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2. VSEPR theory - Wikipedia

   en.wikipedia.org/wiki/VSEPR_theory

   [1]: 416 The geometry of the central atoms and their non-bonding electron pairs in turn determine the geometry of the larger whole molecule. The number of electron pairs in the valence shell of a central atom is determined after drawing the Lewis structure of the molecule, and expanding it to show all bonding groups and lone pairs of electrons.

3. Stable marriage problem - Wikipedia

   en.wikipedia.org/wiki/Stable_marriage_problem

   In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element.

4. Closest pair of points problem - Wikipedia

   en.wikipedia.org/wiki/Closest_pair_of_points_problem

   The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...

5. Relation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Relation_(mathematics)

   In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...

6. Screw theory - Wikipedia

   en.wikipedia.org/wiki/Screw_theory

   Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors [1] – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies.

7. Stable roommates problem - Wikipedia

   en.wikipedia.org/wiki/Stable_roommates_problem

   To find it, start at such a p 0 containing at least two individuals in their reduced list, and define recursively q i+1 to be the second on p i 's list and p i+1 to be the last on q i+1 's list, until this sequence repeats some p j, at which point a rotation is found: it is the sequence of pairs starting at the first occurrence of (p j, q j ...

8. Congruence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Congruence_(geometry)

   ASA and AAS are sometimes combined into a single condition, AAcorrS – any two angles and a corresponding side. [3] RHS (right-angle-hypotenuse-side), also known as HL (hypotenuse-leg): If two right-angled triangles have their hypotenuses equal in length, and a pair of other sides are equal in length, then the triangles are congruent.

9. Cavalieri's principle - Wikipedia

   en.wikipedia.org/wiki/Cavalieri's_principle

   Consider the rectangle bounding a single cycloid arch. From the definition of a cycloid, it has width 2π r and height 2 r , so its area is four times the area of the circle. Calculate the area within this rectangle that lies above the cycloid arch by bisecting the rectangle at the midpoint where the arch meets the rectangle, rotate one piece ...