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Problem in probability theory
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that
Problem_of_points
Computational geometry problem
pair of points problem or closest pair problem is a problem of computational geometry: given n {\displaystyle n} points in metric space, find a pair of points
Closest pair of points problem
Closest_pair_of_points_problem
Thought experiment in ethics
Trolley Problem and the Dropping of Atomic Bombs, Masahiro Morioka considers the dropping of atomic bombs as an example of the trolley problem and points out
Trolley_problem
Mathematical problem involving optimal stopping theory
The secretary problem demonstrates a scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics
Secretary_problem
Probability of shared birthdays
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday
Birthday_problem
Five coplanar points have a subset forming a convex quadrilateral
approach, that N = 30 {\displaystyle N=30} . The problem of finding sets of n points minimizing the number of convex quadrilaterals is equivalent to minimizing
Happy_ending_problem
Concept in probability theory and gambling
Fermat in 1656 (two years after the more famous correspondence on the problem of points). Pascal's version was summarized in a 1656 letter from Pierre de
Gambler's_ruin
NP-hard problem in combinatorial optimization
points. Of course, this problem is solvable by finitely many trials. Rules which would push the number of trials below the number of permutations of the
Travelling_salesman_problem
Mathematical problem
followed by a paper by Adam Elga. A formal analysis of the problem of belief formation in decision problems with imperfect recall was provided first by Michele
Sleeping_Beauty_problem
Mathematical problem
The three prisoners problem appeared in Martin Gardner's "Mathematical Games" column in Scientific American in 1959. It is mathematically equivalent to
Three_prisoners_problem
Problem in geometric probability
geometric probability, the broken stick problem asks for the probability that one can form a triangle from the three parts of a line segment that has been split
Broken_stick_problem
Problem in geometric probability
Sylvester's four point problem in geometric probability asks for the probability that four randomly chosen points in the Euclidean plane form a convex
Sylvester's four point problem
Sylvester's_four_point_problem
Geometry problem on grid points
Unsolved problem in mathematics How many points can be placed in an n-by-n grid so that no three of them lie on a line? More unsolved problems in mathematics
No-three-in-line_problem
Mathematical problem
Unsolved problem in mathematics How many colors are needed to color the plane so that no two points at unit distance are the same color? More unsolved
Hadwiger–Nelson_problem
Problem asking the probability that the sun will rise tomorrow
sunrise problem can be expressed as follows: "What is the probability that the sun will rise tomorrow?" The sunrise problem illustrates the difficulty of using
Sunrise_problem
Mental exercise in probability and statistics
In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc
Urn_problem
Balanced or random resource allocation
balanced allocations) problem is a classic problem in probability theory that has many applications in computer science. The problem involves m balls and
Balls_into_bins_problem
How many integer lattice points there are in a circle
In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and
Gauss_circle_problem
Distance estimation problems in computational geometry
problems stated in terms of points only are sometimes referred to as closest point problems, although the term "closest point problem" is also used synonymously
Proximity_problems
On reflection in a spherical mirror
that is tangent to the circle and has the given points as its foci. Although special cases of this problem were studied by Ptolemy in the 2nd century CE
Alhazen's_problem
Question in geometric probability
problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: Suppose we have a floor made of parallel strips of wood
Buffon's_needle_problem
Problem in probability theory
collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product
Coupon_collector's_problem
Physics problem related to laws of motion and gravity
specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses orbiting each other
Three-body_problem
Probability problem
moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence (m0, m1, m2, ...) be the sequence of moments
Hausdorff_moment_problem
Concept in probability theory
to accompany during a trip. One problem was the so-called problem of points, a classic problem already then (treated by Luca Pacioli as early as 1494, and
Classical definition of probability
Classical_definition_of_probability
Paradox in probability theory
surrounds a set of questions in probability theory, which are also known as the two children problem, Mr. Smith's children and the Mrs. Smith problem. The initial
Boy_or_girl_paradox
Puzzle in logic and mathematics
The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for
Two_envelopes_problem
Geometry problem about finding touching circles
In Euclidean plane geometry, the problem of Apollonius (also called Apollonius's problem or the Apollonian problem) is to construct circles that are tangent
Problem_of_Apollonius
Probability problem
Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1, m2, ...) to be of the form m
Stieltjes_moment_problem
Problem in statistical estimation
In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without
German_tank_problem
Probability problem
answer to the problem means that (m0, m1, m2, ...) is the sequence of moments of some positive Borel measure μ. The Stieltjes moment problem, Vorobyev moment
Hamburger_moment_problem
Problem in geometry
Moser's circle problem asks how many regions a circle can be divided into by choosing n {\displaystyle n} points along the circumference of the circle and
Moser's_circle_problem
Equilibrium points near two orbiting bodies
celestial mechanics, the Lagrange points (/ləˈɡrɑːndʒ/), also called the Lagrangian points or libration points, are points of equilibrium for small-mass objects
Lagrange_point
