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'''Mathematician''' is a [[scholar]] skill. It is used by scholars when thinking about mathematical [[topics]]:
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'''Mathematician''' is a [[scholar]] skill. It is used by scholars when thinking about mathematical [[topics]].
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{| class = "wikitable sortable" style="width: 60%"
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! scope="col" style="width: 25%;" | Topic
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! scope="col" style="width: 50%;" | Description
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! scope="col" style="width: 25%;" | Wikipedia link
 +
! scope="col" style="width: 25%;" | Subdivision
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|-
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|Divergence of harmonic series
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|The divergence of the harmonic series
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|[[wikipedia:Harmonic series (mathematics)|Harmonic series (mathematics)]]
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|Algebra
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|-
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|Equations
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|The technique of balancing and completion for solving equations
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|[[wikipedia:The Compendious Book on Calculation by Completion and Balancing|The Compendious Book on Calculation by Completion and Balancing]], [[wikipedia:Algebra|Algebra]], and [[wikipedia:Equation|Equation]]
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|Algebra
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|-
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|Large sums
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|Simple formulas for certain arbitrarily large sums
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|[[wikipedia:Summation|Summation]]
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|Algebra
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|-
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|Pascal's triangle
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|A triangular configuration of numbers relating to the successive powers of any sum
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|[[wikipedia:Pascal's triangle|Pascal's triangle]]
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|Algebra
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|-
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|Quadratic by completing square
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|The solving of quadratic equations by completion of the square
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|[[wikipedia:Completing the square|Completing the square]]
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|Algebra
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|-
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|Quadratic formula
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|A formula which solves quadratic equations
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|[[wikipedia:Quadratic formula|Quadratic formula]]
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|Algebra
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|-
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|Solving higher order polynomials
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|Methods for solving certain equations involving powers higher than the quadratic
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|[[wikipedia:Galois theory|Galois theory]] <!--probably...-->
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|Algebra
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|-
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|Systems of equations
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|Methods of solving systems of equations
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|[[wikipedia:Linear system|Linear system]]
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|Algebra
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|-
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|Area enclosed by line and parabola
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|The area enclosed by a parabola and a line
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|[[wikipedia:The Quadrature of the Parabola|The Quadrature of the Parabola]]
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|Geometry
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|-
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|Area of circle
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|
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|[[wikipedia:Area of a disk|Area of a disk]]
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|Geometry
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|-
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|Area of triangle from side lengths
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|
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|[[wikipedia:Heron's formula|Heron's formula]]
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|Geometry
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|-
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|Basic geometry
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|Geometric objects: points, lines, circles, triangles, and so on
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|[[wikipedia:Geometry|Geometry]]
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|Geometry
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|-
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|Chords
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|The properties of chords
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|[[wikipedia:Chord (geometry)|Chord (geometry)]]
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|Geometry
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|-
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|Chord tables
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|A table of chord lengths indexed by angle
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|[[wikipedia:Ptolemy's table of chords|Ptolemy's table of chords]]
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|Geometry
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|-
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|Conic sections
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|The categorization and properties of conic sections
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|[[wikipedia:Conic section|Conic section]]
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|Geometry
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|-
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|Existence of pi
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|The relationship between the area of a circle and its radius, involving the ratio of the circumference of the circle to its diameter
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|[[wikipedia:Pi|Pi]]
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|Geometry
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|-
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|Geometric mean
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|The relationship between the length of the altitude of a right triangle and the lengths of the segments into which it divides the hypotenuse
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|[[wikipedia:Geometric mean theorem|Geometric mean theorem]]
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|Geometry
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|-
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|Inscribed triangle on diameter is right
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|The angles of triangles inscribed in a circle with one edge on the diameter
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|[[wikipedia:Thales' theorem|Thales' theorem]]
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|Geometry
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|-
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|Irrational numbers
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|The existence of incommensurable ratios
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|[[wikipedia:Irrational number|Irrational number]]
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|Geometry
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|-
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|Isosceles base angles equal
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|The equality of the base angle of isosceles triangles
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|[[wikipedia:Pons asinorum|Pons asinorum]]
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|Geometry
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|-
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|Law of sines
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|
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|[[wikipedia:Law of sines|Law of sines]]
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|Geometry
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|-
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|Pi to 6 digits
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|
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|[[wikipedia:Zu Chongzhi#Mathematics|Zu Chongzhi § Mathematics]] and [[wikipedia:Milü|Milü]]
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|Geometry
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|-
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|Pythagorean theorem
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|The relationship between the lengths of the hypotenuse of a right triangle and the other two sides
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|[[wikipedia:Pythagorean theorem|Pythagorean theorem]]
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|Geometry
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|-
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|Pythagorean triples 3 digit
