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Topic: Antipodal point

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  Antipodal point - Wikipedia, the free encyclopedia
In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite it — so situated that a line drawn from the one to the other passes through the centre of the sphere and forms a true diameter.
In mathematics, the concept of antipodal points is generalized to spheres of any dimension: two points on the sphere are antipodal if they are opposite through the centre; for example, taking the centre as origin, they are points with related vectors v and −v.
In other words, each line through the centre intersects the sphere in two points, one for each ray out from the centre, and these two points are antipodal.
en.wikipedia.org /wiki/Antipodal_point   (315 words)

 Antipode - Wikipedia, the free encyclopedia
Antipode - 1 : the parts of the earth diametrically opposite -- usually used as pl. 2 : the exact opposite or contrary
The word antipode is a back-formed singular from the word antipodes, which originally was not plural.
For the abstract mathematical concept that arose from the geographical usage, see antipodal point.
en.wikipedia.org /wiki/Antipodal   (120 words)

 Antipodal point - TheBestLinks.com - Antipodes, Australia, Borsuk-Ulam theorem, Circle, ...
Antipodal points on the surface of a sphere are diametrically opposite; on the other side of a globe.
More generally, in mathematics, antipodal points on a sphere of any dimension are those opposite through the centre; for example, taking the centre as origin, they are points with related vectors v and −v.
The word Antipodes (pronounced an TIP uh deez) is also used in the United Kingdom to refer to Australia and New Zealand.
www.thebestlinks.com /Antipodes.html   (249 words)

 Glossary of Astronomy, Complexity and Mathematics
Antipodal point: The point that is directly on the opposite side of a planet or moon from a specific location, such as an impact site.
The nadir is the opposite point to the zenith and lies on the opposite side of the Earth beneath where you're located.
The leading apex of the triangle is known as the leading Lagrange point or L4; the trailing apex is the trailing Lagrange point or L5.
www.geocities.com /syzygywjp/Glossary.html   (7023 words)

 Cartography Vocabulary Chapter 2
The position of the projected graticule relative to the ordinary position of the geographical grid on the earth is the: (a) antipodal point; (b) ellipsoid; (c) sexagesimal; (d) Tissot's indicatrix; (e) projection aspect.
Lines or points with a scale factor of 1.0 when transformed from the spherical surface to the plane surface or that have no distortion are described as being: (a) standard; (b) loxodrome; (c) nominal; (d) geoid; (e) developable.
The point on the opposite side of the earth is termed the: (a) loxodrome; (b) GPS; (c) GRS80; (d) antipodal point; (e) geodesy.
www.jsu.edu /depart/geography/mhill/cart/cvch2.html   (1441 words)

 [No title]
The derivative measures the slope of the graph of f(x) at the point.
Points P in the plane can be identified by vectors pointing from 0 to P. A vector in space is defined by two points P,Q in space.
Points P in space can be identified by vectors pointing from 0 to P. Two vectors which can be translated into each other are considered equal.
www.math.harvard.edu /~knill/sofia/data/math21a.txt   (4764 words)

 Terms and Definitions
The point that is directly on the opposite side of the planet; e.g., the Earth's north pole is antipodal to its south pole.
A closed curve that is formed from two foci or points in which the sum of the distances from any point on the curve to the two foci is a constant.
The point at which the solar wind meets the interstellar medium or solar wind from other stars.
www.solarviews.com /eng/terms.htm   (4644 words)

 Maths_01   (Site not responding. Last check: 2007-10-12)
He claimed that if you assumed the earth was a sphere and that its temperature distribution was continuous on the sphere then you could always find antipodal points with the same temperature.
The point -r is the antipodal or opposite point to r on the sphere.
The function g is thus the temperature difference function between antipodal points on the sphere.
www.users.bigpond.com /tjmorrow/maths/m_01.htm   (390 words)

 Question Corner -- Understanding Projective Geometry
The remaining points in projective space are horizontal lines through the origin in 3-d space; these are the "points at infinity".
On a sphere, the shortest path between two points is an arc that is part of a "great circle" on the sphere (one whose centre is the centre of the sphere).
The points on the equator are the "points at infinity".
www.math.toronto.edu /mathnet/questionCorner/projective.html   (2444 words)

