Polar space

In mathematics, in the field of geometry, a polar space of rank n (n ≥ 3), or projective index n − 1, consists of a set P, conventionally the set of points, together with certain subsets of P, called subspaces, that satisfy these axioms:

  • Every subspace is isomorphic to a projective geometry Rd(K) with −1 ≤ d ≤ (n − 1) and K a division ring. By definition, for each subspace the corresponding d is its dimension.
  • The intersection of two subspaces is always a subspace.
  • For each point p not in a subspace A of dimension of n − 1, there is a unique subspace B of dimension n − 1 such that A ∩ B is (n − 2)-dimensional. The points in A ∩ B are exactly the points of A that are in a common subspace of dimension 1 with p.
  • There are at least two disjoint subspaces of dimension n − 1.

    • It is possible to define and study a slightly bigger class of objects using only relationship between points and lines: a polar space is a partial linear space (P,L), so that for each point p ∈ P and each line l ∈ L, the set of points of l collinear to p, is either a singleton or the whole l.

    Read more
    This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Polar_space

    Podcasts:

    Email this Page Play all in Full Screen Show More Related Videos
    PLAYLIST TIME:

    Latest News for: polar space

    Bitcoin investor finances SpaceX flight for polar journey

    The Bitcoin News 03 Apr 2025
    A remarkable event in the history of space travel recently occurred when Bitcoin investor Chun Wang funded a SpaceX flight that took him and three other adventurers across the North and South Polar regions.

    Flat Earthers 'in shambles' after astronauts release new footage of our planet | Daily Mail Online

    The Daily Mail 03 Apr 2025
    Civilian astronauts captured astounding footage of Earth from space that clearly shows the planet's curvature, sparking outrage among flat Earthers ... and ice blanketing one of Earth's two polar regions.

    Katy Perry, Gayle King slammed for feminist spin on Bezos space flight

    The Mercury News 03 Apr 2025
    King has been called out before for participating in this space flight, especially given that she’s a journalist at a time when Bezos and Sanchez have become polarizing public figures, having ...

    Humans orbit Earth over north, south poles for first time with SpaceX Fram2 mission

    Interesting Engineering 02 Apr 2025
    They launched from Kennedy Space Center, Florida into a polar orbit, where they will spend three to five days conducting scientific research ... There are two reasons why space missions rarely fly in polar orbits.

    SpaceX Makes History By Orbiting Over The Earth's Poles. Why Haven't We Done It Before?

    IFL Science 02 Apr 2025
    They do not need to pass exactly over the North and South Poles; a deviation of 10 degrees is still classed as a polar orbit," the European Space Agency (ESA) explains ... NASA and other space agencies ...

    Who is SpaceX Crypto Astronaut Chun Wang? What Coins Does Crypto Space Millionaire HODL?

    99 Bitcoins 02 Apr 2025
    At 9.46 PM Monday, Falcon 9 roared off the pad at Kennedy Space Center, hauling a four-member crew destined for polar orbits. Over the next few days, they’ll chart untouched latitudes and conduct key studies on how space changes the human body.

    SpaceX Launches Private Astronauts on First Crewed Polar Orbit

    The Daily Tribune - Bahrain 02 Apr 2025
    “With the same pioneering spirit as early polar explorers, we aim to bring back new data and knowledge to advance the long-term goals of space exploration,” mission commander Chun Wang said before the launch.

    Fram2 astronauts reveal first-ever view of Earth’s poles from space, Elon Musk responds - “This is the first time humans have been in orbit…”

    The Times of India 02 Apr 2025
    With the historic launch of the Fram2 mission, SpaceX made history by putting out the first-ever viewed video from space of Earth's polar caps.

    Bitcoin investor buys an entire SpaceX flight for the ultimate polar adventure

    The Daily Times 02 Apr 2025
    A bitcoin investor is headed to space with three ...

    Trump's Columbia University ultimatum puts academic freedom in peril

    Newsday 02 Apr 2025
    American higher education is grounded in the principle of autonomy — universities as spaces for inquiry, dissent, and intellectual diversity. In today’s polarized climate, that ideal has often collided ...

    Bitcoin investor begins historic polar space adventure

    Hong Kong Standard 01 Apr 2025
    Wang has already visited the polar regions in person and wants to view them from space ... The crew plans two dozen experiments - including taking the first human X-rays in space - and brought along more ...

    Bitcoin investor buys space flight for polar adventure

    Taipei Times 01 Apr 2025
    SpaceX’s Falcon 9 rocket is launched, carrying four commercial astronauts into a 90-degree inclination polar orbit on the Fram2 mission at the Kennedy Space Center in Cape Canaveral, Florida, on Monday.

    Bitcoin investor, a Maltese citizen, buys an entire SpaceX flight for the ultimate polar adventure

    The Malta Independent 01 Apr 2025
    Wang has already visited the polar regions in person and wants to view them from space ... The crew plans two dozen experiments - including taking the first human X-rays in space - and brought along more ...

    What we know so far: Fram2 orbits Earth's poles in SpaceX astronaut mission of firsts

    Florida Today 01 Apr 2025
    All four are explorers of extreme places on Earth, such as the polar regions ... Just less than 114 years after the first crew reached the South Pole, Fram2 became the first to reach it from space.First astronauts to reach a polar orbit.

    WATCH REPLAY: SpaceX Successfully Launches Fram2 Mission to Polar Orbit from Kennedy Space Center on Monday

    Space Coast Daily 01 Apr 2025
    ET, Falcon 9 launched Fram2 to a polar orbit from Launch Complex 39A at NASA’s Kennedy Space Center in Florida ... ET, Falcon 9 launched Fram2 to a polar orbit from Launch Complex 39A at NASA’s Kennedy Space Center in Florida.

    Article Search

    tools
    ×
    ×
    ×
    ×