vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Sundial
The entire object that casts a shadow or light onto the dial face is known as the sundial 's gnomon . However , it is usually only an edge of the gnomon ( or another linear feature ) that casts the shadow used to determine the time ; this linear feature is known as the sundial 's style . The style is usually aligned parallel to the axis of the celestial sphere , and therefore is aligned with the local geographical meridian . In some sundial designs , only a point - like feature , such as the tip of the style , is used to determine the time and date ; this point - like feature is known as the sundial 's nodus . Some sundials use both a style and a nodus to determine the time and date .
Kuiper belt
The presence of Neptune has a profound effect on the Kuiper belt 's structure due to orbital resonances . Over a timescale comparable to the age of the Solar System , Neptune 's gravity destabilises the orbits of any objects that happen to lie in certain regions , and either sends them into the inner Solar System or out into the scattered disc or interstellar space . This causes the Kuiper belt to have pronounced gaps in its current layout , similar to the Kirkwood gaps in the asteroid belt . In the region between 40 and 42 AU , for instance , no objects can retain a stable orbit over such times , and any observed in that region must have migrated there relatively recently . The
H II region
H II regions come in an enormous variety of sizes . They are usually clumpy and inhomogeneous on all scales from the smallest to largest . Each star within an H II region ionises a roughly spherical region -- known as a Strömgren sphere -- of the surrounding gas , but the combination of ionisation spheres of multiple stars within a H II region and the expansion of the heated nebula into surrounding gases creates sharp density gradients that result in complex shapes . Supernova explosions may also sculpt H II regions . In some cases , the formation of a large star cluster within an H II region results in the region being hollowed out from within . This is the case for NGC 604 , a giant H II region in the Triangulum Galaxy . For a H II region which can not be resolved , some information on the spatial structure ( the electron density as a function of the distance from the center , and an estimate of the clumpiness ) can be inferred by performing an inverse Laplace transform on the frequency spectrum .
Reuleaux triangle
In connection with the inscribed square problem , Eggleston ( 1958 ) observed that the Reuleaux triangle provides an example of a constant - width shape in which no regular polygon with more than four sides can be inscribed , except the regular hexagon , and he described a small modification to this shape that preserves its constant width but also prevents regular hexagons from being inscribed in it . He generalized this result to three dimensions using a cylinder with the same shape as its cross section .
Wikipedia:Citing sources
Brown , R ( 2006 ) . `` Size of the Moon '' , Scientific American , 51 ( 78 ) . Miller , E ( 2005 ) . The Sun , Academic Press .
Lunar distance (astronomy)
This section is intended to illustrate some of the historically significant or otherwise interesting methods of determining the lunar distance , and is not intended to be an exhaustive or all - encompassing list .
Meander
In contrast to sine waves , the loops of a meandering stream are more nearly circular . The curvature varies from a maximum at the apex to zero at a crossing point ( straight line ) , also called an inflection , because the curvature changes direction in that vicinity . The radius of the loop is the straight line perpendicular to the down - valley axis intersecting the sinuous axis at the apex . As the loop is not ideal , additional information is needed to characterize it . The orientation angle is the angle between sinuous axis and down - valley axis at any point on the sinuous axis . Concave
Moon landing
To return to Earth , the escape velocity of the Moon must be overcome for the spacecraft to escape the gravity well of the Moon . Rockets must be used to leave the Moon and return to space . Upon reaching Earth , atmospheric entry techniques are used to absorb the kinetic energy of a returning spacecraft and reduce its speed for safe landing . These functions greatly complicate a moon landing mission and lead to many additional operational considerations . Any moon departure rocket must first be carried to the Moon 's surface by a moon landing rocket , increasing the latter 's required size . The Moon departure rocket , larger moon landing rocket and any Earth atmosphere entry equipment such as heat shields and parachutes must in turn be lifted by the original launch vehicle , greatly increasing its size by a significant and almost prohibitive degree .
Lunar distance (astronomy)
The earliest account of an attempt to measure the distance to the Moon using this technique was by the 4th - century - BC Greek astronomer and mathematician Aristarchus of Samos and later by Hipparchus , whose calculations produced a result of 59 - 67 R . This method later found its way into the work of Ptolemy , who produced a result of 64 1 / 6 R at its farthest point . Meridian
Hindu temple
The four cardinal directions help create the axis of a Hindu temple , around which is formed a perfect square in the space available . The circle of mandala circumscribes the square . The square is considered divine for its perfection and as a symbolic product of knowledge and human thought , while circle is considered earthly , human and observed in everyday life ( moon , sun , horizon , water drop , rainbow ) . Each supports the other . The square is divided into perfect 64 ( or in some cases 81 ) sub-squares called padas . Each pada is conceptually assigned to a symbolic element , sometimes in the form of a deity . The central square ( s ) of the 64 or 81 grid is dedicated to the Brahman ( not to be confused with Brahmin ) , and are called Brahma padas . The
Earth
In geodesy , the exact shape that Earth 's oceans would adopt in the absence of land and perturbations such as tides and winds is called the geoid . More precisely , the geoid is the surface of gravitational equipotential at mean sea level .
