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Certain paper-folding problems do not have efficient algorithms. Computational intractability results show that there are no such polynomial-time algorithms that currently exist to solve certain folding problems. For example, it is NP-hard to evaluate whether a given crease pattern folds into any flat origami. [47]
He argued that the toolbox of physics enables a practitioner like Edward Witten to go beyond standard mathematics, in particular the geometry of 4-manifolds. The tools of a physicist are cited as quantum field theory , special relativity , non-abelian gauge theory , spin , chirality , supersymmetry , and the electromagnetic duality .
This is a list of noteworthy publications in physics, organized by type. General audience. List of books on popular physics concepts; Textbooks. List of textbooks on ...
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives ...
No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. […] Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them." [48]
In physics, a unified field theory (UFT) is a type of field theory that allows all fundamental forces and elementary particles to be written in terms of a single type of field. According to modern discoveries in physics, forces are not transmitted directly between interacting objects but instead are described and interpreted by intermediary ...
During this period there was little distinction between physics and mathematics; [18] as an example, Newton regarded geometry as a branch of mechanics. [19] Non-Euclidean geometry, as formulated by Carl Friedrich Gauss, János Bolyai, Nikolai Lobachevsky, and Bernhard Riemann, freed physics from the limitation of a single Euclidean geometry. [20]
According to Asher Peres [4] and David Kaiser, [5] the publication of the 1982 proof of the no-cloning theorem by Wootters and Zurek [2] and by Dieks [3] was prompted by a proposal of Nick Herbert [6] for a superluminal communication device using quantum entanglement, and Giancarlo Ghirardi [7] had proven the theorem 18 months prior to the published proof by Wootters and Zurek in his referee ...