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The Collatz conjecture states that all paths eventually lead to 1. The Collatz conjecture[a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.
First "push" the loop into a three-dimensional subspace, which is always possible, though technical to explain. Four-dimensional space occurs in classical knot theory, however, and an important topic is the study of slice knots and ribbon knots. A notorious open problem asks whether every slice knot is also ribbon.
Iteration. Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of ...
Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Loop (topology) Two loops a, b in a torus. In mathematics, a loop in a topological space X is a continuous function f from the unit interval I = [0,1] to X such that f(0) = f(1). In other words, it is a path whose initial point is equal to its terminal point. [1] A loop may also be seen as a continuous map f from the pointed unit circle S1 into ...
100 prisoners problem. Each prisoner has to find their own number in one of 100 drawers, but may open only 50 of the drawers. The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive.
alternating, hyperbolic. In mathematics, the Borromean rings[ a ] are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the three is cut or removed. Most commonly, these rings are drawn as three ...