"triangle in which the ratio of the duplicated side to the base side equals the golden ratio. It is acute, with angles 36°, 72°, and 72°, making it the only triangle with angles in the proportions 1:2:2. The heptagonal triangle, with sides coinciding with a side, the shorter diagonal, and the longer diagonal of a regular heptagon, is obtuse, with angles formula_28 and formula_29 The only triangle with consecutive integers for an altitude and the sides is acute, having sides (13,14,15) and altitude from side 14 equal to 12. The smallest-perimeter triangle with integer sides in arithmetic progression, and the"
"Reflex A reflex, or reflex action, is an involuntary and nearly instantaneous movement in response to a stimulus. A reflex is made possible by neural pathways called reflex arcs which can act on an impulse before that impulse reaches the brain. The reflex is then an automatic response to a stimulus that does not receive or need conscious thought. Myotatic reflexes The myotatic reflexes (also known as ""deep tendon reflexes""), provide information on the integrity of the central nervous system and peripheral nervous system. Generally, decreased reflexes indicate a peripheral problem, and lively or exaggerated reflexes a central one. A"
"activity of a reflex on a scale from 0 to 4. While 2+ is considered normal, some healthy individuals are hypo-reflexive and register all reflexes at 1+, while others are hyper-reflexive and register all reflexes at 3+. Reflex A reflex, or reflex action, is an involuntary and nearly instantaneous movement in response to a stimulus. A reflex is made possible by neural pathways called reflex arcs which can act on an impulse before that impulse reaches the brain. The reflex is then an automatic response to a stimulus that does not receive or need conscious thought. Myotatic reflexes The myotatic"
"a triangle is right, obtuse, or acute, as follows. Let ""c"" be chosen to be the longest of the three sides and (otherwise there is no triangle according to the triangle inequality). The following statements apply: Edsger W. Dijkstra has stated this proposition about acute, right, and obtuse triangles in this language: where ""α"" is the angle opposite to side ""a"", ""β"" is the angle opposite to side ""b"", ""γ"" is the angle opposite to side ""c"", and sgn is the sign function. A Pythagorean triple has three positive integers ""a"", ""b"", and ""c"", such that In other words, a"
"Optokinetic response The optokinetic response is a combination of a slow-phase and fast-phase eye movements. It is seen when an individual follows a moving object with their eyes, which then moves out of the field of vision at which point their eye moves back to the position it was in when it first saw the object. The reflex develops at about 6 months of age. Optokinetic nystagmus (OKN) is nystagmus that occurs in response to a rotation movement. It is present normally. The optokinetic response allows the eye to follow objects in motion when the head remains stationary (e.g., observing"
"inradius ""r"" and circumradius ""R"", For an acute triangle with area ""K"", In an acute triangle, the sum of the circumradius ""R"" and the inradius ""r"" is less than half the sum of the shortest sides ""a"" and ""b"": while the reverse inequality holds for an obtuse triangle. For an acute triangle with medians ""m"" , ""m"" , and ""m"" and circumradius ""R"", we have while the opposite inequality holds for an obtuse triangle. Also, an acute triangle satisfies in terms of the excircle radii ""r"" , ""r"" , and ""r"" , again with the reverse inequality holding for an"
"deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative. In mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) to serve as variables standing for the size of some angle. (To avoid confusion with its other meaning, the symbol is typically not used for this purpose.) Lower case Roman letters (""a"", ""b"", ""c"", . . . ) are also used,"
"(not extended). In an obtuse triangle (one with an obtuse angle), the foot of the altitude to the obtuse-angled vertex falls in the interior of the opposite side, but the feet of the altitudes to the acute-angled vertices fall on the opposite extended side, exterior to the triangle. This is illustrated in the adjacent diagram: in this obtuse triangle, an altitude dropped perpendicularly from the top vertex, which has an acute angle, intersects the extended horizontal side outside the triangle. The three (possibly extended) altitudes intersect in a single point, called the orthocenter of the triangle, usually denoted by ."
