A constant lunar tug on the Earth's equatorial bulge—a paunchy distortion of the planet's sphericity caused by its spin—keeps things in order.
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When Zimmermann spoke of pluralism and the "sphericity of time," he was making a claim about the essential simultaneity of experience, not about doing whatever one liked.
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If sphericity is violated, then the variance calculations may be distorted, which would result in an F-ratio that is inflated. Sphericity can be evaluated when there are three or more levels of a repeated measure factor and, with each additional repeated measures factor, the risk for violating sphericity increases. If sphericity is violated, a decision must be made as to whether a univariate or multivariate analysis is selected. If a univariate method is selected, the repeated- measures ANOVA must be appropriately corrected depending on the degree to which sphericity has been violated.
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By evaluating epsilon, we can determine the degree to which sphericity has been violated. If the variances of differences between all possible pairs of groups are equal and sphericity is exactly met, then epsilon will be exactly 1, indicating no departure from sphericity. If the variances of differences between all possible pairs of groups are unequal and sphericity is violated, epsilon will be below 1. The further epsilon is from 1, the worse the violation.
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75 or nothing is known about sphericity, the Greenhouse–Geisser correction should be applied. Another alternative procedure is using the multivariate test statistics (MANOVA) since they do not require the assumption of sphericity. However, this procedure can be less powerful than using a repeated measures ANOVA, especially when sphericity violation is not large or sample sizes are small. O’Brien and Kaiser suggested that when you have a large violation of sphericity (i.e.
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While Mauchly's test is one of the most commonly used to evaluate sphericity, the test fails to detect departures from sphericity in small samples and over-detects departures from sphericity in large samples. Consequently, the sample size has an influence on the interpretation of the results. In practice, the assumption of sphericity is extremely unlikely to be exactly met so it is prudent to correct for a possible violation without actually testing for a violation.
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Then the part is honed to improve a form characteristic such as roundness, flatness, cylindricity, or sphericity.
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The Huynh–Feldt correction, however, is believed to be too liberal and overestimates sphericity. This would result in incorrectly rejecting the alternative hypothesis that sphericity does not hold, when it does. Girden recommended a solution to this problem: when epsilon is > .75, the Huynh–Feldt correction should be applied and when epsilon is < .
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However, when the probability of Mauchly's test statistic is less than or equal to \alpha (i.e., p < \alpha), sphericity cannot be assumed and we would therefore conclude that there are significant differences between the variances of the differences. Sphericity is always met for two levels of a repeated measure factor and is, therefore, unnecessary to evaluate. Statistical software should not provide output for a test of sphericity for two levels of a repeated measure factor; however, some versions of SPSS produce an output table with degrees of freedom equal to 0, and a period in place of a numeric p value.
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Sphericity is an important assumption of a repeated-measures ANOVA. It is the condition where the variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) are equal. The violation of sphericity occurs when it is not the case that the variances of the differences between all combinations of the conditions are equal.
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Despite the scientific fact of Earth's sphericity, pseudoscientific flat Earth conspiracy theories are espoused by modern flat Earth societies and, increasingly, by unaffiliated individuals using social media.
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Mauchly's sphericity test or Mauchly's W is a statistical test used to validate a repeated measures analysis of variance (ANOVA). It was developed in 1940 by John Mauchly.
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39, No. 1 (1976), pp. 106–127 (107) A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation (1519–1522).Pigafetta, Antonio (1906).
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If sphericity is met, then \varepsilon = 1 . If sphericity is not met, then epsilon will be less than 1 (and the degrees of freedom will be overestimated and the F-value will be inflated). To correct for this inflation, multiply the Greenhouse–Geisser estimate of epsilon to the degrees of freedom used to calculate the F critical value. An alternative correction that is believed to be less conservative is the Huynh–Feldt correction (1976).
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The maturity of a sediment is related not only to the sorting (mean grain size and deviations), but also to the fragment sphericity, rounding and composition. Quartz-only sands are more mature than arkose or greywacke.
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E. Grant, Planets. Stars, & Orbs: The Medieval Cosmos, 1200-1687, (Cambridge: Cambridge Univ. Pr., 1994), pp. 626-630. Lindberg and Ronald Numbers write: "There was scarcely a Christian scholar of the Middle Ages who did not acknowledge [Earth's] sphericity and even know its approximate circumference".
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This is known as contrast variation. In addition to this effect the anomalous scatter is more sensitive to any deviation from sphericity of the electron cloud around the atom. This can lead to resonant effects involving transitions in the outer shell of the atom: resonant anomalous X-ray scattering.
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Fragment shape gives information on the length of sediment transport. The more rounded the clasts, the more water or wind- worn they are. Particle shape includes form and rounding. Form indicates whether a grain is more equant (round, spherical) or platy (flat, disc-like, oblate); as well as sphericity.
