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  2. Melbourne–Evans collision - Wikipedia

    en.wikipedia.org/wiki/Melbourne–Evans_collision

    [4] [5] Additionally, during the lead-up to the exercise, Crabb had strongly warned that all repositioning manoeuvres performed by the escorts had to commence with a turn away from Melbourne. [ 3 ] Despite these warnings, a near-miss occurred in the early hours of 31 May when Larson turned towards the carrier after being ordered to the plane ...

  3. Incidence geometry - Wikipedia

    en.wikipedia.org/wiki/Incidence_geometry

    In his work [9] on proving the independence of the set of axioms for projective n-space that he developed, [10] he produced a finite three-dimensional space with 15 points, 35 lines and 15 planes, in which each line had only three points on it. [11] The planes in this space consisted of seven points and seven lines and are now known as Fano planes.

  4. Moduli space - Wikipedia

    en.wikipedia.org/wiki/Moduli_space

    The real projective space P n is a moduli space that parametrizes the space of lines in R n+1 which pass through the origin. Similarly, complex projective space is the space of all complex lines in C n+1 passing through the origin.

  5. Chern class - Wikipedia

    en.wikipedia.org/wiki/Chern_class

    It is an exercise in elementary geometry to see that the complex tangent space to ... The k-th Chern class of E, which is usually denoted c k (E), ...

  6. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

  7. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    Important classes of convex polyhedra include the family of prismatoid, the Platonic solids, the Archimedean solids and their duals the Catalan solids, and the regular polygonal faces polyhedron. The prismatoids are the polyhedron whose vertices lie on two parallel planes and their faces are likely to be trapezoids and triangles. [ 18 ]

  8. Passage of Humaitá - Wikipedia

    en.wikipedia.org/wiki/Passage_of_Humaitá

    It lay at the corner of the Quadrilateral – the line of earthworks that protected Humaitá from seizure on its landward side – at the site where the disastrous land battle had taken place. Its river artillery alone comprised 35 heavy guns; [ 105 ] indeed the Paraguayans had partly denuded Humaitá of guns to reinforce Curupayty. [ 106 ]

  9. Cubic surface - Wikipedia

    en.wikipedia.org/wiki/Cubic_surface

    Given an identification between a cubic surface on X and the blow-up of at 6 points in general position, the 27 lines on X can be viewed as: the 6 exceptional curves created by blowing up, the birational transforms of the 15 lines through pairs of the 6 points in , and the birational transforms of the 6 conics containing all but one of the 6 ...