v50 Steam/Premium information for editors
  • v50 information can now be added to pages in the main namespace. v0.47 information can still be found in the DF2014 namespace. See here for more details on the new versioning policy.
  • Use this page to report any issues related to the migration.
This notice may be cached—the current version can be found here.

Difference between revisions of "Topic/table/mathematics"

From Dwarf Fortress Wiki
Jump to navigation Jump to search
(move table from DF2014:Topic)
 
(Add some skills of the mathematics and logician topics.)
Line 4: Line 4:
 
! scope="col" style="width: 25%;" | Wikipedia link
 
! scope="col" style="width: 25%;" | Wikipedia link
 
! scope="col" style="width: 25%;" | Subdivision
 
! scope="col" style="width: 25%;" | Subdivision
 +
! scope="col" style="width: 25%;" | Skills used in research
 
|-
 
|-
 
|Divergence of harmonic series
 
|Divergence of harmonic series
Line 9: Line 10:
 
|[[wikipedia:Harmonic series (mathematics)|Harmonic series (mathematics)]]
 
|[[wikipedia:Harmonic series (mathematics)|Harmonic series (mathematics)]]
 
|Algebra
 
|Algebra
 +
|[[Mathematician]]
 
|-
 
|-
 
|Equations
 
|Equations
Line 14: Line 16:
 
|[[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]]
 
|[[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
 
|Algebra
 +
|
 
|-
 
|-
 
|Large sums
 
|Large sums
Line 19: Line 22:
 
|[[wikipedia:Summation|Summation]]
 
|[[wikipedia:Summation|Summation]]
 
|Algebra
 
|Algebra
 +
|[[Mathematician]]
 
|-
 
|-
 
|Pascal's triangle
 
|Pascal's triangle
Line 24: Line 28:
 
|[[wikipedia:Pascal's triangle|Pascal's triangle]]
 
|[[wikipedia:Pascal's triangle|Pascal's triangle]]
 
|Algebra
 
|Algebra
 +
|
 
|-
 
|-
 
|Quadratic by completing square
 
|Quadratic by completing square
Line 29: Line 34:
 
|[[wikipedia:Completing the square|Completing the square]]
 
|[[wikipedia:Completing the square|Completing the square]]
 
|Algebra
 
|Algebra
 +
|
 
|-
 
|-
 
|Quadratic formula
 
|Quadratic formula
Line 34: Line 40:
 
|[[wikipedia:Quadratic formula|Quadratic formula]]
 
|[[wikipedia:Quadratic formula|Quadratic formula]]
 
|Algebra
 
|Algebra
 +
|
 
|-
 
|-
 
|Solving higher order polynomials
 
|Solving higher order polynomials
Line 39: Line 46:
 
|[[wikipedia:Galois theory|Galois theory]] <!--probably...-->
 
|[[wikipedia:Galois theory|Galois theory]] <!--probably...-->
 
|Algebra
 
|Algebra
 +
|
 
|-
 
|-
 
|Systems of equations
 
|Systems of equations
Line 44: Line 52:
 
|[[wikipedia:Linear system|Linear system]]
 
|[[wikipedia:Linear system|Linear system]]
 
|Algebra
 
|Algebra
 +
|
 
|-
 
|-
 
|Area enclosed by line and parabola
 
|Area enclosed by line and parabola
Line 49: Line 58:
 
|[[wikipedia:The Quadrature of the Parabola|The Quadrature of the Parabola]]
 
|[[wikipedia:The Quadrature of the Parabola|The Quadrature of the Parabola]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Area of circle
 
|Area of circle
Line 54: Line 64:
 
|[[wikipedia:Area of a disk|Area of a disk]]
 
|[[wikipedia:Area of a disk|Area of a disk]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Area of triangle from side lengths
 
|Area of triangle from side lengths
Line 59: Line 70:
 
|[[wikipedia:Heron's formula|Heron's formula]]
 
|[[wikipedia:Heron's formula|Heron's formula]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Basic geometry
 
|Basic geometry
Line 64: Line 76:
 
|[[wikipedia:Geometry|Geometry]]
 
|[[wikipedia:Geometry|Geometry]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Chords
 
|Chords
Line 69: Line 82:
 
|[[wikipedia:Chord (geometry)|Chord (geometry)]]
 