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The Erdapfel, the oldest surviving terrestrial globe (1492/93) The first direct demonstration of Earth's sphericity came in the form of the first circumnavigation in history, an expedition captained by Portuguese explorer Ferdinand Magellan.Nowell, Charles E. ed. (1962). Magellan's Voyage around the World: Three Contemporary Accounts. Evanston: NU Press.
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When running an analysis of variance to analyse a data set, the data set should meet the following criteria: #Normality: scores for each condition should be sampled from a normally distributed population. #Homogeneity of variance: each population should have the same error variance. #Sphericity of the covariance matrix: ensures the F ratios match the F distribution For the between-subject effects to meet the assumptions of the analysis of variance, the variance for any level of a group must be the same as the variance for the mean of all other levels of the group. When there is homogeneity of variance, sphericity of the covariance matrix will occur, because for between-subjects independence has been maintained.
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Clark Quarry is a cut and fill fluvial deposit overlying a marine sand, near Brunswick, Georgia, United States in Glynn County. The marine unit is characterized by a well-sorted, subrounded, low sphericity, fine- grained quartz arenite representing sediments of the Princess Anne Terrace. This site is in the pleistocene era on the geologic timescale.
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Ceramic microspheres are used primarily as grinding media. Hollow microspheres loaded with drug in their outer polymer shell were prepared by a novel emulsion solvent diffusion method and spray drying technique. Microspheres vary widely in quality, sphericity, uniformity, particle size and particle size distribution. The appropriate microsphere needs to be chosen for each unique application.
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Conditions under which mean square ratios in repeated measurements designs have exact F-distributions. Journal of the American Statistical Association, 65, 1582–1589 adjustments to the degrees of freedom because they can correct for issues that can arise should the sphericity of the covariance matrix assumption be violated.Howell, D. (2010). Statistical Methods for Psychology (7th edition).
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Another view of the period is reflected by more specific notions such as the 19th-century claimHistorian Jeffrey Burton Russell, in his book Inventing the Flat Earth "... shows how nineteenth-century anti-Christians invented and spread the falsehood that educated people in the Middle Ages believed that the earth was flat" Russell's summary of his book that everyone in the Middle Ages thought the world was flat.A recent study of medieval concepts of the sphericity of the Earth notes that "since the eighth century, no cosmographer worthy of note has called into question the sphericity of the Earth." Klaus Anselm Vogel, "Sphaera terrae - das mittelalterliche Bild der Erde und die kosmographische Revolution", PhD dissertation, Georg-August-Universität Göttingen, 1995, p. 19 In fact, lecturers in medieval universities commonly advanced the idea that the Earth was a sphere.
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Not all was lost or forgotten - Bede in his De naturum rerum affirms the sphericity of the earth. But his arguments are those of Aristotle, taken from Pliny. Bede adds nothing original. There is more of note in the later medieval period. Wright (1923) cites a description by Walcher of Malvern of a lunar eclipse in Italy (October 19, 1094), which occurred shortly before dawn.
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Well, in fact, it is Draper and White, specifically, both of them, who bear most of the blame for popularizing this baseless view to the extent that nowadays, 80 percent of school teachers still foist this upon poor innocent school children. The fact is that of course the sphericity of the Earth was well established by the fifth century BC by the Greeks, and a good measure of its circumference made by the third century BC. And these facts were never forgotten in learned Western Culture." Principe goes on to say, "White tells of a brave Columbus who fought mightily for the revolutionary notion of the earth’s sphericity. And here he helps us out (damning himself) with a footnote that reads “W. Irving, Life of Columbus” Yes, indeed, this is Washington Irving of Rip Van Winkle and headless horseman fame, who wrote a fictionalized account of Columbus in 1838.
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The acentric factor is a conceptual number introduced by Kenneth Pitzer in 1955, proven to be very useful in the description of matter. It has become a standard for the phase characterization of single & pure components. The other state description parameters are molecular weight, critical temperature, critical pressure, and critical volume (or critical compressibility). The acentric factor is said to be a measure of the non-sphericity (centricity) of molecules.
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Description of sedimentary rock microstructure aims to provide information on the conditions of deposition of the sediment, the paleo-environment, and the provenance of the sedimentary material. Methods involve description of clast size, sorting, composition, rounding or angularity, sphericity and description of the matrix. Sedimentary microstructures, specifically, may include microscopic analogs of larger sedimentary structural features such as cross- bedding, syn-sedimentary faults, sediment slumping, cross-stratification, etc.
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Of the three corrections, Huynh-Feldt is considered the least conservative, while Greenhouse–Geisser is considered more conservative and the lower-bound correction is the most conservative. When epsilon is > .75, the Greenhouse–Geisser correction is believed to be too conservative, and would result in incorrectly rejecting the null hypothesis that sphericity holds. Collier and colleagues showed this was true when epsilon was extended to as high as .90.
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24 The subject is constructed with a grouping of faceted planar forms that together form a tight cohesive structure. The models facial features are simply constructed with only a few surface planes juxtaposed in geometric terms at various angles. Sphericity of the head is broken by angular cuts, forming triangular (ears), rectangles (the nose) and arcs (cheekbones), visible in the photograph. The shoulders and neck form a robust base upon which the head rests.