Jupiter
Along with the Sun , the gravitational influence of Jupiter has helped shape the Solar System . The orbits of most of the system 's planets lie closer to Jupiter 's orbital plane than the Sun 's equatorial plane ( Mercury is the only planet that is closer to the Sun 's equator in orbital tilt ) , the Kirkwood gaps in the asteroid belt are mostly caused by Jupiter , and the planet may have been responsible for the Late Heavy Bombardment of the inner Solar System 's history . This
Rainbow
Both arcs are brightly coloured ring segments centred on the zenith , but in different positions in the sky : The circumzenithal arc is notably curved and located high above the Sun ( or Moon ) with its convex side pointing downwards ( creating the impression of an `` upside down rainbow '' ) ; the circumhorizontal arc runs much closer to the horizon , is more straight and located at a significant distance below the Sun ( or Moon ) . Both arcs have their red side pointing towards the sun and their violet part away from it , meaning the circumzenithal arc is red on the bottom , while the circumhorizontal arc is red on top .
Reuleaux triangle
The Reuleaux triangle is the first of a sequence of Reuleaux polygons , whose boundaries are curves of constant width formed from regular polygons with an odd number of sides . Some of these curves have been used as the shapes of coins . The Reuleaux triangle can also be generalized into three dimensions in multiple ways : the Reuleaux tetrahedron ( the intersection of four balls whose centers lie on a regular tetrahedron ) does not have constant width , but can be modified by rounding its edges to form the Meissner tetrahedron , which does . Alternatively , the surface of revolution of the Reuleaux triangle also has constant width .
Geologic time scale
Some other planets and moons in the Solar System have sufficiently rigid structures to have preserved records of their own histories , for example , Venus , Mars and the Earth 's Moon . Dominantly fluid planets , such as the gas giants , do not preserve their history in a comparable manner . Apart from the Late Heavy Bombardment , events on other planets probably had little direct influence on the Earth , and events on Earth had correspondingly little effect on those planets . Construction of a time scale that links the planets is , therefore , of only limited relevance to the Earth 's time scale , except in a Solar System context . The existence , timing , and terrestrial effects of the Late Heavy Bombardment is still debated .
Mars
Mars may have moons smaller than 50 to 100 metres ( 160 to 330 ft ) in diameter , and a dust ring is predicted to exist between Phobos and Deimos .
Mars
Mars is scarred by a number of impact craters : a total of 43,000 craters with a diameter of 5 km ( 3.1 mi ) or greater have been found . The largest confirmed of these is the Hellas impact basin , a light albedo feature clearly visible from Earth . Due to the smaller mass of Mars , the probability of an object colliding with the planet is about half that of Earth . Mars is located closer to the asteroid belt , so it has an increased chance of being struck by materials from that source . Mars is more likely to be struck by short - period comets , i.e. , those that lie within the orbit of Jupiter . In spite of this , there are far fewer craters on Mars compared with the Moon , because the atmosphere of Mars provides protection against small meteors and surface modifying processes have erased some craters .
Triangle
An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half . The three angle bisectors intersect in a single point , the incenter , usually denoted by I , the center of the triangle 's incircle . The incircle is the circle which lies inside the triangle and touches all three sides . Its radius is called the inradius . There are three other important circles , the excircles ; they lie outside the triangle and touch one side as well as the extensions of the other two . The centers of the in - and excircles form an orthocentric system . The
Sundial
Given that sundials use light to indicate time , a line of light may be formed by allowing the sun 's rays through a thin slit or focusing them through a cylindrical lens . A spot of light may be formed by allowing the sun 's rays to pass through a small hole or by reflecting them from a small circular mirror .
Kuiper belt
The original version of the currently most popular model , the `` Nice model '' , reproduces many characteristics of the Kuiper belt such as the `` cold '' and `` hot '' populations , resonant objects , and a scattered disc , but it still fails to account for some of the characteristics of their distributions . The model predicts a higher average eccentricity in classical KBO orbits than is observed ( 0.10 -- 0.13 versus 0.07 ) and its predicted inclination distribution contains too few high inclination objects . In addition , the frequency of binary objects in the cold belt , many of which are far apart and loosely bound , also poses a problem for the model . These are predicted to have been separated during encounters with Neptune , leading some to propose that the cold disc formed at its current location , representing the only truly local population of small bodies in the solar system .
