Daftar bentuk matematika

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Berikut ini adalah daftar dari beberapa bentuk matematis terdefinisi dengan baik .

Kurva aljabar

Kurva rasional

Derajat 2

Derajat 3

Derajat 4

Derajat 5

Kuintik l'Hospital^[1]

Derajat 6

Keluarga dengan derajat variabel

Episikloid
Epispiral
Epitrokoid
Hiposikloid
Kurva Lissajous
Spiral Poinsot: Sebenarnya bukan spiral
Kurva biasa rasional
Kurva Rose

Kurva dari genus satu

Kurva dengan genus lebih dari satu

Keluarga kurva dengan genus variabel

Lemniskat polinomial
Kurva Fermat
Spiral sinusoidal: Sebenarnya bukan spiral
Superelips
Permukaan Hurwitz

Kurva transendental

Konstruksi sesepenggal

Kurva yang dihasilkan oleh kurva lain

Evolut
Glissette
Involut
Isoptik memuat Ortoptik
Caustic memuat Diakaustik dan Katakaustik
Konkoid
Kurva invers
Kurva pedal negatif
Kurva pedal
Kurva ruji
Kurva sejajar
Ortotomik
Roulette
Sisoid
Strofoid

Kurva ruang

Permukaan dalam ruang 3 dimensi

Minimal surfaces

Non-orientable surfaces

Kuadrik

Permukaan bola semu

Permukaan aljabar

See the list of algebraic surfaces.

Cayley cubic
Barth sextic
Clebsch cubic
Monkey saddle (saddle-like surface for 3 legs.)
Torus
Dupin cyclide (inversion of a torus)
Payung Whitney

Permukaan lainnya

Right conoid (a ruled surface)

Fraktal

Fraktal acak

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von Koch curve with random interval
von Koch curve with random orientation
Boundary of Brownian motion^{[butuh rujukan]}
2D polymer^{[butuh rujukan]}
Percolation front in 2D, Corrosion front in 2D^{[butuh rujukan]}
diffusion-limited aggregation
Random walk with no self-intersection^[8]
3D polymer^{[butuh rujukan]}
2D percolation cluster hull^{[butuh rujukan]}
2D percolation cluster
Brownian motion
Lichtenberg figure
Brownian motion
Percolation theory
Multiplicative cascade

Politop beraturan

Berikut adalah tabel yang memperlihatkan ringkasan mengenai politop beraturan yang dihitung dengan dimensi.

Dimensi	Cembung	Takcembung	Teselasi cembung Euklides	Teselasi cembung hiperbolik	Teselasi takcembung hiperbolik	Teselasi Hiperbolik dengan sel takhingga dan/atau gambar verteks	Politop abstrak
1	1 ruas garis	0	1	0	0	0	1
2	∞ polygons	∞ star polygons	1	1	0	0	∞
3	5 Platonic solids	4 Kepler–Poinsot solids	3 tilings	∞	∞	∞	∞
4	6 convex polychora	10 Schläfli–Hess polychora	1 honeycomb	4	0	11	∞
5	3 convex 5-polytopes	0	3 tetracombs	5	4	2	∞
6	3 convex 6-polytopes	0	1 pentacombs	0	0	5	∞
7+	3	0	1	0	0	0	∞

There are no nonconvex Euclidean regular tessellations in any number of dimensions.

Polytope elements

The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.

Puncak, sebuah elemen dimensi 0
Sisi, sebuah elemen dimensi 1
Wajah, sebuah elemen dimensi 2
Sel, sebuah elemen dimensi 3
Hipersel, sebuah elemen dimensi 4
Facet, sebuah (n-1)
Ridge, sebuah elemen dimensi (n-2)
Peak, sebuah elemen dimensi (n-3)

For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak.

Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.

Teselasi

The classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.

Dimensi nol

Titik (geometri)

Politop regular satu dimensi

Terdapat hanya satu politop dalam 1 dimensi, yang batasnya terdapat dua titik akhir ruas garis, diwakili oleh simbol Schläfli kosong {}.

Politop regular dua dimensi

Cembung

Merosot (bola)

Takcembung

Teselasi

Apeirogon

Politop regular tiga dimensi

Polihedron

Cembung

Platonic solid
- Tetrahedron, the 3-space Simplex
- Cube, the 3-space hypercube
- Octahedron, the 3-space Cross-polytope
- Dodecahedron
- Icosahedron

Degenerate (spherical)

Takcembung

Kepler–Poinsot polyhedra

Tessellations

Euclidean tilings

Hyperbolic tilings

Hyperbolic star-tilings

Four-dimensional regular polytopes

convex regular 4-polytope
- 5-cell, the 4-space Simplex
- 8-cell, the 4-space Hypercube
- 16-cell, the 4-space Cross-polytope
- 24-cell
- 120-cell
- 600-cell

Degenerate (spherical)

