List of PlanetMath Objects

• A chart of terms from foreign languages used in mathematics
• A chart of the letters of the Greek alphabet

Objects related to my thesis:

• Cyclic ring
• Behavior
• The integers mod n
• Zero ring

Objects related to my teaching strategies:

• Mnemonic device
• Absolute value inequalities
• Argument
• Converting a repeating decimal to a fraction
• Determining signs of trigonometric functions
• Even-even-odd rule
• Factoring a sum or difference of two cubes
• Freshman's dream error
• Keep-Flip-Change
• Sohcahtoa

Objects related to basic mathematics:

• Radical
• Square root
• Polynomial
• Integer part
• Fractional part

Objects related to analytic number theory:

• Multiplicative function
• Additive function
• n-free number
• n-full number
• Exactly divides
• The divisor function
• The number of nondistinct prime factors function
• Formula for the convolution inverse of a completely multiplicative function
• Asymptotic estimate
• Convolution method
• Hyperbola method
• Critical strip
• Value of the Riemann zeta function at s=0
• "Is asymptotic to" is an equivalence relation
• Wirsing condition
• Ramanujan tau function

Objects related to algebraic number theory:

• Minimal polynomial
• Radical
• Solvable by radicals
• Expressible
• Alternative proof that square root of 2 is irrational
• Quadratic fields that are not isomorphic
• Pure cubic field
• Units of real cubic fields with exactly one real embedding
• Cyclotomic field
• Biquadratic field
• Biquadratic extension
• Power Basis
• Example of a Bezout domain that is not a PID
• Galois groups of finite abelian extensions of the rationals
• A proof regarding norms and traces of algebraic numbers
• A proof of prime ideal decomposition in quadratic extensions of the rationals

• Order
• Inverses in rings
• Unity plus nilpotent is unit
• Alternative proof that a finite integral domain is a field
• The set of complex numbers is not an ordered field
• Basic facts about ordered rings
• Non-commutative rings of order four
• Isomorphism of rings of real and complex matrices
• A proof that Spec R is quasi-compact

• Euler-Fermat theorem
• Generator
• Exponent
• Opposite group
• Hyperbolic metric space
• Hyperbolic group

• Primitive
• Point
• Collinear
• Endpoint
• Linear pair
• Polygon
• Triangle
• Semiperimeter
• Note on SSA
• CPCTC
• Determining from angles that a triangle is isosceles
• Angles of an isosceles triangle
• Pons asinorum
• Isosceles triangle theorem
• Converse of isosceles triangle theorem
• Rhomboid
• Trapezoid
• Right trapezoid
• Isosceles trapezoid
• Symmetry
• Regular polygon
• Area of a regular polygon
• Area
• Great circle
• Cube
• Antiprism
• Volume

• Compass and straightedge construction
• Perpendicular (dropping and erecting)
• Angle bisector
• Equilateral triangle
• Copy the angle
• Center of circle
• Square
• Similar triangles
• Geometric mean
• Inverse point
• Regular pentagon
• Variants on compass and straightedge constructions
• Trisection of angle
• Theorem on constructible angles
• Theorem on constructible numbers
• Criterion for constructibility of regular polygon
• Classical problems of constructibility

• Slope angle
• Terminal ray
• Trigonometric identities

• Non-Euclidean geometry
• Comparison of common geometries
• Biangle
• Beltrami-Klein model
• Conformal disc model
• Upper half plane model
• Parallel lines in hyperbolic geometry
• Defect
• Ideal triangle
• Limiting triangle
• Lambert quadrilateral
• Saccheri quadrilateral
• AAA theorem
• AAS is not valid in spherical geometry

• List of common limits
• Logarithmic proof of product rule
• Logarithmic proof of quotient rule
• Subinterval
• Riemann sum
• Left hand rule
• Midpoint rule
• Right hand rule
• Partition
• Example of estimating a Riemann integral
• Integration of polynomial
• Alternative proof of derivative of x to the n
• Derivatives of sin x and cos x
• Weierstrass substitution formulas
• Hyperbolic identities
• Continuous functions on the extended real numbers
• Complex function
• Annulus
• Meromorphic extension
• A proof of the fundamental theorem of algebra
• Almost continuous function
• Lusin's Theorem
• A proof of Fatou-Lebesgue theorem
• Lebesgue integral over a subset of the measure space
• Lebesgue integration of nonnegative measurable functions
• Lebesgue integration of Lebesgue integrable functions
• Modes of convergence of sequences of measurable functions
• The traveling hump sequence
• A proof of the parallelogram law

• Contradiction
• Paradox
• Necessary and sufficient
• Circular reasoning
• Universal assumption
• Indexing set
• Ordered pairs
• Partition
• Criterion for a set to be transitive
• The well-ordering principle implies the axiom of choice
• The axiom of choice implies Zermelo's postulate
• A proof of the pigeonhole principle

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