|[[wikipedia:Chord (geometry)|Chord (geometry)]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Chord tables
 
|Chord tables
Line 74: Line 88:
 
|[[wikipedia:Ptolemy's table of chords|Ptolemy's table of chords]]
 
|[[wikipedia:Ptolemy's table of chords|Ptolemy's table of chords]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Conic sections
 
|Conic sections
Line 79: Line 94:
 
|[[wikipedia:Conic section|Conic section]]
 
|[[wikipedia:Conic section|Conic section]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Existence of pi
 
|Existence of pi
Line 84: Line 100:
 
|[[wikipedia:Pi|Pi]]
 
|[[wikipedia:Pi|Pi]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Geometric mean
 
|Geometric mean
Line 89: Line 106:
 
|[[wikipedia:Geometric mean theorem|Geometric mean theorem]]
 
|[[wikipedia:Geometric mean theorem|Geometric mean theorem]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Inscribed triangle on diameter is right
 
|Inscribed triangle on diameter is right
Line 94: Line 112:
 
|[[wikipedia:Thales' theorem|Thales' theorem]]
 
|[[wikipedia:Thales' theorem|Thales' theorem]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Irrational numbers
 
|Irrational numbers
Line 99: Line 118:
 
|[[wikipedia:Irrational number|Irrational number]]
 
|[[wikipedia:Irrational number|Irrational number]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Isosceles base angles equal
 
|Isosceles base angles equal
Line 104: Line 124:
 
|[[wikipedia:Pons asinorum|Pons asinorum]]
 
|[[wikipedia:Pons asinorum|Pons asinorum]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Law of sines
 
|Law of sines
Line 109: Line 130:
 
|[[wikipedia:Law of sines|Law of sines]]
 
|[[wikipedia:Law of sines|Law of sines]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Pi to 6 digits
 
|Pi to 6 digits
Line 114: Line 136:
 
|[[wikipedia:Zu Chongzhi#Mathematics|Zu Chongzhi § Mathematics]] and [[wikipedia:Milü|Milü]]
 
|[[wikipedia:Zu Chongzhi#Mathematics|Zu Chongzhi § Mathematics]] and [[wikipedia:Milü|Milü]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Pythagorean theorem
 
|Pythagorean theorem
Line 119: Line 142:
 
|[[wikipedia:Pythagorean theorem|Pythagorean theorem]]
 
|[[wikipedia:Pythagorean theorem|Pythagorean theorem]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Pythagorean triples 3 digit
 
|Pythagorean triples 3 digit
Line 124: Line 148:
 
|[[wikipedia:Pythagorean triples|Pythagorean triples]]
 
|[[wikipedia:Pythagorean triples|Pythagorean triples]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Pythagorean triples 4 digit
 
|Pythagorean triples 4 digit
Line 129: Line 154:
 
|[[wikipedia:Pythagorean triples|Pythagorean triples]]
 
|[[wikipedia:Pythagorean triples|Pythagorean triples]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Pythagorean triples small
 
|Pythagorean triples small
Line 134: Line 160:
 
|[[wikipedia:Pythagorean triples|Pythagorean triples]]
 
|[[wikipedia:Pythagorean triples|Pythagorean triples]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Similar and congruent triangles
 
|Similar and congruent triangles
Line 139: Line 166:
 
|[[wikipedia:Similarity (geometry)|Similarity (geometry)]] and [[wikipedia:Congruence (geometry)|Congruence (geometry)]]
 
|[[wikipedia:Similarity (geometry)|Similarity (geometry)]] and [[wikipedia:Congruence (geometry)|Congruence (geometry)]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Sum-difference trig identities
 
|Sum-difference trig identities
Line 144: Line 172:
 
|[[wikipedia:List of trigonometric identities#Angle sum and difference identities|List of trigonometric identities § Angle sum and difference identities]]
 
|[[wikipedia:List of trigonometric identities#Angle sum and difference identities|List of trigonometric identities § Angle sum and difference identities]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Surface area of sphere
 
|Surface area of sphere
Line 149: Line 178:
 
|[[wikipedia:Sphere#Surface area|Sphere § Surface area]]
 
|[[wikipedia:Sphere#Surface area|Sphere § Surface area]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Volume of cone
 
|Volume of cone
Line 154: Line 184:
 
|[[wikipedia:Cone#Volume|Cone § Volume]]
 
