# Knowledge objects Understand concepts through definitions, assumptions and formulas, then follow guides, practice and evidence. 1 [2](/en/knowledge/?page=2#results) … [13](/en/knowledge/?page=13#results)[Next →](/en/knowledge/?page=2#results) 302 results · Page 1 of 13 Knowledge object ## [Points, lines, and planes](/en/mko/mko-point-line-plane/?from=%2Fen%2Fknowledge%2F) Points, lines, and planes provide foundational geometric language for position, direction, collinearity, coplanarity, and incidence. mko-point-line-plane · Geometry Knowledge object ## [Angle](/en/mko/mko-angle/?from=%2Fen%2Fknowledge%2F) In elementary Euclidean geometry, an angle is formed by two rays with a common endpoint, and its opening can be described in degrees. mko-angle · Geometry Knowledge object ## [Triangle](/en/mko/mko-triangle/?from=%2Fen%2Fknowledge%2F) In the plane, three distinct noncollinear points together with the three segments joining them form a nondegenerate triangle. mko-triangle · Geometry Knowledge object ## [Right triangle](/en/mko/mko-right-triangle/?from=%2Fen%2Fknowledge%2F) A triangle having one interior angle that is a right angle. mko-right-triangle · Geometry Knowledge object ## [Euclidean length](/en/mko/mko-euclidean-length/?from=%2Fen%2Fknowledge%2F) The distance between two points in the plane is defined as the nonnegative square root of the sum of squared coordinate differences. mko-euclidean-length · Geometry Knowledge object ## [Pythagorean theorem](/en/mko/mko-euclid-pythagorean-theorem/?from=%2Fen%2Fknowledge%2F) In a right triangle, the sum of the squares of the two leg lengths equals the square of the hypotenuse length. mko-euclid-pythagorean-theorem · Geometry Knowledge object ## [Natural number](/en/mko/mko-natural-number/?from=%2Fen%2Fknowledge%2F) Natural numbers are basic numbers for counting and discrete order; this entry adopts the convention that they include 0. mko-natural-number · Arithmetic and number systems Knowledge object ## [Integer](/en/mko/mko-integer/?from=%2Fen%2Fknowledge%2F) The integers consist of zero, the positive integers, and the negative integers, extending natural numbers to represent opposite directions and differences. mko-integer · Arithmetic and number systems Knowledge object ## [Rational number](/en/mko/mko-rational-number/?from=%2Fen%2Fknowledge%2F) A rational number can be represented as a ratio of two integers with a nonzero denominator. mko-rational-number · Arithmetic and number systems Knowledge object ## [Real number](/en/mko/mko-real-number/?from=%2Fen%2Fknowledge%2F) The real numbers contain the rational numbers and complete the rational system by adding its missing limit points. mko-real-number · Analysis Knowledge object ## [Arithmetic operations](/en/mko/mko-arithmetic-operations/?from=%2Fen%2Fknowledge%2F) Addition, subtraction, multiplication, and division are a family of basic operations on two quantities within a specified number system and domain. mko-arithmetic-operations · Arithmetic and number systems Knowledge object ## [Variables and algebraic expressions](/en/mko/mko-variable-expression/?from=%2Fen%2Fknowledge%2F) An algebraic expression uses variables, constants, and defined operations to represent a mathematical quantity depending on its inputs. mko-variable-expression · Algebra Knowledge object ## [Equation](/en/mko/mko-equation/?from=%2Fen%2Fknowledge%2F) An equation requires two expressions to take equal values over a specified variable domain; a solution is an allowed value that makes the equality true. mko-equation · Algebra Knowledge object ## [Linear equation in one variable](/en/mko/mko-linear-equation/?from=%2Fen%2Fknowledge%2F) A linear equation in one variable can be written as ax+b=0 with a nonzero linear coefficient a. mko-linear-equation · Algebra Knowledge object ## [Set](/en/mko/mko-set/?from=%2Fen%2Fknowledge%2F) A set treats selected objects within a specified context as a whole and describes its contents through element membership. mko-set · Foundations and logic Knowledge object ## [Proposition](/en/mko/mko-proposition/?from=%2Fen%2Fknowledge%2F) A proposition is a meaningful statement that can be asserted or denied and discussed as true or false within a specified logical context. mko-proposition · Foundations and logic Knowledge object ## [Logical connectives](/en/mko/mko-logical-connectives/?from=%2Fen%2Fknowledge%2F) Negation, conjunction, disjunction, implication, and biconditional form compound propositions from existing propositions. mko-logical-connectives · Foundations and logic Knowledge object ## [Mathematical proof](/en/mko/mko-proof/?from=%2Fen%2Fknowledge%2F) A mathematical proof is a checkable argument establishing a specified conclusion from explicit premises and rules of inference. mko-proof · History, philosophy and methodology Knowledge object ## [Set membership](/en/mko/mko-set-membership/?from=%2Fen%2Fknowledge%2F) The notation x∈A states that the element x belongs to the set A. mko-set-membership · Foundations and logic Knowledge object ## [Subset](/en/mko/mko-subset/?from=%2Fen%2Fknowledge%2F) A⊆B means that every element of A is also an element of B. mko-subset · Foundations and logic Knowledge object ## [Set operations](/en/mko/mko-set-operations/?from=%2Fen%2Fknowledge%2F) Union, intersection, difference, and relative complement construct new sets from existing sets through element-membership conditions. mko-set-operations · Foundations and logic Knowledge object ## [Sample space](/en/mko/mko-sample-space/?from=%2Fen%2Fknowledge%2F) A sample space lists all possible elementary outcomes for one specified random experiment. mko-sample-space · Probability and statistics Knowledge object ## [Event](/en/mko/mko-event/?from=%2Fen%2Fknowledge%2F) An event describes a set of outcomes of interest in a random experiment. mko-event · Probability and statistics Knowledge object ## [Function mapping](/en/mko/mko-function-mapping/?from=%2Fen%2Fknowledge%2F) The notation f:X→Y states that the function f maps the domain X into the codomain Y. mko-function-mapping · Foundations and logic 1 [2](/en/knowledge/?page=2#results) … [13](/en/knowledge/?page=13#results)[Next →](/en/knowledge/?page=2#results) 302 results · Page 1 of 13