Time
Artifacts from the Paleolithic suggest that the moon was used to reckon time as early as 6,000 years ago . Lunar calendars were among the first to appear , either 12 or 13 lunar months ( either 354 or 384 days ) . Without intercalation to add days or months to some years , seasons quickly drift in a calendar based solely on twelve lunar months . Lunisolar calendars have a thirteenth month added to some years to make up for the difference between a full year ( now known to be about 365.24 days ) and a year of just twelve lunar months . The numbers twelve and thirteen came to feature prominently in many cultures , at least partly due to this relationship of months to years . Other early forms of calendars originated in Mesoamerica , particularly in ancient Mayan civilization . These calendars were religiously and astronomically based , with 18 months in a year and 20 days in a month , plus five epagomenal days at the end of the year .
Kuiper belt
Being distant from the Sun and major planets , Kuiper belt objects are thought to be relatively unaffected by the processes that have shaped and altered other Solar System objects ; thus , determining their composition would provide substantial information on the makeup of the earliest Solar System . Due to their small size and extreme distance from Earth , the chemical makeup of KBOs is very difficult to determine . The principal method by which astronomers determine the composition of a celestial object is spectroscopy . When an object 's light is broken into its component colors , an image akin to a rainbow is formed . This image is called a spectrum . Different substances absorb light at different wavelengths , and when the spectrum for a specific object is unravelled , dark lines ( called absorption lines ) appear where the substances within it have absorbed that particular wavelength of light . Every element or compound has its own unique spectroscopic signature , and by reading an object 's full spectral `` fingerprint '' , astronomers can determine its composition .
Ancient Egyptian deities
Deities were linked with specific regions of the universe . In Egyptian tradition , the world includes the earth , the sky , and the Duat . Surrounding them is the dark formlessness that existed before creation . In general , the deities were said to dwell in the sky , although those whose roles were linked with other parts of the universe were said to live in those places instead . Most events of mythology , set in a time before the withdrawal of the deities from the human realm , take place in an earthly setting . The deities there sometimes interact with those in the sky . The Duat , in contrast , is treated as a remote and inaccessible place , and the deities who dwell there have difficulty communicating with those in the world of the living . The space outside the cosmos is said to be very distant . It too , is inhabited by deities , some hostile and some beneficial to the others and their orderly world .
Sundial
The shadow - casting object , known as a gnomon , may be a long thin rod or other object with a sharp tip or a straight edge . Sundials employ many types of gnomon . The gnomon may be fixed or moved according to the season . It may be oriented vertically , horizontally , aligned with the Earth 's axis , or oriented in an altogether different direction determined by mathematics .
Main sequence
Other factors that broaden the main sequence band on the HR diagram include uncertainty in the distance to stars and the presence of unresolved binary stars that can alter the observed stellar parameters . However , even perfect observation would show a fuzzy main sequence because mass is not the only parameter that affects a star 's color and luminosity . Variations in chemical composition caused by the initial abundances , the star 's evolutionary status , interaction with a close companion , rapid rotation , or a magnetic field can all slightly change a main - sequence star 's HR diagram position , to name just a few factors . As an example , there are metal - poor stars ( with a very low abundance of elements with higher atomic numbers than helium ) that lie just below the main sequence and are known as subdwarfs . These stars are fusing hydrogen in their cores and so they mark the lower edge of main sequence fuzziness caused by variance in chemical composition .
Magnetosphere of Jupiter
At the opposite side of the planet , the solar wind stretches Jupiter 's magnetic field lines into a long , trailing magnetotail , which sometimes extends well beyond the orbit of Saturn . The structure of Jupiter 's magnetotail is similar to Earth 's . It consists of two lobes ( blue areas in the figure ) , with the magnetic field in the southern lobe pointing toward Jupiter , and that in the northern lobe pointing away from it . The lobes are separated by a thin layer of plasma called the tail current sheet ( orange layer in the middle ) . Like Earth 's , the Jovian tail is a channel through which solar plasma enters the inner regions of the magnetosphere , where it is heated and forms the radiation belts at distances closer than 10 R from Jupiter .
Area of a circle
For example , the unit sphere S 2 ( 1 ) ( \ displaystyle S ^ ( 2 ) ( 1 ) ) is a model for the two - dimensional elliptic plane . It carries an intrinsic metric that arises by measuring geodesic length . The geodesic circles are the parallels in a geodesic coordinate system .
Sundial
The distinguishing characteristic of the equatorial dial ( also called the equinoctial dial ) is the planar surface that receives the shadow , which is exactly perpendicular to the gnomon 's style . This plane is called equatorial , because it is parallel to the equator of the Earth and of the celestial sphere . If the gnomon is fixed and aligned with the Earth 's rotational axis , the sun 's apparent rotation about the Earth casts a uniformly rotating sheet of shadow from the gnomon ; this produces a uniformly rotating line of shadow on the equatorial plane . Since the sun rotates 360 ° in 24 hours , the hour - lines on an equatorial dial are all spaced 15 ° apart ( 360 / 24 ) .