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Each of these corrections have been developed to alter the degrees of freedom and produce an F-ratio where the Type I error rate is reduced. The actual F-ratio does not change as a result of applying the corrections; only the degrees of freedom. The test statistic for these estimates is denoted by epsilon (ε) and can be found on Mauchly's test output in SPSS. Epsilon provides a measure of departure from sphericity.
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Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle. Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing. In geometric dimensioning and tolerancing, control of a cylinder can also include its fidelity to the longitudinal axis, yielding cylindricity. The analogue of roundness in three dimensions (that is, for spheres) is sphericity.
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Microspherulites are microscopic spherical particles with diameter less than two mm, usually in the 100 micrometre range, mainly consisting of mineral material (the Greek litos means "stone"). Only bodies created by natural physico-chemical processes, with no contribution of either biological (in aqueous sedimentary environments this contribution is possible) or human activity, are considered to be microspherulites. Generally speaking, the common feature (sphericity) indicates that each sphere represents an internal equilibrium of forces within a fluid medium (water, air).
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In particular the distance obtained for the Hyades has historically been an important step in the distance ladder. Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a supernova remnant or planetary nebula, can be observed over time, then an expansion parallax distance to that cloud can be estimated. Those measurements however suffer from uncertainties in the deviation of the object from sphericity.
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Subsequent studies have reported an angular diameter (i.e., apparent size) ranging from 0.042 to 0.056 arcseconds; that range of determinations is ascribed to non- sphericity, limb darkening, pulsations and varying appearance at different wavelengths. It is also surrounded by a complex, asymmetric envelope, roughly 250 times the size of the star, caused by mass loss from the star itself. The Earth-observed angular diameter of Betelgeuse is exceeded only by those of R Doradus and the Sun.
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Islamic astronomy was developed on the basis of a spherical earth inherited from Hellenistic astronomy.Ragep, F. Jamil: "Astronomy", in: Krämer, Gudrun (ed.) et al.: Encyclopaedia of Islam, THREE, Brill 2010, without page numbers The Islamic theoretical framework largely relied on the fundamental contributions of Aristotle (De caelo) and Ptolemy (Almagest), both of whom worked from the premise that the Earth was spherical and at the centre of the universe (geocentric model). Early Islamic scholars recognized Earth's sphericity,Muhammad Hamidullah.
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12th-century depiction of a spherical Earth with the four seasons (book Liber Divinorum Operum by Hildegard of Bingen) A possible non-literary but graphic indication that people in the Middle Ages believed that the Earth (or perhaps the world) was a sphere is the use of the orb (globus cruciger) in the regalia of many kingdoms and of the Holy Roman Empire. It is attested from the time of the Christian late-Roman emperor Theodosius II (423) throughout the Middle Ages; the Reichsapfel was used in 1191 at the coronation of emperor Henry VI. However the word means "circle", and there is no record of a globe as a representation of the Earth since ancient times in the west until that of Martin Behaim in 1492. Additionally it could well be a representation of the entire "world" or cosmos. A recent study of medieval concepts of the sphericity of the Earth noted that "since the eighth century, no cosmographer worthy of note has called into question the sphericity of the Earth".
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Matvey Matveyevich Gusev () ( in Vyatka, Russia- in Berlin, Germany) was a Russian astronomer who worked at Pulkovo Observatory near St. Petersburg from 1850 to 1852 and then at Vilnius Observatory. In 1860 he founded the first scientific journal dedicated to math and physics in Russia: Vestnik matematicheskikh nauk (). He became the director of the Vilnius Observatory in 1865. He was first to prove the non-sphericity of the Moon, concluding in 1860 that it is elongated in the direction of the Earth.
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One of the most commonly reported effect size statistics for rANOVA is partial eta- squared (ηp2). It is also common to use the multivariate η2 when the assumption of sphericity has been violated, and the multivariate test statistic is reported. A third effect size statistic that is reported is the generalized η2, which is comparable to ηp2 in a one-way repeated measures ANOVA. It has been shown to be a better estimate of effect size with other within-subjects tests.
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700–784), in the middle of the 8th century, discussed or taught some geographical or cosmographical ideas that St Boniface found sufficiently objectionable that he complained about them to Pope Zachary. The only surviving record of the incident is contained in Zachary's reply, dated 748, where he wrote:English translation by The original Latin reads: (MGH, 1, 80, pp. 178–79). Some authorities have suggested that the sphericity of the Earth was among the aspects of Vergilius's teachings that Boniface and Zachary considered objectionable.Laistner, (1966, p. 184).
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Roundness is dominated by the shape's gross features rather than the definition of its edges and corners, or the surface roughness of a manufactured object. A smooth ellipse can have low roundness, if its eccentricity is large. Regular polygons increase their roundness with increasing numbers of sides, even though they are still sharp-edged. In geology and the study of sediments (where three-dimensional particles are most important), roundness is considered to be the measurement of surface roughness and the overall shape is described by sphericity.