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|Examples of triples of large whole numbers which, when taken together, are the lengths of the sides of a right triangle
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|[[wikipedia:Pythagorean triples|Pythagorean triples]]
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|Geometry
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|-
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|Pythagorean triples 4 digit
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|Examples of triples of very large whole numbers which, when taken together, are the lengths of the sides of a right triangle
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|[[wikipedia:Pythagorean triples|Pythagorean triples]]
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|Geometry
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|-
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|Pythagorean triples small
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|Examples of triples of small whole numbers which, when taken together, are the lengths of the sides of a right triangle
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|[[wikipedia:Pythagorean triples|Pythagorean triples]]
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|Geometry
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|-
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|Similar and congruent triangles
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|The properties of similar and congruent triangles
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|[[wikipedia:Similarity (geometry)|Similarity (geometry)]] and [[wikipedia:Congruence (geometry)|Congruence (geometry)]]
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|Geometry
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|-
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|Sum-difference trig identities
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|Trigonometric identities relating to the sums and differences of angles
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|[[wikipedia:List of trigonometric identities#Angle sum and difference identities|List of trigonometric identities § Angle sum and difference identities]]
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|Geometry
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|-
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|Surface area of sphere
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|The computation of the surface area of a sphere
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|[[wikipedia:Sphere#Surface area|Sphere § Surface area]]
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|Geometry
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|-
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|Volume of cone
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|The computation of the volume of a cone
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|[[wikipedia:Cone#Volume|Cone § Volume]]
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|Geometry
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|-
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|Volume of pyramid
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|The computation of the volume of different pyramids
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|[[wikipedia:Pyramid (geometry)#Volume|Pyramid (geometry) § Volume]]
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|Geometry
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|-
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|Volume of sphere
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|The computation of the volume of a sphere
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|[[wikipedia:Sphere#Volume|Sphere § Volume]]
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|Geometry
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|-
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|Axioms
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|Axiomatic reasoning
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|[[wikipedia:Axiomatic system|Axiomatic system]]
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|Method
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|-
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|Method of exhaustion
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|An approximation of the ratio of a circumference of a circle to its diameter, using the area of polygons and the method of exhaustion
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|[[wikipedia:Method of exhaustion|Method of exhaustion]]
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|Method
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|-
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|Proof by contradiction
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|The method of proof by contradiction
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|[[wikipedia:Proof by contradiction|Proof by contradiction]]
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|Method
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|-
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|Algebra
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|Notation for abbreviating the unknown and other elements of an equation in a systematic and useful fashion
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|[[wikipedia:Algebra|Algebra]]
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|Notation
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|-
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|Negative numbers
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|Notation for negative quantities
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|[[wikipedia:Negative number|Negative number]]
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|Notation
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|-
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|Place values
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|Positional notation
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|[[wikipedia:Positional notation|Positional notation]]
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|Notation
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|-
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|Scientific notation
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|Notation for very large numbers
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|[[wikipedia:Scientific notation|Scientific notation]]
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|Notation
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|-
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|Symbol for addition
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|The idea of using symbolic notation for addition
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|[[wikipedia:Plus and minus signs#Plus sign|Plus and minus signs § Plus sign]]
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|Notation
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|-
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|Zero
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|A symbol for nothingness
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|[[wikipedia:0 (number)|0 (number)]]
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|Notation
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|-
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|Approximation of root 2
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|An approximation for the length of the diagonal of a square
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|[[wikipedia:Square root of 2#History|Square root of 2 § History]]
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|Numbers
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|-
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|Chinese remainder algorithm
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|An algorithm for computing a number which has given remainders when divided by several given primes
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|[[wikipedia:Chinese remainder theorem|Chinese remainder theorem]]
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|Numbers
 +
|-
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|Division
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|An algorithm for dividing one number into another, possibly yielding a remainder
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|[[wikipedia:Euclidean division|Euclidean division]]
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|Numbers
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|-
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|Euclid's Theorem
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|A proof that there are infinitely many prime numbers
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|[[wikipedia:Euclid's theorem|Euclid's theorem]]
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|Numbers
 +
|-
 +
|Euclidean Algorithm
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| An algorithm for computing the greatest common divisor of two numbers
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|[[wikipedia:Euclidean algorithm|Euclidean algorithm]]
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|Numbers
 +
|-
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|Irrationality of root 2
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|A proof that the length of a diagonal of a square is incommensurable with its edge
 +
|[[wikipedia:Square root of 2#Proofs of irrationality|Square root of 2 § Proofs of irrationality]]
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|Numbers
 +
|-
 +
|Sieve algorithm for primes
 +
|
 +
|[[wikipedia:Sieve of Eratosthenes|Sieve of Eratosthenes]]
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|Numbers
 +
|-
 +
|Unique prime factorization
 +
|The unique decomposition of a number into products of its prime divisors
 +
|[[wikipedia:Fundamental theorem of arithmetic|Fundamental theorem of arithmetic]]
 +
|Numbers
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|}
  
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{{DF2014:Topic/table/mathematics}}
 
  
 
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