumeral muscular dystrophy (FSHD). The lower and middle fibers are affected initially, and the upper fibers are commonly spared until late in the disease. Although rare, underdevelopment or absence of
216-401: A more symmetric version When one of the parallel sides has shrunk to a point (say a = 0), this formula reduces to Heron's formula for the area of a triangle. Another equivalent formula for the area, which more closely resembles Heron's formula, is where s = 1 2 ( a + b + c + d ) {\displaystyle s={\tfrac {1}{2}}(a+b+c+d)}
252-399: A single output based on a select signal. Typical designs will employ trapezoids without specifically stating they are multiplexors as they are universally equivalent. Rhomboid muscles The rhomboid muscles ( / ˈ r ɒ m b ɔɪ d / ), often simply called the rhomboids , are rhombus -shaped muscles associated with the scapula . There are two rhomboid muscles on each side of
288-538: A transposition of the terms. This was reversed in British English in about 1875, but it has been retained in American English to the present. The following table compares usages, with the most specific definitions at the top to the most general at the bottom. There is some disagreement whether parallelograms , which have two pairs of parallel sides, should be regarded as trapezoids. Some define
324-438: A trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. Some sources use the term proper trapezoid to describe trapezoids under the exclusive definition, analogous to uses of the word proper in some other mathematical objects. Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition ), making
360-485: A trapezoid is given by where a and b are the lengths of the parallel sides, h is the height (the perpendicular distance between these sides), and m is the arithmetic mean of the lengths of the two parallel sides. In 499 AD Aryabhata , a great mathematician - astronomer from the classical age of Indian mathematics and Indian astronomy , used this method in the Aryabhatiya (section 2.8). This yields as
396-732: Is a parallelogram, and there are two pairs of bases. A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast with the special cases below. A trapezoid is usually considered to be a convex quadrilateral in Euclidean geometry , but there are also crossed cases. If ABCD is a convex trapezoid, then ABDC is a crossed trapezoid. The metric formulas in this article apply in convex trapezoids. The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and
SECTION 10
#1732791404138432-441: Is a trapezoid: Additionally, the following properties are equivalent, and each implies that opposite sides a and b are parallel: The midsegment of a trapezoid is the segment that joins the midpoints of the legs. It is parallel to the bases. Its length m is equal to the average of the lengths of the bases a and b of the trapezoid, The midsegment of a trapezoid is one of the two bimedians (the other bimedian divides
468-431: Is possible for acute trapezoids or right trapezoids (as rectangles). A parallelogram is (under the inclusive definition) a trapezoid with two pairs of parallel sides. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). It is possible for obtuse trapezoids or right trapezoids (rectangles). A tangential trapezoid is a trapezoid that has an incircle . A Saccheri quadrilateral
504-442: Is similar to a trapezoid in the hyperbolic plane, with two adjacent right angles, while it is a rectangle in the Euclidean plane . A Lambert quadrilateral in the hyperbolic plane has 3 right angles. Four lengths a , c , b , d can constitute the consecutive sides of a non-parallelogram trapezoid with a and b parallel only when The quadrilateral is a parallelogram when d − c = b −
540-410: Is the semiperimeter of the trapezoid. (This formula is similar to Brahmagupta's formula , but it differs from it, in that a trapezoid might not be cyclic (inscribed in a circle). The formula is also a special case of Bretschneider's formula for a general quadrilateral ). From Bretschneider's formula, it follows that The bimedian connecting the parallel sides bisects the area. The lengths of
576-404: The accessory nerve . Sensation, including pain and the sense of joint position ( proprioception ), travel via the ventral rami of the third (C3) and fourth (C4) cervical spinal nerves . Since it is a muscle of the upper limb, the trapezius is not innervated by dorsal rami , despite being placed superficially in the back. Contraction of the trapezius muscle can have two effects: movement of
612-414: The trapezoidal rule for estimating areas under a curve. An acute trapezoid has two adjacent acute angles on its longer base edge. An obtuse trapezoid on the other hand has one acute and one obtuse angle on each base . An isosceles trapezoid is a trapezoid where the base angles have the same measure. As a consequence the two legs are also of equal length and it has reflection symmetry . This
648-457: The angle bisectors to angles A and B intersect at P , and the angle bisectors to angles C and D intersect at Q , then In architecture the word is used to refer to symmetrical doors, windows, and buildings built wider at the base, tapering toward the top, in Egyptian style. If these have straight sides and sharp angular corners, their shapes are usually isosceles trapezoids . This was
684-420: The diagonals are where a is the short base, b is the long base, and c and d are the trapezoid legs. If the trapezoid is divided into four triangles by its diagonals AC and BD (as shown on the right), intersecting at O , then the area of △ {\displaystyle \triangle } AOD is equal to that of △ {\displaystyle \triangle } BOC , and
720-403: The extended nonparallel sides and the intersection point of the diagonals, bisects each base. The center of area (center of mass for a uniform lamina ) lies along the line segment joining the midpoints of the parallel sides, at a perpendicular distance x from the longer side b given by The center of area divides this segment in the ratio (when taken from the short to the long side) If
756-493: The human trapezius, although it is not commonly used in modern texts. In other mammals, it refers to a portion of the analogous muscle. The superior or upper (or descending) fibers of the trapezius originate from the spinous process of C7, the external occipital protuberance , the medial third of the superior nuchal line of the occipital bone (both in the back of the head), and the ligamentum nuchae . From this origin, they proceed downward and laterally to be inserted into
SECTION 20