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematical paradox
including the Kolmogorov axioms. The problem can be reframed by describing the boxes as each having one drawer on each of two sides. Each drawer contains a
Bertrand's_box_paradox
Two-dimensional packing problem
n points in a unit square in order to maximize the minimal separation, dn, between points. To convert between these two formulations of the problem, the
Circle_packing_in_a_square
Unsolved problem in mathematics For how many points is it always possible to projectively transform the points into convex position? More unsolved problems in
McMullen_problem
Three tangent circles in a triangle
two triangle centers, the Ajima–Malfatti points of a triangle. The problem of maximizing the total area of three circles in a triangle is never solved
Malfatti_circles
Problem of minimizing sum of transport costs
the problem of computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although
Weber_problem
mathematical field of combinatorial geometry, the Littlewood–Offord problem is the problem of determining the number of subsums of a set of vectors that fall
Littlewood–Offord_problem
Computer software bug occurring in 2038
after 03:14:07 UTC on 19 January 2038. The problem exists in systems which measure Unix time—the number of seconds elapsed since the Unix epoch (00:00:00
Year_2038_problem
Finding the smallest circle that contains all given points
geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The corresponding problem in n-dimensional
Smallest-circle_problem
Election result probability theorem
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with
Bertrand's_ballot_theorem
On point sets with no small-area triangles
problem in mathematics What is the asymptotic growth rate of the area of the smallest triangle determined by three out of n {\displaystyle n} points in
Heilbronn_triangle_problem
Circle-packing on the surface of a sphere
the Tammes problem is a problem in packing a given number of points on the surface of a sphere such that the minimum distance between points is maximized
Tammes_problem
trigonometric moment problem. The trigonometric moment problem is solvable, that is, { c k } k = 0 n {\displaystyle \{c_{k}\}_{k=0}^{n}} is a sequence of Fourier coefficients
Trigonometric_moment_problem
Problem in probability
Banach's match problem is a classic problem in probability attributed to Stefan Banach. Feller says that the problem was inspired by a humorous reference
Banach's_matchbox_problem
Probability theory paradox
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités
Bertrand paradox (probability)
Bertrand_paradox_(probability)
coordinates of p. The maxima of a point set S are all the maximal points of S. The problem of finding all maximal points, sometimes called the problem of the
Maxima_of_a_point_set
Aspect of control theory
sheep problem or Mabinogian urn is a problem in stochastic control introduced by David Williams (mathematician) in 1991, who named it after a herd of magic
Mabinogion_sheep_problem
Trying to map moments to a measure that generates them
mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ {\displaystyle \mu } to the sequence of moments m n =
Moment_problem
In game theory, the Waldegrave problem is a problem first described in the second edition of Pierre Raymond de Montmort`s Essay d'analyse sur les jeux
Waldegrave_problem
Probability problem
The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice. In 1693 Samuel Pepys and
Newton–Pepys_problem
On short connecting nets with added points
the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization
Steiner_tree_problem
Mathematical problem
problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that
Coin_problem
Does the plane contains a dense set of points whose distances are all rational
Unsolved problem in mathematics Is there a dense set of points in the plane at rational distances from each other? More unsolved problems in mathematics
Erdős–Ulam_problem
Probability puzzle
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal
Monty_Hall_problem
Variation of Buffon's needle
In geometric probability, the problem of Buffon's noodle is a variation on the well-known problem of Buffon's needle, named after Georges-Louis Leclerc
Buffon's_noodle
Method to solve constrained optimization problems
qualification. However, not all stationary points yield a solution of the original problem, as the method of Lagrange multipliers yields only a necessary
Lagrange_multiplier
Combinatorial optimization problem
problem with a wide range of applications from finance and economics to machine learning. QUBO is an NP hard problem, and for many classical problems
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Philosophical problem about why neural processes give rise to inner experience at all
In philosophy of mind, the hard problem of consciousness (or simply the hard problem) is to explain how and why organisms have qualia, phenomenal consciousness
Hard_problem_of_consciousness
American-Turkish mathematician (born 1992)
collaborators gave a second proof that Hilbert's tenth problem has a negative answer over the ring of integers of every algebraic number field, a result originally
Levent_Alpöge
Paradox involving a game with repeated coin flipping
resident of Saint Petersburg, who in 1738 published his thoughts about the problem in the Commentaries of the Imperial Academy of Science of Saint Petersburg
St._Petersburg_paradox
Several sets of circles associated with Apollonius of Perga
circles, formed by solving Apollonius's problem iteratively. A circle is usually defined as the set of points P at a given distance r (the circle's radius)
Circles_of_Apollonius
Computational problem of interest in computer science
unsolved problems in computer science The k-server problem is a problem of theoretical computer science in the category of online algorithms, one of two abstract
K-server_problem
Millennium Prize Problem
unsolved problem in mathematics since the early 20th century. The equations are a system of partial differential equations that describe the motion of a fluid
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
Optimisation problem in triangle geometry
