# DF2014:Mathematician

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Mathematician is a scholar skill. It is used by scholars when thinking about mathematical topics.

Topic Description Wikipedia link Subdivision
Divergence of harmonic series The divergence of the harmonic series Harmonic series (mathematics) Algebra
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
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
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
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
Place values Positional notation Positional notation Notation
Scientific notation Notation for very large numbers Scientific notation Notation
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
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
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
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