Non-convex

Star or (Schläfli–Hess) regular 4-polytope

Tessellations of Euclidean 3-space

Degenerate tessellations of Euclidean 3-space

Tessellations of hyperbolic 3-space

Five-dimensional regular polytopes and higher

Simplex	Hypercube	Cross-polytope
5-simplex	5-cube	5-orthoplex
6-simplex	6-cube	6-orthoplex
7-simplex	7-cube	7-orthoplex
8-simplex	8-cube	8-orthoplex
9-simplex	9-cube	9-orthoplex
10-simplex	10-cube	10-orthoplex
11-simplex	11-cube	11-orthoplex

Tessellations of Euclidean 4-space

Tessellations of Euclidean 5-space and higher

Tessellations of hyperbolic 4-space

Tessellations of hyperbolic 5-space

Apeirotopes

Apeirotope

Abstract polytopes

Abstract polytope
- 11-cell
- 57-cell

Non-regular polytopes

Bagian ini kosong. Anda bisa membantu dengan melengkapinya. (November 2014)

2D with 1D surface

Polygons named for their number of sides

Tilings

Uniform polyhedra

Regular polyhedron
- Platonic solid
- Kepler–Poinsot polyhedron (regular star polyhedra)
- Abstract regular polyhedra (Projective polyhedron)
Archimedean solid
Prismatic uniform polyhedron
- Prism
- Antiprism

Uniform star polyhedron

Duals of uniform polyhedra

Catalan solid

non-convex

Johnson solids

Other nonuniform polyhedra

Spherical polyhedra

Honeycombs

Convex uniform honeycomb

Dual uniform honeycomb

Others

Convex uniform honeycombs in hyperbolic space

Other

Regular and uniform compound polyhedra

Polyhedral compound and Uniform polyhedron compound

Convex regular 4-polytope

5-cell, Tesseract, 16-cell, 24-cell, 120-cell, 600-cell

Abstract regular polytope

11-cell, 57-cell

Schläfli–Hess 4-polytope (Regular star 4-polytope)

Icosahedral 120-cell, Small stellated 120-cell, Great 120-cell, Grand 120-cell, Great stellated 120-cell, Grand stellated 120-cell, Great grand 120-cell, Great icosahedral 120-cell, Grand 600-cell, Great grand stellated 120-cell

Uniform 4-polytope

Prismatic uniform polychoron

Honeycombs

5D with 4D surfaces

regular 5-polytope
- 5-dimensional cross-polytope
- 5-dimensional hypercube
- 5-dimensional simplex

Five-dimensional space, 5-polytope and uniform 5-polytope

Prismatic uniform 5-polytope: For each polytope of dimension n, there is a prism of dimension n+1.^{[butuh rujukan]}

Honeycombs

Six dimensions

Seven dimensions

Eight dimension

Eight-dimensional space, uniform 8-polytope

Honeycombs

Nine dimensions

9-polytope

Hyperbolic honeycombs

E₉ honeycomb

Ten dimensions

10-polytope

Dimensional families

Regular polytope and List of regular polytopes

Uniform polytope

Honeycombs

Geometri

Segitiga
Automedian triangle
Delaunay triangulation
Segitiga sama sisi
Golden triangle
Hyperbolic triangle (non-Euclidean geometry)
Segitiga sama kaki
Segitiga Kepler
Segitiga Reuleaux
Segitiga siku-siku
Sierpinski triangle (fractal geometry)
Special right triangles
Spiral of Theodorus
Thomson cubic
Triangular bipyramid
Triangular prism
Triangular pyramid
Triangular tiling

Geometry and other areas of mathematics

Glyphs and symbols

Referensi

^ "Courbe a Réaction Constante, Quintique De L'Hospital" [Kurva Reaksi Konstan, Quintic l'Hospital].
^ https://web.archive.org/web/20041114002246/http://www.mathcurve.com/courbes2d/isochron/isochrone%20leibniz. Diarsipkan dari versi asli tanggal 14 November 2004. Tidak memiliki atau tanpa |title= (bantuan)
^ https://web.archive.org/web/20041113201905/http://www.mathcurve.com/courbes2d/isochron/isochrone%20varignon. Diarsipkan dari versi asli tanggal 13 November 2004. Tidak memiliki atau tanpa |title= (bantuan)
^ Ferreol, Robert. "Spirale de Galilée". www.mathcurve.com.
^ Weisstein, Eric W. "Seiffert's Spherical Spiral". mathworld.wolfram.com.
^ Weisstein, Eric W. "Slinky". mathworld.wolfram.com.
^ "Monkeys tree fractal curve". Diarsipkan dari versi asli tanggal 21 September 2002.
^ WOLFRAM Demonstrations Project http://demonstrations.wolfram.com/SelfAvoidingRandomWalks/#more. Diakses tanggal 14 June 2019. Tidak memiliki atau tanpa |title= (bantuan)
^ Weisstein, Eric W. "Hedgehog". mathworld.wolfram.com.
^ "Courbe De Ribaucour" [Ribaucour curve]. mathworld.wolfram.com.

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