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This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras. List of algorithms. List of axioms. List of conjectures. List of data structures. List of derivatives and integrals in alternative calculi. List of equations.
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint.
Fundamental theorem of arithmetic. Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel's first incompleteness theorem. Gödel's second incompleteness theorem. Goodstein's theorem. Green's theorem (to do) Green's theorem when D is a simple region. Heine–Borel theorem.
e. Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This may also include the philosophical study of the relation of this framework with reality.
Thales (624–546 BCE) and Hippocrates of Chios (c. 470–410 BCE) gave some of the first known proofs of theorems in geometry. Eudoxus (408–355 BCE) and Theaetetus (417–369 BCE) formulated theorems but did not prove them. Aristotle (384–322 BCE) said definitions should describe the concept being defined in terms of other concepts already ...
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.
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. [2] It was popularized in English by Hugo Steinhaus in the 1950 edition of his book Mathematical ...
This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms , list of theorems and list of conjectures .
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