 [No title]
She is saying there is some point on the Earth's surface, let's call it 'X', at which the temperature would be completely uneffected if a hole were to be drilled through the Earth all the way to the other side.
In geography, the antipodes (from Greek anti- "opposed" and pous "foot") of any place on Earth is its antipodal point; that is, the region on the Earth's surface which is diametrically opposite to it.
By definition the "antipode" of a point on a sphere is the point defined by the intersection of a line through the original point and the center of the sphere and the surface of the sphere and that is not the original point.
volokh.com /posts/1142373636.comments.html   (6859 words)

 math lessons - Stereographic projection
One approaches that point at infinity by continuing in any direction at all; in that respect this situation is unlike the projective plane, which has many points at infinity.
Let the points of the sphere be projected stereographically onto a plane which is tangent to the pole.
Loxodromes may also found by transforming any point with a Möbius transformation, in particular one with a "characteristic constant" that has an nonzero argument and a modulus not equal to one, and which has fixed points that map to diametrically opposite points on the sphere.
www.mathdaily.com /lessons/Stereographic_projection   (351 words)

 Easter Island   (Site not responding. Last check: 2007-10-12)
The azimuth from the axis point to Giza is 9° and the azimuth from the axis point to Easter is 154°.
The angle of the terrestrial triangle at the axis point is 145°.
This is the same triangle that is formed by the three volcanic peaks on Easter and the same triangle that is found in a pentagram.
home.hiwaay.net /~jalison/easter.html   (384 words)

Antipodal continental outlines are shown (where needed to understand the map) over the ocean as dashed lines.
The intersection points of the line $y=x$ with the logistic curve are, using terms from chaos theory, attractors on either end, and a repelling fixed point in the middle, possibly near the inflection point of the curve.
Another point that is useful for using as a ``central" weight is a Steiner point; in a triangle, it is that point which minimizes total network length joining the three vertices.
www-personal.umich.edu /~copyrght/image/solstice/sols191.html   (10724 words)

 Antipodal point - TheBestLinks.com - Antipode, Australia, Borsuk-Ulam theorem, Circle, ...
Antipodal point - TheBestLinks.com - Antipode, Australia, Borsuk-Ulam theorem, Circle,...
Antipode, Antipodal point, Australia, Borsuk-Ulam theorem, Circle, Diameter...
An antipodal point is sometimes called an antipode, a back-formed word that originated from the mistaken idea that antipodes is the plural of antipode.
www.thebestlinks.com /Antipode.html   (249 words)

 Zoom Astronomy Glossary: A
An aimpoint is a point in the plane of a planet's orbit that a spacecraft aims for (either for a fly by of that planet or to enter that planet's orbit).
For an object (a planet or comet) orbiting the Sun, the aphelion is the point in its orbit which is farthest from the sun.
Azimuth is the angle of the object from the observer's north point (projected onto the horizon).
www.enchantedlearning.com /subjects/astronomy/glossary   (4918 words)

Consider the view from a point on the prime-meridian of longitude and at the latitude phi.
By symmetry, the points alpha=0 and alpha=pi are at the ends of its diameter.
The antipodal point (the point at the other end of the diameter of the sphere; that is, through the center of the sphere) may be obtained by replacing phi with phi+pi, to yield the antipodal point as
www.rism.com /Trig/perspective.htm   (2717 words)

Topology is a branch of mathematics concerned with those properties of geometric configurations (as sets of points) which are unaltered by elastic deformations (as a stretching or a twisting) that are homeomorphisms.
a p-collar is the union of all p-neighborhoods of points on a path, used in constructing a tube out of a path (as in knot theory).
Two points lie in the same path component of a space X iff there is a path in X from one point to the other.
mcraefamily.com /MathHelp/BasicSetTopologyGlossary.htm   (2717 words)

 Siriusly - Supplement [Geographic Geometry]   (Site not responding. Last check: 2007-10-12)
The circle is oriented so that the two points where the circle crosses the equator are on the horizontal axis, and the two points where the circle reaches its greatest latitudes are on the vertical axis.
The straight line distance from Easter Island to its antipodal point in the Indus Valley (7,924 miles), which is also the diameter of the Earth, is 3.1416 times the straight line distance from Easter Island to Machupicchu (2,522 miles), a precise expression of phi.
Measuring the amplitude from the top of the wavelength to the bottom (from 30° N to 30° S), the amplitude is equal to the radius of the Earth, and the ratio between the frequency and the amplitude of the wave is 2pi.
dudeman.net /siriusly/0/sup/geogeom.shtml   (5894 words)

If one imagines a stick passed through the very centre of the earth, the points where the stick enters the surface and where it exits are antipodal to one another.
At least one pair of antipodal points are required on a circumnavigation to define a great circle route.
When it became apparent that I would have to go towards Honolulu to pick up spares and then dicovering the damage to the mast that required me to put into Honolulu, the antipodal point at 24.11 north 143.22 east became self-selecting.
www.bymnews.com /new/content/view/31099/50   (277 words)