Exoplanet
The brightness of optical images of Fomalhaut b could be due to starlight reflecting off a circumplanetary ring system with a radius between 20 and 40 times that of Jupiter 's radius , about the size of the orbits of the Galilean moons .
Jupiter
Jupiter 's magnetic field is fourteen times as strong as that of Earth , ranging from 4.2 gauss ( 0.42 mT ) at the equator to 10 -- 14 gauss ( 1.0 -- 1.4 mT ) at the poles , making it the strongest in the Solar System ( except for sunspots ) . This field is thought to be generated by eddy currents -- swirling movements of conducting materials -- within the liquid metallic hydrogen core . The volcanoes on the moon Io emit large amounts of sulfur dioxide forming a gas torus along the moon 's orbit . The gas is ionized in the magnetosphere producing sulfur and oxygen ions . They , together with hydrogen ions originating from the atmosphere of Jupiter , form a plasma sheet in Jupiter 's equatorial plane . The plasma in the sheet co-rotates with the planet causing deformation of the dipole magnetic field into that of magnetodisk . Electrons within the plasma sheet generate a strong radio signature that produces bursts in the range of 0.6 -- 30 MHz .
Sundial
The time is indicated where a shadow or light falls on the dial face , which is usually inscribed with hour lines . Although usually straight , these hour lines may also be curved , depending on the design of the sundial ( see below ) . In some designs , it is possible to determine the date of the year , or it may be required to know the date to find the correct time . In such cases , there may be multiple sets of hour lines for different months , or there may be mechanisms for setting / calculating the month . In addition to the hour lines , the dial face may offer other data -- such as the horizon , the equator and the tropics -- which are referred to collectively as the dial furniture .
Ancient Greek architecture
The light of Greece may be another important factor in the development of the particular character of ancient Greek architecture . The light is often extremely bright , with both the sky and the sea vividly blue . The clear light and sharp shadows give a precision to the details of landscape , pale rocky outcrops and seashore . This clarity is alternated with periods of haze that varies in colour to the light on it . In this characteristic environment , the ancient Greek architects constructed buildings that were marked by precision of detail . The gleaming marble surfaces were smooth , curved , fluted , or ornately sculpted to reflect the sun , cast graded shadows and change in colour with the ever - changing light of day . The
Meander
Scroll bars often look lighter at the tops of the ridges and darker in the swales . This is because the tops can be shaped by wind , either adding fine grains or by keeping the area unvegetated , while the darkness in the swales can be attributed to silts and clays washing in during high water periods . This added sediment in addition to water that catches in the swales is in turn is a favorable environment for vegetation that will also accumulate in the swales .
Lunar distance (astronomy)
During the Apollo missions in 1969 , astronauts placed retroreflectors on the surface of the Moon for the purpose of refining the accuracy of this technique . The measurements are ongoing and involve multiple laser facilities . The instantaneous accuracy of the Lunar Laser Ranging experiments can exceed sub-millimeter resolution , and is the most reliable method of determining the lunar distance , to date .
Divergent boundary
At divergent boundaries , two plates move away from each other and the space that this creates is filled with new crustal material sourced from molten magma that forms below . The origin of new divergent boundaries at triple junctions is sometimes thought to be associated with the phenomenon known as hotspots . Here , exceedingly large convective cells bring very large quantities of hot asthenospheric material near the surface and the kinetic energy is thought to be sufficient to break apart the lithosphere . The hot spot which may have initiated the Mid-Atlantic Ridge system currently underlies Iceland which is widening at a rate of a few centimeters per year .
Sundial
On any given day , the Sun appears to rotate uniformly about this axis , at about 15 ° per hour , making a full circuit ( 360 ° ) in 24 hours . A linear gnomon aligned with this axis will cast a sheet of shadow ( a half - plane ) that , falling opposite to the Sun , likewise rotates about the celestial axis at 15 ° per hour . The shadow is seen by falling on a receiving surface that is usually flat , but which may be spherical , cylindrical , conical or of other shapes . If the shadow falls on a surface that is symmetrical about the celestial axis ( as in an armillary sphere , or an equatorial dial ) , the surface - shadow likewise moves uniformly ; the hour - lines on the sundial are equally spaced . However , if the receiving surface is not symmetrical ( as in most horizontal sundials ) , the surface shadow generally moves non-uniformly and the hour - lines are not equally spaced ; one exception is the Lambert dial described below .
Earth's orbit
The Hill sphere ( gravitational sphere of influence ) of the Earth is about 1,500,000 kilometers ( 0.01 AU ) in radius , or approximately 4 times the average distance to the moon . This is the maximal distance at which the Earth 's gravitational influence is stronger than the more distant Sun and planets . Objects orbiting the Earth must be within this radius , otherwise they can become unbound by the gravitational perturbation of the Sun .