"particularly in infants. When factitious blindness or malingering is suspected, check for optokinetic nystagmus to determine whether there is an intact visual pathway. Optokinetic response The optokinetic response is a combination of a slow-phase and fast-phase eye movements. It is seen when an individual follows a moving object with their eyes, which then moves out of the field of vision at which point their eye moves back to the position it was in when it first saw the object. The reflex develops at about 6 months of age. Optokinetic nystagmus (OKN) is nystagmus that occurs in response to a rotation"
"rectus, the superior rectus, the inferior oblique, and the superior oblique. When the muscles exert different tensions, a torque is exerted on the globe that causes it to turn, in almost pure rotation, with only about one millimeter of translation. Thus, the eye can be considered as undergoing rotations about a single point in the center of the eye. Rapid eye movement, REM, typically refers to the sleep stage during which the most vivid dreams occur. During this stage, the eyes move rapidly. It is not in itself a unique form of eye movement. Saccades are quick, simultaneous movements of"
"reflex seizures can be categorized as either intrinsic or extrinsic. For a give person, the stimulus that triggers may be intrinsic, extrinsic, or a combination of both. Extrinsic stimuli are sensory stimuli that originate from the person's environment. Similar to intrinsic stimuli, extrinsic stimuli can be divided into two categories, either simple or complex. Examples of simple extrinsic stimuli include flashing lights or touch while complex extrinsic stimuli can include music, language, reading, or stimulation from eating. Some of the more common types of reflex epilepsy include light and music. Photosensitive epilepsy is an abnormal sensitivity of the brain to"
"Accommodation reflex The accommodation reflex (or accommodation-convergence reflex) is a reflex action of the eye, in response to focusing on a near object, then looking at a distant object (and vice versa), comprising coordinated changes in vergence, lens shape and pupil size (accommodation). It is dependent on cranial nerve II (afferent limb of reflex), superior centers (interneuron) and cranial nerve III (efferent limb of reflex). The change in the shape of the lens is controlled by the ciliary muscles inside the eye. Changes in contraction of the ciliary muscles alter the focal distance of the eye, causing nearer or future"
"smallest-perimeter integer-sided triangle with distinct sides, is obtuse: namely the one with sides (2, 3, 4). The only triangles with one angle being twice another and having integer sides in arithmetic progression are acute: namely, the (4,5,6) triangle and its multiples. There are no acute integer-sided triangles with area = perimeter, but there are three obtuse ones, having sides (6,25,29), (7,15,20), and (9,10,17). The smallest integer-sided triangle with three rational medians is acute, with sides (68, 85, 87). Heron triangles have integer sides and integer area. The oblique Heron triangle with the smallest perimeter is acute, with sides (6, 5,"
"of a limit in mathematics, and this connection is explained more fully below. The asymptotes most commonly encountered in the study of calculus are of curves of the form . These can be computed using limits and classified into ""horizontal"", ""vertical"" and ""oblique"" asymptotes depending on their orientation. Horizontal asymptotes are horizontal lines that the graph of the function approaches as ""x"" tends to +∞ or −∞. As the name indicates they are parallel to the ""x""-axis. Vertical asymptotes are vertical lines (perpendicular to the ""x""-axis) near which the function grows without bound. Oblique asymptotes are diagonal lines such that"
"Reflex asystolic syncope Reflex asystolic syncope, reflex anoxic seizures or RAS are a form of syncope encountered mainly, but not exclusively, in young children. Reflex anoxic seizures are not epileptic seizures or epilepsy. This is usually a consequence of a reduction in cerebral perfusion by oxygenated blood. It can be a result of either a sudden reduction in the blood flow to the brain, a drop in the oxygen content of the blood supplying the brain, or a combination of the two. Syncope can have different meanings ranging from transient loss of consciousness, usually accompanied by a decrease or loss"
"to the action of the inferior rectus and superior oblique muscles. When the eye is abducted, the rectus muscles are the prime vertical movers. Elevation is due to the action of the superior rectus, and depression is due to the action of the inferior rectus. When the eye is adducted, the oblique muscles are the prime vertical movers. Elevation is due to the action of the inferior oblique muscle, while depression is due to the action of the superior oblique muscle. The oblique muscles are also primarily responsible for torsional movements. The brain exerts ultimate control over both voluntary and"