 Map Projections: Azimuthal Projections   (Site not responding. Last check: 2007-10-12)
Given reference point A, the azimuth remains unchanged from points B and C on the sphere to corresponding B' and C' on an azimuthal map.
The result is the map backface, which covers the entire plane (regions near the source point lie at infinity, and that point itself cannot be mapped).
However, for lesser overall distortion the latter may be presented in a separate map centered on the antipodal point.
www.progonos.com /furuti/MapProj/Normal/ProjAz/projAz.html   (836 words)

 Globe - Biocrawler   (Site not responding. Last check: 2007-10-12)
The most common type has long, thin strips that touch at the equator, and narrow to a point at the north pole and the south pole.
The more strips there are, the less stretching and crumpling is required to make the paper map fit the sphere.
From a geometric point of view, all points on a sphere are equivalent -- one could select any arbitrary point on the earth, and create a paper map that covers the earth with strips that come together at that point and the antipodal point.
www.biocrawler.com /encyclopedia/Globe   (405 words)

 Terms and Definitions
One of the solutions to the three-body problem discovered by the eighteenth century French mathematician Lagrange; the two stable Lagrangian points, L-4 and L-5, lie in the orbit of the primary body, leading and trailing it by a 60-degree arc.
The path of an object that is moving around a second object or point.
Satellites which orbit at the Lagrangian points, 60° ahead of and 60° behind another satellite.
www.iki.rssi.ru /solar/eng/terms.htm   (4393 words)

 Astronomy Dictionary
the point on the celestial sphere where the sun crosses the celestial equator from north to south.
the north and south celestial poles are points on the celestial sphere where earths axis of rotation intersects the celestial sphere.
At this point the star begins to loose mass in the form of stellar wind.
users.skynet.be /sky03361/dictionary/dictionary.html   (9103 words)

 MW - Antipode Maps
For every point on earth, there is another point exactly opposite, the farthest point on earth away from you.
Pretty much all of the continental United States has antipodal points in the middle of the Indian Ocean.
Antipodal points for Ile Amsterdam (Mapquest Map of N 37°50', W -103°35') and
www.matthewweathers.com /year2004/antipode_maps.htm   (351 words)

 Appendix 6 of THE ATLANTIS BLUEPRINT   (Site not responding. Last check: 2007-10-12)
The thickest ice on Antarctica is antipodal to the thickest ice on Greenland.
The cross-polar point to the thickest ice on Greenland is on the New Siberian Islands, which were formerly the home of a host of temperate-adapted animals.
The antipodal point to the New Siberian Islands is Lesser Antarctica, which would have enjoyed a temperate climate 12,000 years ago.
www.flem-ath.com /stws10.htm   (257 words)

 [No title]   (Site not responding. Last check: 2007-10-12)
The antipodal point to DC is about 52 S, 102 E, in the southeastern Indian Ocean.
When talking about marsupials versus placentals, though, he was pointing to how obvious the difference (in tear duct location) was but it took me a long time to see it.
On a related point, I think (counting my daughter and Clark's son), the median education level present was master's degree.
www.coe.uga.edu /~pkeck/ediacara/howlerfest/96Grumbine.txt   (1244 words)

 [No title]
I put the origin x=0 at the point A. I know that the circumference of the earth is 24,856 miles therefore the point antipodal to A that I called A’ is at 24,856/2=12,428 miles.
I then define a function f(x) which equals the temperature at x subtract the temperature at the point antipodal to x.
If I choose a specific point on the Tropic of Cancer the temperature at this point won’t be the same at his antipodal point, which will be on the Tropic of the Capricorn because the Tropic of Cancer have higher temperature than Tropic of Capricorn.
alien.dowling.edu /~petko/calc1/homework.doc   (628 words)

 Solar System Dynamics
Antipodal to the Caloris Basin is an area of chaotic terrain.
The main point, that the water budget delivered to the habitable zone depends sensitively on the existence and properties of giant planets, can be extended to other volatiles as well,including organics.
The most stable state of Uranus may be with its rotational axis pointed toward the Sun, so that the Solar hemisphere would be entirely in the inner solar system Minkowski acceleration phase and the anti-Solar hemisphere would be in entirely in the outer Segal Conformal acceleration phase.
www.valdostamuseum.org /hamsmith/solsyscol.html   (8221 words)

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