|[[wikipedia:Cone#Volume|Cone § Volume]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Volume of pyramid
 
|Volume of pyramid
Line 159: Line 190:
 
|[[wikipedia:Pyramid (geometry)#Volume|Pyramid (geometry) § Volume]]
 
|[[wikipedia:Pyramid (geometry)#Volume|Pyramid (geometry) § Volume]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Volume of sphere
 
|Volume of sphere
Line 164: Line 196:
 
|[[wikipedia:Sphere#Volume|Sphere § Volume]]
 
|[[wikipedia:Sphere#Volume|Sphere § Volume]]
 
|Geometry
 
|Geometry
 +
|
 
|-
 
|-
 
|Axioms
 
|Axioms
Line 169: Line 202:
 
|[[wikipedia:Axiomatic system|Axiomatic system]]
 
|[[wikipedia:Axiomatic system|Axiomatic system]]
 
|Method
 
|Method
 +
|[[Logician]]
 
|-
 
|-
 
|Method of exhaustion
 
|Method of exhaustion
Line 174: Line 208:
 
|[[wikipedia:Method of exhaustion|Method of exhaustion]]
 
|[[wikipedia:Method of exhaustion|Method of exhaustion]]
 
|Method
 
|Method
 +
|
 
|-
 
|-
 
|Proof by contradiction
 
|Proof by contradiction
Line 179: Line 214:
 
|[[wikipedia:Proof by contradiction|Proof by contradiction]]
 
|[[wikipedia:Proof by contradiction|Proof by contradiction]]
 
|Method
 
|Method
 +
|[[Logician]]
 
|-
 
|-
 
|Algebra
 
|Algebra
Line 184: Line 220:
 
|[[wikipedia:Algebra|Algebra]]
 
|[[wikipedia:Algebra|Algebra]]
 
|Notation
 
|Notation
 +
|
 
|-
 
|-
 
|Negative numbers
 
|Negative numbers
Line 189: Line 226:
 
|[[wikipedia:Negative number|Negative number]]
 
|[[wikipedia:Negative number|Negative number]]
 
|Notation
 
|Notation
 +
|[[Logician]]
 
|-
 
|-
 
|Place values
 
|Place values
Line 194: Line 232:
 
|[[wikipedia:Positional notation|Positional notation]]
 
|[[wikipedia:Positional notation|Positional notation]]
 
|Notation
 
|Notation
 +
|[[Logician]]
 
|-
 
|-
 
|Scientific notation
 
|Scientific notation
Line 199: Line 238:
 
|[[wikipedia:Scientific notation|Scientific notation]]
 
|[[wikipedia:Scientific notation|Scientific notation]]
 
|Notation
 
|Notation
 +
|[[Logician]]
 
|-
 
|-
 
|Symbol for addition
 
|Symbol for addition
Line 204: Line 244:
 
|[[wikipedia:Plus and minus signs#Plus sign|Plus and minus signs § Plus sign]]
 
|[[wikipedia:Plus and minus signs#Plus sign|Plus and minus signs § Plus sign]]
 
|Notation
 
|Notation
 +
|
 
|-
 
|-
 
|Zero
 
|Zero
Line 209: Line 250:
 
|[[wikipedia:0 (number)|0 (number)]]
 
|[[wikipedia:0 (number)|0 (number)]]
 
|Notation
 
|Notation
 +
|[[Logician]]
 
|-
 
|-
 
|Approximation of root 2
 
|Approximation of root 2
Line 214: Line 256:
 
|[[wikipedia:Square root of 2#History|Square root of 2 § History]]
 
|[[wikipedia:Square root of 2#History|Square root of 2 § History]]
 
|Numbers
 
|Numbers
 +
|
 
|-
 
|-
 
|Chinese remainder algorithm
 
|Chinese remainder algorithm
Line 219: Line 262:
 
|[[wikipedia:Chinese remainder theorem|Chinese remainder theorem]]
 
|[[wikipedia:Chinese remainder theorem|Chinese remainder theorem]]
 
|Numbers
 
|Numbers
 +
|
 
|-
 
|-
 
|Division
 
|Division
Line 224: Line 268:
 
|[[wikipedia:Euclidean division|Euclidean division]]
 
|[[wikipedia:Euclidean division|Euclidean division]]
 
