User:Tea2min/Scratch

Polyhedra from equilateral triangles and squares only

Regular deltahedra

• 
  Tetrahedron (triangular pyramid)
• 
  Octahedron
• 
  Icosahedron

Pyramids

Elongated triangular pyramid

• 
  Tetrahedron (triangular pyramid)
• 
  Elongated triangular pyramid (J₇)

Square pyramid

• 
  Square pyramid (J₁)
• 
  Elongated square pyramid (J₈)
• 
  Gyroelongated square pyramid (J₁₀)

Bipyramids

Bipyramids

• 
  Triangular bipyramid
• 
  Square bipyramid (Octahedron)
• 
  Pentagonal bipyramid

Elongated bipyramids

• 
  Elongated triangular bipyramid (J₁₄)
• 
  Elongated square bipyramid (J₁₅)
• 
  Elongated pentagonal bipyramid (J₁₆)

Gyroelongated bipyramids

• 
  Gyroelongated square bipyramid (J₁₇)
• 
  Pentagonal gyroelongated bipyramid (icosahedron)

Triangular prism

Triangular prism

• 
  Triangular prism
• 
  Elongated triangular pyramid (J₇)

Triangular prism

• 
  Triangular prism
• 
  Gyrobifastigium (J₂₆)

Triangular prism

• 
  Triangular prism
• 
  Augmented triangular prism (J₄₉)
• 
  Biaugmented triangular prism (J₅₀)
• 
  Triaugmented triangular prism (J₅₁)

Square antiprism

Square antiprism

• 
  Square antiprism
• 
  Gyroelongated square pyramid (J₁₀)
• 
  Gyroelongated square bipyramid (J₁₇)
• 
  Snub disphenoid (J₈₄)
• 
  Snub square antiprism (J₈₅)

Bicupolae

Triangular bicupolae

• 
  Triangular orthobicupola (J₂₇)
• 
  Triangular gyrobicupola (Cuboctahedron)

Square bicupolae

• 
  Square orthobicupola (J₂₈)
• 
  Square gyrobicupola (J₂₉)

Elongated triangular orthobicupola

• 
  Triangular orthobicupola (J₂₇)
• 
  Elongated triangular orthobicupola (J₃₅)

Gyroelongated triangular bicupola

• 
  Triangular orthobicupola (J₂₇)
• 
  Gyroelongated triangular bicupola (J₄₄)
• 
  Triangular gyrobicupola (Cuboctahedron)

Elongated square orthobicupola

• 
  Square orthobicupola (J₂₈)
• 
  Elongated square orthobicupola (rhombicuboctahedron)

Elongated square gyrobicupola

• 
  Square gyrobicupola (J₂₉)
• 
  Elongated square gyrobicupola (J₃₇)

Gyroelongated square bicupola

• 
  Square orthobicupola (J₂₈)
• 
  Gyroelongated square bicupola (J₄₅)
• 
  Square gyrobicupola (J₂₉)

Others

?

• 
  Snub cube
• 
  Sphenocorona
• 
  Sphenomegacorona

History of Scheme

Older standards

• RRS ("The Revised Report on Scheme", G.L. Steele et al., AI Memo 452, MIT, Jan 1978)
• R²RS ("The Revised Revised Report on the Algorithmic Language Scheme", Clinger, AI Memo 848, MIT Aug 1985)
• R³RS ("Dedicated to the Memory of ALGOL 60", Revised(3) Report on the Algorithmic Language Scheme)
• R⁴RS (Revised(4) Report on the Algorithmic Language Scheme)

R⁵RS and R⁶RS are already referenced from Scheme (programming language).

History of call/cc

• interaction with dynamic-wind (R5RS call/cc & dynamic-wind in terms of r4rs, faking dynamic-wind, dynamic-wind, A new specification for dynamic-wind, call/wc, and call/nwc, implementing dynamic-wind)
• interaction with values and call-with-values

Cosine powers

$(\cos \alpha )^{n}={\frac {1}{2^{n}}}\sum _{k=0}^{n}{\binom {n}{k}}\cos((2k-n)\alpha )$

$(\cos \alpha )^{2n}={\frac {1}{4^{n}}}\left\{{\binom {2n}{n}}+2\sum _{k=1}^{n}{\binom {2n}{n-k}}\cos(2k\alpha )\right\}$

$(\cos \alpha )^{2n+1}={\frac {1}{4^{n}}}\sum _{k=0}^{n}{\binom {2n+1}{n-k}}\cos((2k+1)\alpha )$

Hermite polynomials

$H_{2n}(x)=(2n)!\ \sum _{k=0}^{n}{\frac {(-1)^{n-k}}{(2k)!(n-k)!}}(2x)^{2k}$

$H_{2n+1}(x)=(2n+1)!\ \sum _{k=0}^{n}{\frac {(-1)^{n-k}}{(2k+1)!(n-k)!}}(2x)^{2k+1}$

Persons with first name Hanan

• Hanan al-Shaykh, a Lebanese author of contemporary Arab women's literature
• Hanan Ashrawi, a Palestinian legislator, activist, and scholar
• Hanan Habibzai, an Afghan journalist and writer
• Hanan Qassab Hassan, a prominent Syrian writer and academic
• Hanan Ahmed Khaled, an Egyptian female athlete
• Hanan Porat, a former Israeli politician
• Hanan Rubin, a German-born Israeli politician
• Hanan Tork, an Egyptian actress and former ballerina

Semimathematics

• Semicomputable function
• Semi-continuity
• Semi-deterministic Büchi automaton
• Semi-differentiability
• Semidirect product
• Semi-elliptic operator
• Semifield
• Semigroup
• Semigroup action
• Semigroupoid
• Semi-Hilbert space
• Semi-implicit Euler method
• Semi-infinite
• Semi-infinite programming
• Semilattice
• Semi-local ring
• Seminorm → Norm (mathematics)
• Seminormal subgroup
• Semiorder
• Semiperfect number
• Semiperfect ring
• Semipermutable subgroup
• Semiprime
• Semiprime ring
• Semiprimitive ring
• Semiregular space
• Semiring
• Semi-s-cobordism
• Semiset
• Semisimple algebra
• Semisimple algebraic group
• Semisimple Lie algebra
• Semisimple module
• Semi-simple operator
• Semistable abelian variety
• Semi-Thue system

Field of rational functions

In mathematics, given a field K, the field of rational functions K(X) is the field of all rational functions in the variable X with coefficients in K. It is the field of fractions of the polynomial ring K[X].

The field of rational functions is not to be confused with the field of rationals, which is the field of fractions for the ring of integers.

Given a field K, the ring K[X] of polynomials in the variable X with coefficients in K is an integral domain so that the field of fractions of K[X] can be constructed. K(X)/K is a field extension of infinite degree.

References

• David Dummit (2003). Abstract Algebra (third ed.). Wiley. ISBN 0-471-43334-9. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

Category:Field theory Category:Rational functions