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Height — Grokipedia Fact-checked by Grok 3 months ago Height Ara Eve Leo Sal 1x Human height, or stature, is the vertical distance from the bottom of the feet to the top of the head in a standing human body . [1] It serves as a key anthropometric measure reflecting skeletal growth and overall physical development. [2] Height is predominantly influenced by genetic factors, with heritability estimates ranging from 80% to 90% in well-nourished populations, indicating that inherited variants account for the majority of variation among individuals. [3] [4] Environmental influences, particularly childhood nutrition and exposure to disease , modulate this genetic potential, especially in populations with suboptimal conditions. [4] [5] Males typically exceed females in average height by about 7% globally, a dimorphism rooted in sex-specific genetic and hormonal mechanisms. [6] Global averages for adults born in the late 20th century approximate 171 cm for men and 159 cm for women, though these vary substantially across regions due to differences in genetic ancestry and historical nutrition . [6] In the United States, recent data report mean heights of 175 cm for men and 161 cm for women. [7] Over the past century, secular increases in height—up to 20 cm in some cohorts—have occurred in many nations, primarily attributable to improved protein intake and reduced infectious burdens during growth periods, though gains have plateaued or reversed in certain high-income settings amid rising obesity . [8] [9] These trends underscore height as a sensitive indicator of population-level health and environmental quality. [5] Etymology and General Concepts Etymology The English noun height , denoting the vertical distance from the base to the top of an object or the highest point of something, originates from Old English hīehþu (or variant Anglian hehþo ), which referred to the summit, highest part, or even the heavens. [10] [11] This form derives from the Proto-Germanic abstract noun hauhiþō , constructed from the root of hauhaz ("high") combined with the suffix -iþō , used to form nouns indicating quality or state. [10] Cognates appear in other Germanic languages , such as Old High German hōhida ("height"). [11] By Middle English (circa 1100–1500), the word evolved into forms like heighte or heighthe , retaining its core sense of elevation or stature while also extending metaphorically to imply excellence or loftiness, as in moral or social standing. [10] [12] The modern spelling "height" standardized in the Early Modern English period, though a folk-etymological variant heighth (influenced by analogy with nouns like width ) persisted in some dialects into the 19th and 20th centuries, particularly in American English speech, before being classified as nonstandard. [13] The term's primary physical connotation solidified over time, distinguishing it from related adjectives like high , which retained broader adjectival uses. [12] Definition and Units of Measurement Height is the vertical distance measured from the base to the top of an object or figure, typically perpendicular to the base. [14] This measurement distinguishes height from other dimensions like length or width by emphasizing the upright or perpendicular extent, often referred to as the "tallness" of the subject when oriented level. [15] In geometric contexts, height may also denote the perpendicular distance between a vertex and the opposite base or side of a shape . [16] The International System of Units (SI) designates the meter (m) as the base unit for height, defined precisely as the distance light travels in vacuum in 1/299,792,458 of a second. [17] Common decimal multiples and submultiples include the kilometer (km = 1,000 m) for large-scale elevations, the centimeter (cm = 0.01 m) for human stature and smaller objects, and the millimeter (mm = 0.001 m) for precise measurements. [18] In customary systems prevalent in the United States and some other regions, height is typically measured in feet (ft) and inches (in), where 1 ft equals 12 in and 1 in equals exactly 2.54 cm. [18] Conversions between systems are standardized, with 1 m equaling approximately 3.28084 ft, facilitating international comparisons despite regional preferences. [19] For human height , clinical and anthropometric standards often specify centimeters in metric countries and feet/inches in imperial ones, ensuring consistency in data reporting. [20] Height in Mathematics and Geometry Fundamental Definitions In geometry , height refers to the perpendicular distance measured from a designated base of a figure to its opposite vertex, side, or face. [21] This measurement is fundamental for calculating areas and volumes of polygons and polyhedra, where the base serves as the reference plane or line. [16] For instance, in a triangle , the height is the length of the segment drawn perpendicularly from a vertex to the line containing the opposite side, also termed the