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Zhang Heng viewed these astronomical phenomena in supernatural terms as well. The signs of comets, eclipses, and movements of heavenly bodies could all be interpreted by him as heavenly guides on how to conduct affairs of state. Contemporary writers also wrote about eclipses and the sphericity of heavenly bodies. The music theorist and mathematician Jing Fang (78–37 BC) wrote about the spherical shape of the Sun and Moon while discussing eclipses: > The Moon and the planets are Yin; they have shape but no light.
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Isidore's T and O map, which was seen as representing a small part of a spherical Earth, continued to be used by authors through the Middle Ages, e.g. the 9th-century bishop Rabanus Maurus, who compared the habitable part of the northern hemisphere (Aristotle's northern temperate clime) with a wheel. At the same time, Isidore's works also gave the views of sphericity, for example, in chapter 28 of De Natura Rerum, Isidore claims that the Sun orbits the Earth and illuminates the other side when it is night on this side.
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The sphericity of the Earth is also accounted for in the work of Ptolemy, on which medieval astronomy was largely based. Christian writers whose works clearly reflect the conviction that the Earth is spherical include Saint Bede the Venerable in his Reckoning of Time, written around AD 723. In Columbus's time, the techniques of celestial navigation, which use the position of the sun and the stars in the sky, together with the understanding that the Earth is a sphere, had long been in use by astronomers and were beginning to be implemented by mariners.See, e.g.
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Sphericity is desired because it guarantees a high flowability and packing density, which translates into fast and reproducible spreading of the powder layers. To further optimize flowability, narrow grain size distributions with a low percentage of fine particles like 15 - 45 µm or 20 - 63 µm are typically employed. Currently available alloys used in the process include 17-4 and 15-5 stainless steel, maraging steel, cobalt chromium, inconel 625 and 718, aluminum AlSi10Mg, and titanium Ti6Al4V. The mechanical properties of samples produced using direct metal laser sintering differ from those manufactured using casting.
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T-O maps, unlike zonal maps, illustrate only the habitable portion of the world known to medieval Europeans, limiting their perspective to a relatively small portion of the Earth's northern hemisphere. The landmass was illustrated as a circle (an "O") divided into three portions by a "T". These three divisions were the continents of Asia, Africa and Europe. The popularity of the Macrobian maps and the combination of T-O style continents on some of the larger Macrobian spheres illustrate that Earth's sphericity continued to be understood among scholars during the Middle Ages.
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Repeated measures analysis of variance (RM-ANOVA) has been traditionally used for analysis of repeated measures designs. However, violation of the assumptions of RM-ANOVA can be problematic. Multilevel modeling (MLM) is commonly used for repeated measures designs because it presents an alternative approach to analyzing this type of data with three main advantages over RM-ANOVA: ::1. MLM has Less Stringent Assumptions: MLM can be used if the assumptions of constant variances (homogeneity of variance, or homoscedasticity), constant covariances (compound symmetry), or constant variances of differences scores (sphericity) are violated for RM-ANOVA.
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225 The effects of the Coriolis force on ballistic trajectories should not be confused with the curvature of the paths of missiles, satellites, and similar objects when the paths are plotted on two-dimensional (flat) maps, such as the Mercator projection. The projections of the three-dimensional curved surface of the Earth to a two-dimensional surface (the map) necessarily results in distorted features. The apparent curvature of the path is a consequence of the sphericity of the Earth and would occur even in a non-rotating frame.
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533–633 (533, 554f.) "Chapter 6. Cosmology"Glick, Thomas F., Livesey, Steven John, Wallis, Faith (eds.): "Medieval Science, Technology, and Medicine: An Encyclopedia", Routledge, New York 2005, , p. 463 The works of the classical Indian astronomer and mathematician, Aryabhatta (476–550 AD), deal with the sphericity of the Earth and the motion of the planets. The final two parts of his Sanskrit magnum opus, the Aryabhatiya, which were named the Kalakriya ("reckoning of time") and the Gol ("sphere"), state that the Earth is spherical and that its circumference is 4,967 yojanas.
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1256 AD) wrote a famous work on Astronomy called Tractatus de Sphaera, based on Ptolemy, which primarily considers the sphere of the sky. However, it contains clear proofs of the Earth's sphericity in the first chapter.Olaf Pedersen, "In Quest of Sacrobosco", Journal for the History of Astronomy, 16(1985): 175–221 Many scholastic commentators on Aristotle's On the Heavens and Sacrobosco's Treatise on the Sphere unanimously agreed that the Earth is spherical or round. Grant observes that no author who had studied at a medieval university thought that the Earth was flat.