"in which the Euler line is parallel to one side are acute. This property holds for side BC if and only if formula_2 If angle ""C"" is obtuse then for sides ""a"", ""b"", and ""c"" we have with the left inequality approaching equality in the limit only as the apex angle of an isosceles triangle approaches 180°, and with the right inequality approaching equality only as the obtuse angle approaches 90°. If the triangle is acute then If C is the greatest angle and ""h"" is the altitude from vertex ""C"", then for an acute triangle with the opposite inequality"
"Abscissa and ordinate In mathematics, the abscissa (; plural ""abscissae"" or ""abscissæ"" or ""abscissas"") and the ordinate are respectively the first and second coordinate of a point in a coordinate system. The abscissa of a point is the signed measure of its projection on the primary axis, whose absolute value is the distance between the projection and the origin of the axis, and whose sign is given by the location on the projection relative to the origin (before: negative; after: positive). The ordinate of a point is the signed measure of its projection on the secondary axis, whose absolute value"
"Patellar reflex The patellar reflex or knee-jerk (myotatic) (monosynaptic) (American spelling knee reflex) is a stretch reflex which tests the L2, L3, and L4 segments of the spinal cord. Striking the patellar tendon with a reflex hammer just below the patella stretches the muscle spindle in the quadriceps muscle. This produces a signal which travels back to the spinal cord and synapses (without interneurons) at the level of L3 in the spinal cord, completely independent of higher centres. From there, an alpha motor neuron conducts an efferent impulse back to the quadriceps femoris muscle, triggering contraction. This contraction, coordinated with"
"Reflexive operator algebra In functional analysis, a reflexive operator algebra ""A"" is an operator algebra that has enough invariant subspaces to characterize it. Formally, ""A"" is reflexive if it is equal to the algebra of bounded operators which leave invariant each subspace left invariant by every operator in ""A"". This should not be confused with a reflexive space. Nest algebras are examples of reflexive operator algebras. In finite dimensions, these are simply algebras of all matrices of a given size whose nonzero entries lie in an upper-triangular pattern. In fact if we fix any pattern of entries in an ""n"""
". The power of the point with respect to the circle is equal to both and . Therefore, which is the law of cosines. Using algebraic measures for line segments (allowing negative numbers as lengths of segments) the case of obtuse angle () and acute angle () can be treated simultaneously. By using the law of sines and knowing that the angles of a triangle must sum to 180 degrees, we have the following system of equations (the three unknowns are the angles): Then, by using the third equation of the system, we obtain a system of two equations in"
"Optic equation In number theory, the optic equation is an equation that requires the sum of the reciprocals of two positive integers ""a"" and ""b"" to equal the reciprocal of a third positive integer ""c"": Multiplying both sides by ""abc"" shows that the optic equation is equivalent to a Diophantine equation (a polynomial equation in multiple integer variables). All solutions in integers ""a, b, c"" are given in terms of positive integer parameters ""m, n, k"" by where ""m"" and ""n"" are coprime. The optic equation, permitting but not requiring integer solutions, appears in several contexts in geometry. In a"
"according to This implies that the longest side in an obtuse triangle is the one opposite the obtuse-angled vertex. An acute triangle has three inscribed squares, each with one side coinciding with part of a side of the triangle and with the square's other two vertices on the remaining two sides of the triangle. (In a right triangle two of these are merged into the same square, so there are only two distinct inscribed squares.) However, an obtuse triangle has only one inscribed square, one of whose sides coincides with part of the longest side of the triangle. All triangles"
"Reflex seizure Reflex seizures are epileptic seizures that are consistently induced by a specific stimulus or trigger making them distinct from other epileptic seizures, which are usually unprovoked. Reflex seizures are otherwise similar to unprovoked seizures and may be focal (simple or complex), generalized, myoclonic, or absence seizures. Epilepsy syndromes characterized by repeated reflex seizures are known as reflex epilepsies. Photosensitive seizures are often myoclonic, absence, or focal seizures in the occipital lobe, while musicogenic seizures are associated with focal seizures in the temporal lobe. Triggers may include various stimuli with the most common (75 to 80%) being flickering lights"
"(2012), whether this class forms a category with properties similar to those of Ste. Reflexive space In the area of mathematics known as functional analysis, a reflexive space is a Banach space (or more generally a locally convex topological vector space) that coincides with the continuous dual of its continuous dual space, both as linear space and as topological space. Reflexive Banach spaces are often characterized by their geometric properties. Suppose formula_1 is a normed vector space over the number field formula_2 or formula_3 (the real or complex numbers), with a norm formula_4. Consider its dual normed space formula_5, that"
