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In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. [1] Arithmetic geometry is centered around Diophantine geometry , the study of rational points of algebraic varieties .
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.
Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer . Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry , [ a ] which includes the notions of point , line , plane , distance , angle , surface , and curve , as ...
Arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Subcategories This category has the following 3 subcategories, out of 3 total.
Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication, and division) first
Arithmetic geometry, however, is a contemporary term for much the same domain as that covered by the term Diophantine geometry. The term arithmetic geometry is arguably used most often when one wishes to emphasize the connections to modern algebraic geometry (for example, in Faltings's theorem) rather than to techniques in Diophantine ...
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine equations in higher dimensions. Background