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The simplest mappae mundi were diagrams meant to preserve and illustrate classical learning easily. The zonal maps should be viewed as a kind of teaching aid—easily reproduced and designed to reinforce the idea of the Earth's sphericity and climate zones. T-O maps were designed to schematically illustrate the three land masses of the world as it was known to the Romans and their medieval European heirs. The larger mappae mundi have the space and detail to illustrate further concepts, such as the cardinal directions, distant lands, Bible stories, history, mythology, flora, fauna and exotic races.
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Lower melting temperature enables polyethylene microspheres to create porous structures in ceramics and other materials. High sphericity of polyethylene microspheres, as well as availability of colored and fluorescent microspheres, makes them highly desirable for flow visualization and fluid flow analysis, microscopy techniques, health sciences, process troubleshooting and numerous research applications. Charged polyethylene microspheres are also used in electronic paper digital displays.Paint and Coatings Industry Magazine, January 1st, 2010 : Opaque Polyethylene Microspheres for the coatings applicationsCosmetics and Toiletries, April 2010 Issue: Solid Polyethylene Microspheres for effects in color cosmetics Expandable microspheres are polymer microspheres that are used as a blowing agent in e.g.
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When sphericity has been established, the F-ratio is valid and therefore interpretable. However, if Mauchly's test is significant then the F-ratios produced must be interpreted with caution as the violations of this assumption can result in an increase in the Type I error rate, and influence the conclusions drawn from your analysis. In instances where Mauchly's test is significant, modifications need to be made to the degrees of freedom so that a valid F-ratio can be obtained. In SPSS, three corrections are generated: the Greenhouse–Geisser correction (1959), the Huynh–Feldt correction (1976), and the lower-bound.
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Over time, 760 millimeters of mercury at 0°C came to be regarded as the standard atmospheric pressure. In honour of Torricelli, the torr was defined as a unit of pressure equal to one millimeter of mercury at 0°C. However, since the acceleration due to gravity – and thus the weight of a column of mercury – is a function of elevation and latitude (due to the rotation and non-sphericity of the Earth), this definition is imprecise and varies by location. In 1954, the definition of the atmosphere was revised by the (10th CGPM)BIPM – Resolution 4 of the 10th CGPM.
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He explained the unequal length of daylight from "the roundness of the Earth, for not without reason is it called 'the orb of the world' on the pages of Holy Scripture and of ordinary literature. It is, in fact, set like a sphere in the middle of the whole universe." (De temporum ratione, 32). The large number of surviving manuscripts of The Reckoning of Time, copied to meet the Carolingian requirement that all priests should study the computus, indicates that many, if not most, priests were exposed to the idea of the sphericity of the Earth.
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The heavens were defined as incorruptible and unchanging based on theology and mythology of the past. The Almagest introduced the idea of the sphericity of heavens. The assumption is that the sizes and mutual distances of the stars must appear to vary however one supposes the earth to be positioned, yet no such variation occurred (Bowler, 2010, 55), The aether is the area that describes the universe above the terrestrial sphere. This component of the atmosphere is unknown and named by philosophers, though many do not know what lies beyond the realm of what has been seen by human beings.
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The aether is used to affirm the sphericity of the heavens and this is confirmed by the belief that different shapes have an equal boundary and those with more angles are greater, the circle is greater than all other surfaces, and a sphere greater than all other solids. Therefore, through physical considerations, and heavenly philosophy, there is an assumption that the heavens must be spherical. The Almagest also suggested that the earth was spherical because of similar philosophy. The differences in the hours across the globe are proportional to the distances between the spaces at which they are being observed.
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In addition to documenting about 2,500 stars in his extensive star catalog, Zhang also posited theories about the Moon and its relationship to the Sun: specifically, he discussed the Moon's sphericity, its illumination by reflected sunlight on one side and the hidden nature of the other, and the nature of solar and lunar eclipses. His fu (rhapsody) and shi poetry were renowned in his time and studied and analyzed by later Chinese writers. Zhang received many posthumous honors for his scholarship and ingenuity; some modern scholars have compared his work in astronomy to that of the Greco-Roman Ptolemy (AD 86–161).
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The church fathers favoured the idea of a solid roof or firmament over the earth and this was elaborated early on, but in the Middle Ages most followed authorities such as Thomas Aquinas in accepting sphericity. Jerusalem was accepted as the centre of the world and a refusal to accept the existence of antipodes led many to assume that the other side of the world was entirely aqueous. Opposition to the antipodes did not cease for centuries after Magellan's voyages and also contributed to underestimates of the size of the earth, which happened to help Columbus. Religious feeling encouraged the expansion of Europeans across the globe.
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Scientific investigation has resulted in several culturally transformative shifts in people's view of the planet. Initial belief in a flat Earth was gradually displaced in the Greek colonies of southern Italy during the late 6th century BC by the idea of spherical Earth, which was attributed to both the philosophers Pythagoras and Parmenides. By the end of the 5th century BC, the sphericity of Earth was universally accepted among Greek intellectuals. Earth was generally believed to be the center of the universe until the 16th century, when scientists first conclusively demonstrated that it was a moving object, comparable to the other planets in the Solar System.
