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It is also possible to describe all conic sections in terms of a single focus and a single directrix, which is a given line not containing the focus. A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity e.
Proofs of the mathematical result that the rational number 22 / 7 is greater than π (pi) date back to antiquity. One of these proofs, more recently developed but requiring only elementary techniques from calculus, has attracted attention in modern mathematics due to its mathematical elegance and its connections to the theory of Diophantine approximations.
Mathematics . Lists of mathematics topics cover a variety of topics related to mathematics.Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles.
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.
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.
Mathematics education in the United States varies considerably from one state to the next, and even within a single state. However, with the adoption of the Common Core Standards in most states and the District of Columbia beginning in 2010, mathematics content across the country has moved into closer agreement for each grade level.
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
An Introduction to the Philosophy of Mathematics is a 2012 textbook on the philosophy of mathematics by Mark Colyvan.It has a focus on issues in contemporary philosophy, such as the mathematical realism–anti-realism debate and the philosophical significance of mathematical practice, and largely skips over historical debates.