"stretch reflex is the contraction of a muscle in response to its lengthwise stretch. While the reflexes above are stimulated mechanically, the term H-reflex refers to the analogous reflex stimulated electrically, and tonic vibration reflex for those stimulated to vibration. A tendon reflex is the contraction of a muscle in response to striking its tendon. The Golgi tendon reflex is the inverse of a stretch reflex. Newborn babies have a number of other reflexes which are not seen in adults gradually,and are referred to as primitive reflexes. These automatic reactions to stimuli enable infants to respond to the environment before"
"Acute stress reaction Acute stress reaction (also called acute stress disorder, psychological shock, mental shock, or simply shock) is a psychological condition arising in response to a terrifying or traumatic event, or witnessing a traumatic event that induces a strong emotional response within the individual. It should not be confused with the unrelated circulatory condition of shock/hypoperfusion. Acute stress reaction (ASR) may develop into delayed stress reaction (better known as Posttraumatic stress disorder, or PTSD) if stress is not correctly managed. ASR is characterized by re-living and avoiding reminders of an aversive event, as well as generalized hypervigilance after initial"
"Ocular tilt reaction The Ocular tilt reaction (OTR), comprises skew deviation, head tilt and ocular torsion involving structures of the inner ear responsible for maintenance of balance of the body i.e. the semi-circular canals (SCC), utricle and saccule. Each anterior semi-circular canals has excitatory projections to the ipsilateral superior rectus muscle and its yoke i.e., the contralateral inferior oblique while simultaneously inhibiting the ipsilateral inferior rectus muscle and its yoke i.e. the contralateral superior oblique. Also, each posterior semi-circular canals has excitatory projections to the ipsilateral superior oblique and its yoke i.e. the contralateral inferior rectus, while simultaneously inhibiting the"
"two adjacent acute angles on its longer ""base"" edge, while an obtuse trapezoid has one acute and one obtuse angle on each ""base"". An isosceles trapezoid is a trapezoid where the sides (legs) have the same length, and the base angles have the same measure. It has reflection symmetry. This is possible for acute or right trapezoids. A parallelogram is 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 or right trapezoids. A tangential trapezoid is a trapezoid that has an incircle. A Saccheri quadrilateral"
"obtuse triangle. For an acute triangle with semiperimeter ""s"", and the reverse inequality holds for an obtuse triangle. For an acute triangle with area ""K"", For an acute triangle the distance between the circumcenter ""O"" and the orthocenter ""H"" satisfies with the opposite inequality holding for an obtuse triangle. For an acute triangle the distance between the incircle center ""I"" and orthocenter ""H"" satisfies where ""r"" is the inradius, with the reverse inequality for an obtuse triangle. If one of the inscribed squares of an acute triangle has side length ""x"" and another has side length ""x"" with ""x"" <"
"as hormones in the body. To start the reflex, the afferent impulses are transmitted to the medulla of the brain this involves the stimulus which is then interpreted. The efferent impulses are then triggered by the medulla causing the signal to travel down the larynx and bronchial tree. This then triggers a cascade of events that involve the intercostal muscles, abdominal wall, diaphragm and pelvic floor which in conjunction together create the reflex known as coughing. There are 3 main types of chronic cough which are the following: Typical evaluation of chronic cough begins with diagnosing the persons lifestyle choices"
"three sides of the triangle. Points ""G"", ""H"", and ""I"" are the feet of the altitudes of the triangle. Points ""J"", ""K"", and ""L"" are the midpoints of the line segments between each altitude's vertex intersection (points ""A"", ""B"", and ""C"") and the triangle's orthocenter (point ""S""). For an acute triangle, six of the points (the midpoints and altitude feet) lie on the triangle itself; for an obtuse triangle two of the altitudes have feet outside the triangle, but these feet still belong to the nine-point circle. Although he is credited for its discovery, Karl Wilhelm Feuerbach did not entirely"
"by opposing the internal pressure within the elastic lens, keep it relatively flattened. Opposite of fixating on a near object, the ciliary muscle relaxes and the diameter of the lens increases to increase the lens’ size. The tension along the suspensory ligaments is increased to flatten the lens and decrease the curvature and achieve a lower refractive power. Three regions make up the accommodation neural circuit, the afferent limb, the efferent limb and the ocular motor neurons that are between the afferent and efferent limb. Accommodation reflex The accommodation reflex (or accommodation-convergence reflex) is a reflex action of the eye,"