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Alexander von Humboldt and his fellow scientist Aimé Bonpland at the foot of the Chimborazo volcano, painting by Friedrich Georg Weitsch (1810) Until the beginning of the 19th century, it was thought that Chimborazo was the highest mountain on Earth (measured from sea level), and such reputation led to many attempts on its summit during the 17th and 18th centuries. In 1746, the volcano was explored by French academicians from the French Geodesic Mission. Their mission was to determine the sphericity of the Earth. Their work along with another team in Lapland established that the Earth was an oblate spheroid rather than a true sphere.
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Projections of the sphere like this one have been co-opted as images of the flat Earth model depicting Antarctica as an ice wall surrounding a disk-shaped Earth. The contemporary scientific view of the Earth as a rotating spherical globe, which flat Earth societies contest Modern flat Earth societies are organizations that promote the pseudoscientific belief that the Earth is flat while denying the Earth's sphericity, contrary to over two millennia of scientific consensus. Such groups date from the middle of the 20th century; some adherents are serious and some are not. Those who are serious are often motivated by religion or conspiracy theories.
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Early Greek philosophers alluded to a spherical Earth, though with some ambiguity. Pythagoras (6th century BC) was among those said to have originated the idea, but this might reflect the ancient Greek practice of ascribing every discovery to one or another of their ancient wise men. Some idea of the sphericity of the Earth seems to have been known to both Parmenides and Empedocles in the 5th century BC,Charles H. Kahn, (2001), Pythagoras and the Pythagoreans: a brief history, page 53. Hackett and although the idea cannot reliably be ascribed to Pythagoras, it might nevertheless have been formulated in the Pythagorean school in the 5th century BC although some disagree.
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1246) Tattersall shows that in many vernacular works in 12th- and 13th-century French texts the Earth was considered "round like a table" rather than "round like an apple". "In virtually all the examples quoted ... from epics and from non-'historical' romances (that is, works of a less learned character) the actual form of words used suggests strongly a circle rather than a sphere", though he notes that even in these works the language is ambiguous. Portuguese navigation down and around the coast of Africa in the latter half of the 1400s gave wide-scale observational evidence for Earth's sphericity. In these explorations, the Sun position moved more northward the further south the explorers travelled.
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Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or escaped to Metapontum, where he eventually died. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. It was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones.
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A confirmation of the photonic jet in the microwave scale, observing the backscattering enhancement that occurred when metallic particles were introduced in the focus area. A measurable enhancement of the backscattered light in the visible range was obtained when a gold nanoparticle was placed inside the photonic nanojet region produced by a dielectric microsphere with a 4.4 μm diameter. A use of nanojets produced by transparent microspheres in order to excite optical active materials, under upconversion processes with different numbers of excitation photons, has been analyzed as well. Monodisperse glass microspheres have high sphericity and a very tight particle size distribution, often with CV<10% and specification of >95% of particles in size range.
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In ancient China, the prevailing belief was that the Earth was flat and square, while the heavens were round,Needham, Joseph (1986). Science and Civilization in China: Volume 3. Taipei: Caves Books, Ltd. p. 498. an assumption virtually unquestioned until the introduction of European astronomy in the 17th century. The English sinologist Cullen emphasizes the point that there was no concept of a round Earth in ancient Chinese astronomy: cosmographer The model of an egg was often used by Chinese astronomers such as Zhang Heng (78–139 AD) to describe the heavens as spherical: This analogy with a curved egg led some modern historians, notably Joseph Needham, to conjecture that Chinese astronomers were, after all, aware of the Earth's sphericity.
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These men had specific political purposes in mind when arguing their case, and the historical foundations of their work are unreliable." Principe goes on to write "Despite appearances, White’s arguments are scarcely any better than Draper’s. White uses fallacious arguments and suspect or bogus sources. His methodological errors are collectivism (the unwarrantable extension of an individual’s views to represent that of some larger group of which he is a part), a lack of critical judgement about sources, argument by ridicule and assertion, failure to check primary sources, and quoting selectively and out of context. White popularized the baseless notions that before Columbus and Magellan, the world was thought to be flat and that the Earth’s sphericity was officially opposed by the Church.
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Gharā'ib al-funūn wa-mulah al-`uyūn (The Book of Curiosities of the Sciences and Marvels for the Eyes), 2.1 "On the mensuration of the Earth and its division into seven climes, as related by Ptolemy and others," (ff. 22b–23a) Another estimate given by his astronomers was 56 Arabic miles (111.8 km) per degree, which corresponds to a circumference of 40,248 km, very close to the currently modern values of 111.3 km per degree and 40,068 km circumference, respectively.Edward S. Kennedy, Mathematical Geography, pp=187–8, in ;Ibn Hazm Andalusian polymath Ibn Hazm stated that the proof of the Earth's sphericity "is that the Sun is always vertical to a particular spot on Earth"."How Islamic inventors changed the world".