#1732791404138792-519: The last did not have two sets of parallel sides – a τραπέζια ( trapezia literally 'table', itself from τετράς ( tetrás ) 'four' + πέζα ( péza ) 'foot; end, border, edge'). Two types of trapezia were introduced by Proclus (AD 412 to 485) in his commentary on the first book of Euclid's Elements : All European languages follow Proclus's structure as did English until the late 18th century, until an influential mathematical dictionary published by Charles Hutton in 1795 supported without explanation
828-399: The lengths of the parallel sides. Let the trapezoid have vertices A , B , C , and D in sequence and have parallel sides AB and DC . Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD . Then FG is the harmonic mean of AB and DC : The line that goes through both the intersection point of
864-408: The neck. Dysfunction of the trapezius can result in winged scapula , sometimes further specified as "lateral winging" and in an abnormal mobility or function of the scapula (scapular dyskinesia). There are multiple causes of trapezius dysfunction. Trapezius palsy , due to damage of the spinal accessory nerve , is characterized by difficulty with arm adduction and abduction , and associated with
900-716: The parallelogram a special type of trapezoid. The latter definition is consistent with its uses in higher mathematics such as calculus . This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid. This is also advocated in the taxonomy of quadrilaterals . Under the inclusive definition, all parallelograms (including rhombuses , squares and non-square rectangles ) are trapezoids. Rectangles have mirror symmetry on mid-edges; rhombuses have mirror symmetry on vertices, while squares have mirror symmetry on both mid-edges and vertices. A right trapezoid (also called right-angled trapezoid ) has two adjacent right angles . Right trapezoids are used in
936-409: The posterior border of the lateral third of the clavicle . The middle fibers, or transverse of the trapezius arise from the spinous process of the seventh cervical (both in the back of the neck), and the spinous processes of the first, second, and third thoracic vertebrae . They are inserted into the medial margin of the acromion , and into the superior lip of the posterior border of the spine of
972-422: The product of the areas of △ {\displaystyle \triangle } AOD and △ {\displaystyle \triangle } BOC is equal to that of △ {\displaystyle \triangle } AOB and △ {\displaystyle \triangle } COD . The ratio of the areas of each pair of adjacent triangles is the same as that between
1008-454: The scapula . The inferior or lower (or ascending) fibers of the trapezius arise from the spinous processes of the remaining thoracic vertebrae (T4–T12). From this origin, they proceed upward and laterally to converge near the scapula and end in an aponeurosis , which glides over the smooth triangular surface on the medial end of the spine, to be inserted into a tubercle at the apex of this smooth triangular surface. At its occipital origin,
1044-444: The scapula around the sternoclavicular articulation so that the acromion and inferior angles move up and the medial border moves down (upward rotation). The upper and lower fibers work in tandem with serratus anterior to upwardly rotate the scapulae, and work in opposition to the levator scapulae and the rhomboids , which effect downward rotation. An example of trapezius function is an overhead press . When activating together,
1080-406: The scapulae when the spinal origins are stable, and movement of the spine when the scapulae are stable. Its main function is to stabilize and move the scapula. The upper fibers elevate the scapulae, the middle fibers retract the scapulae, and the lower fibers depress the scapulae. In addition to scapular translation, the trapezius induces scapular rotation. The upper and lower fibers tend to rotate
1116-780: The standard style for the doors and windows of the Inca . The crossed ladders problem is the problem of finding the distance between the parallel sides of a right trapezoid, given the diagonal lengths and the distance from the perpendicular leg to the diagonal intersection. In morphology , taxonomy and other descriptive disciplines in which a term for such shapes is necessary, terms such as trapezoidal or trapeziform commonly are useful in descriptions of particular organs or forms. In computer engineering, specifically digital logic and computer architecture, trapezoids are typically utilized to symbolize multiplexors . Multiplexors are logic elements that select between multiple elements and produce
Trapezius - Misplaced Pages Continue
1152-408: The third thoracic vertebræ and forms, with that of the opposite muscle, a tendinous ellipse. The rest of the muscle arises by numerous short tendinous fibers. It is possible to feel the muscles of the superior trapezius as they become active by holding a weight in one hand in front of the body and, with the other hand, touching the area between the shoulder and the neck. Motor function is supplied by
1188-473: The trapezius has been reported to correlate to neck pain and poor scapular control that are not responsive to physical therapy . Absence of the trapezius has been reported in association with Poland syndrome . It is mainly used in throwing, with the deltoid muscle and rotator cuff . [REDACTED] This article incorporates text in the public domain from page 432 of the 20th edition of Gray's Anatomy (1918) Trapezoid In geometry ,
1224-401: The trapezius is connected to the bone by a thin fibrous lamina, firmly adherent to the skin. The superficial and deep epimysia are continuous with an investing deep fascia that encircles the neck and also contains both sternocleidomastoid muscles. At the middle, the muscle is connected to the spinous processes by a broad semi-elliptical aponeurosis , which reaches from the sixth cervical to
1260-443: The trapezoid into equal areas). The height (or altitude) is the perpendicular distance between the bases. In the case that the two bases have different lengths ( a ≠ b ), the height of a trapezoid h can be determined by the length of its four sides using the formula where c and d are the lengths of the legs and p = a + b + c + d {\displaystyle p=a+b+c+d} . The area K of
1296-415: The upper and lower fibers also assist the middle fibers (along with other muscles such as the rhomboids ) with scapular retraction/adduction. The trapezius also assists in abduction of the shoulder above 90 degrees by rotating the glenoid upward. Injury to cranial nerve XI will cause weakness in abducting the shoulder above 90 degrees. When the scapulae are stable, a co-contraction of both sides can extend
#137862