Editing Topic/table/mathematics

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