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But as some historians have pointed out, the nineteenth-century conflict over Darwinism incorporated disputes over the relative authority of professional scientists and clergy in the fields of science and education. White made this concern manifest in the preface to his History of the Warfare of Science and Theology in Christendom, where he explained the lack of advanced instruction in many American colleges and universities by their "sectarian character". The flat-Earth myth, like other myths, took on artistic form in the many works of art displaying Columbus defending the sphericity of the Earth before the Council of Salamanca. American artists depicted a forceful Columbus challenging the "prejudices, the mingled ignorance and erudition, and the pedantic bigotry" of the churchmen.
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Still, many textbooks of the Early Middle Ages supported the sphericity of the Earth in the western part of Europe.B. Eastwood and G. Graßhoff, Planetary Diagrams for Roman Astronomy in Medieval Europe, ca. 800–1500, Transactions of the American Philosophical Society, 94, 3 (Philadelphia, 2004), pp. 49–50. 12th-century T and O map representing the inhabited world as described by Isidore of Seville in his Etymologiae (chapter 14, ) Europe's view of the shape of the Earth in Late Antiquity and the Early Middle Ages may be best expressed by the writings of early Christian scholars: Bishop Isidore of Seville (560–636) taught in his widely read encyclopedia, the Etymologies, diverse views such as that the Earth "resembles a wheel" resembling Anaximander in language and the map that he provided.
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An often-cited specification applicable to some modern pits describes a hollow sphere of a suitable structural metal, of the approximate size and weight of a bowling ball, with a channel for injection of tritium (in the case of boosted fission weapons), with the internal surface lined with plutonium. The size, usually between a bowling ball and a tennis ball, accuracy of sphericity, and weight and isotopic composition of the fissile material, the principal factors influencing the weapon properties, are often classified. The hollow pits can be made of half shells with three joint welds around the equator, and a tube brazed (to beryllium or aluminium shell) or electron beam or TIG-welded (to stainless steel shell) for injection of the boost gas.BREDL Southern Anti- Plutonium Campaign. Bredl.
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The Sea Pole bathyscaphe is equipped with various communication systems, but the data transfer rate remains a bottleneck, with the transmission rate only being 80 kbit/s, compared to 100 Mbit/s in the usual internet transmissions. As a result, the transmission of an ordinary color image from the bathyscaphe to the mothership takes approximately half a minute. The pressure hull is built of titanium alloy, and the manufacturing method for the pressure hull involves producing two hemispherical parts by tungsten inert gas (TIG) welding six-side plates to a top plate, followed by heat treatments and polishing by machining; the two halves are then TIG welded together to form a complete sphere. The plate thickness is 76 – 78 mm, with deviations of ±4 mm in the completed radius, and sphericity is 0.4% or less.
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Knowledge of the spherical shape of the Earth was received in scholarship of Late Antiquity as a matter of course, in both Neoplatonism and Early Christianity. Calcidius's fourth-century Latin commentary on and translation of Plato's Timaeus, which was one of the few examples of Greek scientific thought that was known in the Early Middle Ages in Western Europe, discussed Hipparchus's use of the geometrical circumstances of eclipses to compute the relative diameters of the Sun, Earth, and Moon. Theological doubt informed by the flat Earth model implied in the Hebrew Bible inspired some early Christian scholars such as Lactantius, John Chrysostom and Athanasius of Alexandria, but this remained an eccentric current. Learned Christian authors such as Basil of Caesarea, Ambrose and Augustine of Hippo were clearly aware of the sphericity of the Earth.
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Though the earliest written mention of a spherical Earth comes from ancient Greek sources, there is no account of how the sphericity of the Earth was discovered.James Evans, (1998), The History and Practice of Ancient Astronomy, page 47, Oxford University Press A plausible explanation given by the historian Otto E. Neugebauer is that it was "the experience of travellers that suggested such an explanation for the variation in the observable altitude of the pole and the change in the area of circumpolar stars, a change that was quite drastic between Greek settlements" around the eastern Mediterranean Sea, particularly those between the Nile Delta and Crimea. Another possible explanation can be traced back to earlier Phoenician sailors. The first circumnavigation of Africa is described as being undertaken by Phoenician explorers employed by Egyptian pharaoh Necho II c.
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A hypothetical geocentric model of the Solar System (upper panel) in comparison to the heliocentric model (lower panel). While the sphericity of the Earth was widely recognized in Greco-Roman astronomy from at least the 4th century BC, the Earth's daily rotation and yearly orbit around the Sun was never universally accepted until the Copernican Revolution. While a moving Earth was proposed at least from the 4th century BC in Pythagoreanism, and a fully developed heliocentric model was developed by Aristarchus of Samos in the 3rd century BC, these ideas were not successful in replacing the view of a static spherical Earth, and from the 2nd century AD the predominant model, which would be inherited by medieval astronomy, was the geocentric model described in Ptolemy's Almagest. The Ptolemaic system was a sophisticated astronomical system that managed to calculate the positions for the planets to a fair degree of accuracy.