problem is an optimization problem that was first stated by Giovanni Fagnano in 1775: For a given acute triangle determine the inscribed triangle of minimal
Fagnano's_problem
Arrangement of points on a sphere
behaviour of the total potential when the number N of points goes to infinity, not for concrete values of N. The solution of the Thomson problem for two
Thomson_problem
Problem in discrete geometry
geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly linear number of distinct distances. It was posed by
Erdős distinct distances problem
Erdős_distinct_distances_problem
Problem in physics and celestial mechanics
In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally
N-body_problem
Problem of computing shortest paths around geometric obstacles
shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest
Euclidean_shortest_path
Problem in celestial mechanics
celestial mechanics, Lambert's problem is concerned with the determination of an orbit from two position vectors and the time of flight, posed in the 18th
Lambert's_problem
Philosophical question
philosophy of religion, the problem of evil, also known as the problem of suffering, is the philosophical question of how to reconcile the existence of evil
Problem_of_evil
On distance sets of high-dimensional sets
named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact d {\displaystyle d} -dimensional
Falconer's_conjecture
Eight disciplines of team-oriented problem solving method
problem from any customer. D4: Determine and Verify Root Causes and Escape Points: Identify all applicable causes that could explain why the problem has
Eight disciplines problem solving
Eight_disciplines_problem_solving
Open problem on 3x+1 and x/2 functions
converge to 1? More unsolved problems in mathematics The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture
Collatz_conjecture
Technique in computer vision
Perspective-n-Point (PnP) is the problem of estimating the pose of a camera given a set of n 3D points in the world and their corresponding 2D projections
Perspective-n-Point
Initial set of valid possible values
space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially
Feasible_region
Existence of a line through two points
problem in 1893, and Tibor Gallai, who published one of the first proofs of this theorem in 1944. A line that contains exactly two of a set of points
Sylvester–Gallai_theorem
Combinatorial optimization problem
In its most general case the problem is stated as follows: given a set of n demand points, a space of feasible locations of a facility and a function to
1-center_problem
list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known
List_of_NP-complete_problems
Optimization problem in computer science
registration Computational geometry – see Closest pair of points problem Cryptanalysis – for lattice problem Databases – e.g. content-based image retrieval Coding
Nearest_neighbor_search
than would be possible from the original points alone. The name of these points comes from the Steiner tree problem, named after Jakob Steiner, in which the
Steiner point (computational geometry)
Steiner_point_(computational_geometry)
Problem of finding the best feasible solution
constrained problems and multimodal problems. In the context of an optimization problem, the search space refers to the set of all possible points or solutions
Optimization_problem
one can choose from n {\displaystyle n} points so that every six points contain at most two triples. The problem is named after Imre Z. Ruzsa and Endre
Ruzsa–Szemerédi_problem
Problem that is difficult or impossible to solve
In planning and policy, a wicked problem is a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements
Wicked_problem
Mathematical problem
gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from the following real-world problem: "In
Art_gallery_problem
Fundamental topographical problem
three points. The problem is to find the positions of P1 and P2. See figure; the angles measured are (α1, β1, α2, β2). Since it involves observations of angles
Hansen's_problem
Plays by Shakespeare characterised by complex and ambiguous tone
material and dark, psychological drama. Shakespeare's problem plays eschew the traditional trappings of both comedy and tragedy, and are sometimes cited as
Shakespearean_problem_play
Point minimizing sum of distances to given points
points in the plane (that is, m = 3 and n = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal
Geometric_median
Unsolved problem in extremal graph theory
Unsolved problem in mathematics What is the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete
Zarankiewicz_problem
geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words
Mean_line_segment_length
Problem in combinatorial optimization
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items
Knapsack_problem
Hypersurface used by a classification algorithm
of a problem space in which the output label of a classifier is ambiguous. If the decision surface is a hyperplane, then the classification problem is
Decision_boundary
1918 U.S. peace proposals after World War I
The Fourteen Points was a statement of principles for peace that was to be used for peace negotiations in order to end World War I. The principles were
Fourteen_Points
Algorithmic problem on point-line incidence
Hopcroft's problem is the problem of testing, for a given system of points and lines in the Euclidean plane, whether at least one of the points lies on at
Hopcroft's_problem
more images of the same 3D scene, taken from different points of view, the correspondence problem refers to the task of finding a set of points in one image
Correspondence_problem
In mathematics, the Fekete problem is, given a natural number N and a real s ≥ 0, to find the points x1,...,xN on the 2-sphere for which the s-energy
Fekete_problem
Type of computational problem
examples of covering problems are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and
Covering_problems
Differential calculus on function spaces
Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are
Calculus_of_variations
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PROBLEM OF-POINTS
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PROBLEM OF-POINTS
PROBLEM OF-POINTS
PROBLEM OF-POINTS
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