|Numbers
 
|Numbers
 +
|[[Mathematician]]
 
|-
 
|-
 
|Euclid's Theorem
 
|Euclid's Theorem
Line 229: Line 274:
 
|[[wikipedia:Euclid's theorem|Euclid's theorem]]
 
|[[wikipedia:Euclid's theorem|Euclid's theorem]]
 
|Numbers
 
|Numbers
 +
|
 
|-
 
|-
 
|Euclidean Algorithm
 
|Euclidean Algorithm
Line 234: Line 280:
 
|[[wikipedia:Euclidean algorithm|Euclidean algorithm]]
 
|[[wikipedia:Euclidean algorithm|Euclidean algorithm]]
 
|Numbers
 
|Numbers
 +
|[[Mathematician]]
 
|-
 
|-
 
|Irrationality of root 2
 
|Irrationality of root 2
Line 239: Line 286:
 
|[[wikipedia:Square root of 2#Proofs of irrationality|Square root of 2 § Proofs of irrationality]]
 
|[[wikipedia:Square root of 2#Proofs of irrationality|Square root of 2 § Proofs of irrationality]]
 
|Numbers
 
|Numbers
 +
|
 
|-
 
|-
 
|Sieve algorithm for primes
 
|Sieve algorithm for primes
Line 244: Line 292:
 
|[[wikipedia:Sieve of Eratosthenes|Sieve of Eratosthenes]]
 
|[[wikipedia:Sieve of Eratosthenes|Sieve of Eratosthenes]]
 
|Numbers
 
|Numbers
 +
|
 
|-
 
|-
 
|Unique prime factorization
 
|Unique prime factorization
Line 249: Line 298:
 
|[[wikipedia:Fundamental theorem of arithmetic|Fundamental theorem of arithmetic]]
 
|[[wikipedia:Fundamental theorem of arithmetic|Fundamental theorem of arithmetic]]
 
|Numbers
 
|Numbers
 +
|[[Mathematician]]
 
|}
 
|}

Revision as of 13:35, 2 January 2020

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
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
Quadratic by completing square The solving of quadratic equations by completion of the square Completing the square Algebra
Quadratic formula A formula which solves quadratic equations Quadratic formula Algebra
Solving higher order polynomials Methods for solving certain equations involving powers higher than the quadratic Galois theory Algebra
Systems of equations Methods of solving systems of equations Linear system Algebra
Area enclosed by line and parabola The area enclosed by a parabola and a line The Quadrature of the Parabola Geometry
Area of circle Area of a disk Geometry
Area of triangle from side lengths Heron's formula Geometry
Basic geometry Geometric objects: points, lines, circles, triangles, and so on Geometry Geometry
Chords The properties of chords Chord (geometry) Geometry
Chord tables A table of chord lengths indexed by angle Ptolemy's table of chords Geometry
Conic sections The categorization and properties of conic sections 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 Pi Geometry
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
Inscribed triangle on diameter is right The angles of triangles inscribed in a circle with one edge on the diameter Thales' theorem Geometry
Irrational numbers The existence of incommensurable ratios Irrational number Geometry
Isosceles base angles equal The equality of the base angle of isosceles triangles Pons asinorum Geometry
Law of sines Law of sines Geometry
Pi to 6 digits Zu Chongzhi § Mathematics and Milü Geometry
Pythagorean theorem The relationship between the lengths of the hypotenuse of a right triangle and the other two sides Pythagorean theorem Geometry
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
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
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
Similar and congruent triangles The properties of similar and congruent triangles Similarity (geometry) and Congruence (geometry) Geometry
Sum-difference trig identities Trigonometric identities relating to the sums and differences of angles List of trigonometric identities § Angle sum and difference identities Geometry
Surface area of sphere The computation of the surface area of a sphere Sphere § Surface area Geometry
Volume of cone The computation of the volume of a cone Cone § Volume Geometry
Volume of pyramid The computation of the volume of different pyramids Pyramid (geometry) § Volume Geometry
Volume of sphere The computation of the volume of a sphere Sphere § Volume Geometry
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
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
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
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
Chinese remainder algorithm An algorithm for computing a number which has given remainders when divided by several given primes Chinese remainder theorem Numbers
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
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
Sieve algorithm for primes Sieve of Eratosthenes Numbers
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=Topic/table/mathematics&oldid=249522"