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Cosmology originally comprised the greater part of his poem, him explaining the world's origins and operations. Some idea of the sphericity of the Earth seems to have been known to Parmenides.Charles H. Kahn, (2001), Pythagoras and the Pythagoreans: a brief history, page 53. Hackett Parmenides also outlined the phases of the moon, highlighted in a rhymed translation by Karl Popper: Smith stated: > Of the cosmogony of Parmenides, which was carried out very much in detail, > we possess only a few fragments and notices, which are difficult to > understand, according to which, with an approach to the doctrines of the > Pythagoreans, he conceived the spherical mundane system, surrounded by a > circle of the pure light (Olympus, Uranus); in the centre of this mundane > system the solid earth, and between the two the circle of the milkyway, of > the morning or evening star, of the sun, the planets, and the moon; which > circle he regarded as a mixture of the two primordial elements.
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For its main use as a fertilizer urea is mostly marketed in solid form, either as prills or granules. The advantage of prills is that, in general, they can be produced more cheaply than granules and that the technique was firmly established in industrial practice long before a satisfactory urea granulation process was commercialized. However, on account of the limited size of particles that can be produced with the desired degree of sphericity and their low crushing and impact strength, the performance of prills during bulk storage, handling and use is generally (with some exceptions) considered inferior to that of granules. High-quality compound fertilizers containing nitrogen co-granulated with other components such as phosphates have been produced routinely since the beginnings of the modern fertilizer industry, but on account of the low melting point and hygroscopic nature of urea it took courage to apply the same kind of technology to granulate urea on its own.
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He also entertained the possibility that the Moon was inhabited. Aristarchus went a step further and computed the distance from Earth, together with its size, obtaining a value of 20 times the Earth radius for the distance (the real value is 60; the Earth radius was roughly known since Eratosthenes). Although the Chinese of the Han Dynasty (202 BC–202 AD) believed the Moon to be energy equated to qi, their 'radiating influence' theory recognized that the light of the Moon was merely a reflection of the Sun (mentioned by Anaxagoras above). This was supported by mainstream thinkers such as Jing Fang, who noted the sphericity of the Moon. Shen Kuo (1031–1095) of the Song Dynasty (960–1279) created an allegory equating the waxing and waning of the Moon to a round ball of reflective silver that, when doused with white powder and viewed from the side, would appear to be a crescent.
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The head, with its stylish coiffure, and the models facial features are simply constructed with only a few surface planes juxtaposed at seemingly right angles. Even the vase, upon close examination, appears treated in geometric terms, its sphericity broken by an angular cut to the right, barely visible in the photograph. The treatment of Csaky's Danseuse, as other works by the artist executed between 1910 and 1913, suggests, as Albert Edward Elsen notes, that Csaky had looked not only at Picasso's earlier painting and sculpture, but also at African tribal masks whose exaggerated features and simplified design accommodated the need to be seen at a distance and to evoke strong feeling.Albert Edward Elsen, Origins of modern sculpture: pioneers and premises, G. Braziller, 1974 Just as in Csaky's Groupe de femmes (1911–12), Danseuse already showed a new way of representing the human figure, an unwillingness to revert to classical, academic or traditional methods of representation.
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The primary problems with increasing ICF performance since the early experiments in the 1970s have been of energy delivery to the target, controlling symmetry of the imploding fuel, preventing premature heating of the fuel (before maximum density is achieved), preventing premature mixing of hot and cool fuel by hydrodynamic instabilities and the formation of a 'tight' shockwave convergence at the compressed fuel center. In order to focus the shock wave on the center of the target, the target must be made with extremely high precision and sphericity with aberrations of no more than a few micrometres over its surface (inner and outer). Likewise the aiming of the laser beams must be extremely precise and the beams must arrive at the same time at all points on the target. Beam timing is a relatively simple issue though and is solved by using delay lines in the beams' optical path to achieve picosecond levels of timing accuracy.
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The ancient Greek philosopher Anaxagoras reasoned that the Sun and Moon were both giant spherical rocks, and that the latter reflected the light of the former. Although the Chinese of the Han Dynasty believed the Moon to be energy equated to qi, their 'radiating influence' theory also recognized that the light of the Moon was merely a reflection of the Sun, and Jing Fang (78–37 BC) noted the sphericity of the Moon. In the 2nd century AD, Lucian wrote the novel A True Story, in which the heroes travel to the Moon and meet its inhabitants. In 499 AD, the Indian astronomer Aryabhata mentioned in his Aryabhatiya that reflected sunlight is the cause of the shining of the Moon. The astronomer and physicist Alhazen (965–1039) found that sunlight was not reflected from the Moon like a mirror, but that light was emitted from every part of the Moon's sunlit surface in all directions. Shen Kuo (1031–1095) of the Song dynasty created an allegory equating the waxing and waning of the Moon to a round ball of reflective silver that, when doused with white powder and viewed from the side, would appear to be a crescent.
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