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Difference between revisions of "DF2014:Topic/table/mathematics"

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#REDIRECT [[Topic/table/mathematics]]
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{| 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
 +
|[[Mathematician]]
 +
|-
 +
|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
 +
|[[Mathematician]]
 +
|-
 +
|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
 +
|[[Mathematician]]
 +
|-
 +
|Volume of pyramid
 +
|The computation of the volume of different pyramids
 +
|[[wikipedia:Pyramid (geometry)#Volume|Pyramid (geometry) § Volume]]
 +
|Geometry
 +
|[[Mathematician]]
 +
|-
 +
|Volume of sphere
 +
|The computation of the volume of a sphere
 +
|[[wikipedia:Sphere#Volume|Sphere § Volume]]
 +
|Geometry
 +
|[[Mathematician]]
 +
|-
 +
|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]]
 +
|-
 +
|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]]
 +
|-
 +
|Scientific notation
 +
|Notation for very large numbers
 +
|[[wikipedia:Scientific notation|Scientific notation]]
 +
|Notation
 +
|[[Logician]]
 +
|-
 +
|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]]
 +
|-
 +
|Zero
 +
|A symbol for nothingness
 +
|[[wikipedia:0 (number)|0 (number)]]
 +
|Notation
 +
|[[Logician]]
 +
|-
 +
|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
 +
|[[Mathematician]]
 +
|-
 +
|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]]
 +
|}

Revision as of 04:03, 20 December 2022

Topic Description Wikipedia link Subdivision Skills used in research
Divergence of harmonic series The divergence of the harmonic series Harmonic series (mathematics) Algebra Mathematician
Equations The technique of balancing and completion for solving equations The Compendious Book on Calculation by Completion and Balancing, Algebra, and Equation Algebra Mathematician
Large sums Simple formulas for certain arbitrarily large sums Summation Algebra Mathematician
Pascal's triangle A triangular configuration of numbers relating to the successive powers of any sum Pascal's triangle Algebra Mathematician
Quadratic by completing square The solving of quadratic equations by completion of the square Completing the square Algebra Mathematician
Quadratic formula A formula which solves quadratic equations Quadratic formula Algebra Mathematician
Solving higher order polynomials Methods for solving certain equations involving powers higher than the quadratic Galois theory Algebra Mathematician
Systems of equations Methods of solving systems of equations Linear system Algebra Mathematician
Area enclosed by line and parabola The area enclosed by a parabola and a line The Quadrature of the Parabola Geometry Mathematician
Area of circle 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 Heron's formula Geometry Mathematician
Basic geometry Geometric objects: points, lines, circles, triangles, and so on Geometry Geometry Mathematician
Chords The properties of chords Chord (geometry) Geometry Mathematician
Chord tables A table of chord lengths indexed by angle Ptolemy's table of chords Geometry Mathematician
Conic sections The categorization and properties of conic sections Conic section Geometry Mathematician
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 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 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 Thales' theorem Geometry Mathematician
Irrational numbers The existence of incommensurable ratios Irrational number Geometry Mathematician
Isosceles base angles equal The equality of the base angle of isosceles triangles Pons asinorum Geometry Mathematician
Law of sines The relatonship between the half chords of lengths and the diameter of the triangle’s circumscribed circle. Law of sines Geometry Mathematician
Pi to 6 digits Zu Chongzhi § Mathematics and Milü Geometry Mathematician
Pythagorean theorem The relationship between the lengths of the hypotenuse of a right triangle and the other two sides 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 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 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 Pythagorean triples Geometry Mathematician
Similar and congruent triangles The properties of similar and congruent triangles Similarity (geometry) and Congruence (geometry) Geometry Mathematician
Sum-difference trig identities Trigonometric identities relating to the sums and differences of angles List of trigonometric identities § Angle sum and difference identities Geometry Mathematician
Surface area of sphere The computation of the surface area of a sphere Sphere § Surface area Geometry Mathematician
Volume of cone The computation of the volume of a cone Cone § Volume Geometry Mathematician
Volume of pyramid The computation of the volume of different pyramids Pyramid (geometry) § Volume Geometry Mathematician
Volume of sphere The computation of the volume of a sphere Sphere § Volume Geometry Mathematician
Axioms Axiomatic reasoning 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 Method of exhaustion Method Logician
Proof by contradiction The method of 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 Algebra Notation Logician
Negative numbers Notation for negative quantities Negative number Notation Logician
Place values Positional notation Positional notation Notation Logician
Scientific notation Notation for very large numbers Scientific notation Notation Logician
Symbol for addition The idea of using symbolic notation for addition Plus and minus signs § Plus sign Notation Logician
Zero A symbol for nothingness 0 (number) Notation Logician
Approximation of root 2 An approximation for the length of the diagonal of a square 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 Chinese remainder theorem Numbers Mathematician
Division An algorithm for dividing one number into another, possibly yielding a remainder Euclidean division Numbers Mathematician
Euclid's Theorem A proof that there are infinitely many prime numbers Euclid's theorem Numbers Mathematician
Euclidean Algorithm An algorithm for computing the greatest common divisor of two numbers Euclidean algorithm Numbers Mathematician
Irrationality of root 2 A proof that the length of a diagonal of a square is incommensurable with its edge Square root of 2 § Proofs of irrationality Numbers Mathematician
Sieve algorithm for primes An algorithm for calculating prime numbers Sieve of Eratosthenes Numbers Mathematician
Unique prime factorization The unique decomposition of a number into products of its prime divisors Fundamental theorem of arithmetic Numbers Mathematician
Retrieved from "https://dwarffortresswiki.org/index.php?title=DF2014:Topic/table/mathematics&oldid=275019"