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The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
Japanese theorem for concyclic quadrilaterals (Euclidean geometry) John ellipsoid ; Jordan curve theorem ; Jordan–Hölder theorem (group theory) Jordan–Schönflies theorem (geometric topology) Jordan–Schur theorem (group theory) Jordan's theorem (multiply transitive groups) (group theory) Joubert's theorem ; Jung's theorem
In the AMS Theorem Environment for LaTeX, the hollow square is the default end-of-proof symbol. Unicode explicitly provides the "end of proof" character, U+220E (∎). Some authors use other Unicode symbols to note the end of a proof, including, (U+25AE, a black vertical rectangle), and ‣ (U+2023, a triangular bullet).
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.
With the increase in computing power in the 1960s, significant work began to be done investigating mathematical objects beyond the proof-theorem framework, [27] in experimental mathematics. Early pioneers of these methods intended the work ultimately to be resolved into a classical proof-theorem framework, e.g. the early development of fractal ...
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
Bayes' theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. Beckstrom's law, in economics, states that the value of a network equals the net value added to each user's transactions conducted through that network, summed over all users. Named for Rod Beckstrom.
Please also observe that a theorem is distinct from a theory. A lemma is conceptually the same as a theorem. However a theorem is called a lemma when its proof is only considered to be a step in the proof of some other, more important theorem.
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