altitude. [22] The terms height and altitude are often used synonymously in planar geometry, though altitude strictly denotes the perpendicular segment itself, while height emphasizes its measure. [23] In three-dimensional figures such as prisms or cylinders, height extends this concept to the perpendicular distance between the two parallel bases. [24] This perpendicularity ensures that the height aligns orthogonally to the base, distinguishing it from oblique distances that might otherwise overestimate or underestimate the figure's extent. [20] Height's computation relies on coordinate geometry or trigonometric relations when direct perpendicular measurement is impractical; for example, in a right triangle with legs a and b , the height relative to the hypotenuse can be derived as (a * b) / c , where c is the hypotenuse length . [16] Such definitions underpin theorems like the area formula for triangles, A = (1/2) * base * height , applicable across acute, obtuse, and right configurations, provided the foot of the perpendicular falls appropriately—inside for acute triangles, on a vertex for right, or extended for obtuse. [22] Applications to Geometric Shapes and Figures In two-dimensional geometry , height represents the perpendicular distance from a chosen base to the opposite vertex or parallel side, serving as a fundamental parameter in area computations for polygons. For a triangle , the area A A A is given by A = 1 2 b h A = \frac{1}{2} b h A = 2 1 ​ bh , where b b b is the length of the base and h h h is the perpendicular height to that base; this formula derives from dissecting the triangle into primitive rectangular elements and holds for acute, right, and obtuse triangles alike, with the height potentially falling outside the figure in the latter case. [25] [26] For parallelograms, the area formula simplifies to A = b h A = b h A = bh , where h h h is the perpendicular distance between the parallel bases, reflecting the shape's deformability from a rectangle while preserving area under shear transformations. [27] In trapezoids, which possess exactly one pair of parallel sides, the area is A = b 1 + b 2 2 h A = \frac{b_1 + b_2}{2} h A = 2 b 1 ​ + b 2 ​ ​ h , averaging the lengths of the parallel bases b 1 b_1 b 1 ​ and b 2 b_2 b 2 ​ and multiplying by the height between them; this accounts for the linear interpolation of widths across the figure. [28] Extending to three-dimensional figures, height functions analogously in volume formulas, often perpendicular to the base plane. Prisms, including rectangular, triangular, and other polygonal bases, have volume V = B h V = B h V = B h , where B B B is the base area and h h h the perpendicular height between bases, invariant under lateral translation. [29] Cylinders follow the same relation, V = π r 2 h V = \pi r^2 h V = π r 2 h , treating the circular base area as B B B . Pyramids and cones generalize tapering solids, with volume V = 1 3 B h V = \frac{1}{3} B h V = 3 1 ​ B h , where the factor of one-third arises from the quadratic scaling of cross-sectional area with height in similar figures, as established through integration or Cavalieri's principle comparing slices to prisms. [30] [31] These applications underscore height's role in decomposing complex shapes into integrable primitives, enabling precise quantification without reliance on coordinate systems. Height in Physical and Earth Sciences In Physics and Mechanics In physics and mechanics, height refers to the vertical coordinate or elevation of an object relative to a reference level, often crucial in analyzing gravitational effects on motion and equilibrium. This dimension appears prominently in classical mechanics, where it serves as a positional variable in coordinate systems, influencing energy states, forces, and stability under gravity's near-uniform field near Earth's surface. Gravitational potential energy, a key concept, quantifies the work gravity can perform on an object based on its height: $ U = mgh $, with $ m $ as mass, $ g \approx 9.8 , \mathrm{m/s^2} $ as acceleration due to gravity, and $ h $ as height above the reference. [32] This formula assumes small heights compared to Earth's radius (valid up to ~100 km), deriving from the conservative gravitational force $ \mathbf{F} = -mg \hat{y} $, where potential integrates force over vertical displacement. [33] In dynamic systems, changes in height convert potential energy to kinetic energy via conservation laws, as in pendulums or falling bodies, where $ \Delta U = - \Delta K $ holds absent dissipation. [34] The height of an object's center of mass governs mechanical stability, determining tipping thresholds. Stability improves with lower center-of-mass height relative to base width, as the restoring torque from gravity resists rotation until the center-of-mass projection exits the support base. [35] For vehicles, higher center-of-gravity elevation—e.g., from roof loads or suspension lift—reduces the critical rollover angle, calculable as $ \theta_c = \tan^{-1}